Linear Quadratic regulator

A flight path rate demand modified two-loop lateral missile autopilot design methodology for a class of guided missile, based on state feedback, reduced order Das & Ghosal observer (DGO) and Linear Quadratic Regulator (LQR), is proposed. The open loop undamped model of two-loop autopilot has been stabilized by using pole placement and state feedback. The non-minimum phase feature of rear controlled missile airframes is analyzed. The LQR technique is adopted to ensure optimal pole placement such that the adverse effect of non-minimum phase property on the response of missile autopilot can be reduced considerably and also the system stability can be made better. The overall response of the two-loop autopilot has been significantly improved over the previous ones. Performance (both transient and steady state) comparisons among the classical two loop design, two-loop design using state feedback & Ackermann approach and the present one, are made. Reduced order Das & Ghosal observer (using Generalized Matrix Inverse) is implemented successfully in this design. A program has been developed to find out the appropriate state vector & control input weightage matrices which will give the optimal pole positions and feedback gains according to the desired time domain performance specifications. Finally a numerical example has been considered and the simulated results are discussed in details.

A flight path rate demand modified two-loop lateral missile autopilot design methodology for a class of guided missile, based on state feedback, reduced order Das & Ghosal observer (DGO) and Linear Quadratic Regulator (LQR), is proposed. The open loop undamped model of two-loop autopilot has been stabilized by using pole placement and state feedback. The non-minimum phase feature of rear controlled missile airframes is analyzed. The LQR technique is adopted to ensure optimal pole placement such that the adverse effect of non-minimum phase property on the response of missile autopilot can be reduced considerably and also the system stability can be made better. The overall response of the two-loop autopilot has been significantly improved over the previous ones. Performance (both transient and steady state) comparisons among the classical two loop design, two-loop design using state feedback & Ackermann approach and the present one, are made. Reduced order Das & Ghosal observer (using Generalized Matrix Inverse) is implemented successfully in this design. A program has been developed to find out the appropriate state vector & control input weightage matrices which will give the optimal pole positions and feedback gains according to the desired time domain performance specifications. Finally a numerical example has been considered and the simulated results are discussed in details.

We study the existence and uniqueness of the solution for the following backward stochastic variational inequality with oblique reflection (for short, BSV I (H(t, y), ϕ, F )), written under differential form where H is a bounded symmetric smooth matrix and ϕ is a proper convex lower semicontinuous function, with ∂ϕ being its subdifferential operator. The presence of the product H∂ϕ does not permit the use of standard techniques because it does conserve neither the Lipschitz property of the matrix nor the monotonicity property of the subdifferential operator. We prove that, if we consider the dependence of H only on the time, the equation admits a unique strong solution and, allowing the dependence also on the state of the system, the above BSV I (H(t, y), ϕ, F ) admits a weak solution in the sense of the Meyer-Zheng topology. However, for that purpose we must renounce at the dependence on Z for the generator function and we situate our problem in a Markovian framework.

In this paper, the AQM controller of a first-order controller’s type is proposed. The model of TCP/AQM is described by a second-order system with time delay. An analytical approach to analyze the stability of TCP/AQM Networks is used, based on the D-decomposition method and lemma Kharitonov for quasipolynomial. The proposed method for design first-order controller is verified and compared with other existing AQM schemes, using NS-2 simulator.

We analyze optimal monetary policy in a model with two distinct financial frictions: monopolistically competitive banks that charge endogenous lending spreads, and collateral constraints. We show that welfare maximization is equivalent to stabilization of four goals: inflation, output gap, the “consumption gap” between borrowers and savers, and a “housing gap” that measures the distortion in the distribution of the collateralizable asset between both groups. Collateral constraints create a trade‐off between stabilization goals. Following both productivity and financial shocks, and relative to strict inflation targeting, the optimal policy implies sharper movements in the policy rate, aimed primarily at reducing fluctuations in asset prices and hence in borrowers' net worth. The policy trade‐offs become amplified as banking competition increases, due to the fall in lending spreads and the resulting increase in borrowers' leverage.

Aims and Objectives: Aims and objectives of this study are to get the best fit of the normal tissue tolerance doses to the NTCP model of the linear quadratic model. To compute the NTCP, the modified form of the Poisson cell kill model of NTCP, based on linear quadratic model, is used. The model has been applied to compute the parameters of the NTCP model using clinical tolerance doses of various normal tissues / organs extracted from published reports of various authors. The normal tissue tolerance doses are calculated for partial volumes of the organs using the values of above-said parameters for published data on normal tissue tolerance doses. In this article, a graphical representation of the computed NTCP for bladder, brain, heart and rectum is presented. A fairly good correspondence is found between the curves of 2 sets of data for brain, heart and rectum. Hence the model may, therefore, be used to interpolate clinical data to provide an estimate of NTCP for these organs for any altered fractionated treatment schedule.

The linear-quadratic (LQ) model was modified to the multiple-component (MC) model to address the issues of irradiating tissues that cloud not be explained by the LQ model . The basic equations of the LQ and MC models are unable to explain the issue of proliferation in early reacting tissues and tumors. Proliferation effect in late reacting tissues is hardly a matter of consideration because no excessive proliferation is present in these tissues during radiotherapy treatment, or may have very little influence at the end of the treatment. The proliferation correction factors applied in these models such as the LQ and the MC models (6)(7)(8) were based on the assumption of a constant proliferation rate after its initiation. But, the cells in early reacting normal tissues and tumors divide faster than before, after its initiation, during irradiation to compensate the loss (9) . Hence, the correction factors based on the assumption of a constant proliferation rate may not be able to predict true cell kinetics of early reacting tissues and tumors and may estimate wrong treatment outcome. In this paper, we introduced a proliferation correction factor, in the LQ and the MC models to account for accelerated proliferation rate.

The certainty equivalence principle is used to combine a robust adaptive law with a control structure derived from the linear quadratic (LQ) control problem. The resulting adaptive control scheme is applicable to minimum and nonminimum phase continuous-time plants and is robust with respect to unmodeled dynamics and bounded disturbances. The computational complexity of the continuous-time adaptive LQ control scheme is improved by using a hybrid adaptive law which requires the solution of an algebraic Riccati equation at each interval of time rather than at each time t. Recently, several robust adaptive control schemes have been presented in literature which guarantee global stability and robustness in the presence of unmodeled dynamics and bounded disturbances [ 11 - [6]. These schemes are developed by using the certainty equivalence principle [7] to combine the model reference control (MRC) or pole placement control (PPC) structures, which could be used if the parameters of the plant were known, with a suitable robust adaptive law [4]. The extension of these results to other control structures such as the linear quadratic (LQ) one, has not been done for continuous-time plants. In the discrete-time case, the adaptive LQ control problem was considered by Samson [8] for plants with no plant unmodeled dynamics, whereas the implementation aspects of an adaptive LQ control scheme for discrete-time plants is studied by using extensive simulations and intuitive explanations by Clarke et al. [ 9 ] . In this note we consider the design, analysis, and robustness of an adaptive LQ (ALQ) control scheme for continuous-time plants. We use the certainty equivalence principle to combine a LQ control structure, which could be used to meet the control objective in the case of known parameters, with a continuous-time and hybrid robust adaptive laws. The stability properties of both the continuous-time and hybrid ALQ are analyzed in the presence of unmodeled dynamics, whose class is characterized by frequency-domain (H,) bounds, and bounded disturbances. These bounds indicate ways for improving the performance of the ALQ controller by using appropriate filters in the adaptive law. This note is organized as follows. In Section 11, we consider the LQ problem in the case of known plant parameters. The knowledge of the plant parameters is relaxed in Section 111, where an ALQ controller with a continuous-time adaptive law is developed and analyzed. In Section IV the continuous-time adaptive law is replaced with the computationally more efficient hybrid adaptive law.

The state feedback linear-quadratic optimal control problem for asymptotic stabilization has been extensively studied in the literature. In this paper, the optimal linear and nonlinear control problem is extended to address a weaker version of closed-loop stability, namely, semistability, which involves convergent trajectories and Lyapunov stable equilibria and which is of paramount importance for consensus control of network dynamical systems. Specifically, we show that the optimal semistable state-feedback controller can be solved using a form of the Hamilton-Jacobi-Bellman conditions that does not require the cost-to-go function to be sign-definite. This result is then used to solve the optimal linear-quadratic regulator problem using a Riccati equation approach.

In this study, the Lorenz chaotic system behavior is investigated according to the change in the noise of the system and measurement. The noise was emerged as an important impact on the Lorenz chaotic system. The discrete-time LQR (Linear Quadratic Regulator) control method and discrete-time PI controller method have been used to the noisy system controls. Noise was accepted as a destructor that changes the output behavior of the chaotic system. Noisy system outputs were enforced to move to the equilibrium points by the support of controllers. Optimization of the controller parameters for noiseless system models was performed using a genetic algorithm method. Then, both control system algorithms determined as successful in transporting to the equilibrium point for state variables which are blended with the noise. Changes, associated with the noise conditions are given in the graphics and tables. Besides, the error performance criteria and the control performance criteria were obtained to evaluate the results. This study was performed by MATLAB-Simulink simulation program.

This paper describes the design and implementation of a self-balancing two-wheeled robot, the Equilibrist Robot. The system is similar to the classical unstable, non-linear mechanical control problem of an inverted pendulum on a cart. Using the Linear Quadratic Regulator method and PID for state feedback, this paper shows a control algorithm that solves this problem. This control is able to reject disturbances and stabilize the system using a gyroscope. The control algorithm is implemented using Matlab and Cprograming. The Equilibrist manages to stabilize itself in an upright position, reject disturbances and change its position. Index Terms — Inverted Pendulum, Linear Quadratic Regulator, Servo and Regulator Control, Lego Robot.

This study presents fractional order filters to enhance the performance of the conventional linear quadratic regulator (LQR) method for optimal robust control of a simple civil structure. The introduced filters modify the state variables fed back to the constant gain controller. Four combinations of fractional order filter and LQR are considered and optimized based on a new performance criterion defined in the paper. Introducing fractional order filters is shown to considerably improve the results for both the artificially generated ground motions and previously recorded earthquake data.

In the current study, the quadrotor's nonlinear dynamic model is developed using the Newton-Euler approach. Following that, several nonlinear and linear control strategies for tracking the quadrotor's trajectory are applied. First, by employing distinct controllers for each output variable, direct application of the linear proportional integral derivative (PID) controller to the nonlinear system is realized. This system may also be linearized about an operational point to generate linear controllers, according to the linear quadratic regulator (LQR) demonstration. Nevertheless, in practice, the system dynamics may not always be accurately reflected by this linear approximation and may even be relatively wasteful. Nonlinear regulators, including the feedback linearization (FBL) controller, sliding mode controller (SMC), and modified sliding mode controller (MSMC), perform better in such situations. The trajectory tracking capabilities, dynamic performance, and potential disruption impact of both methods are evaluated and compared. The FBL with LQR was the best controller among them all. The SMC and the MSMC were also very good in tracking the trajectory.

This research aimed to develop a control system for a self-balancing robot (SBR) based on the mathematical model of an inverted pendulum on a two-wheeled cart. The linear quadratic regulator (LQR) control was implemented to maintain the SBR’s balance under normal conditions. A linearization approach was used to convert the dynamic model into a linear form, enabling the application of LQR. Testing was conducted through simulations and a physical SBR prototype equipped with an MPU6050 sensor and NEMA 17 motor. The test results demonstrated the effectiveness of the LQR control in maintaining the SBR’s balance and its responsiveness to disturbances. Although there are differences between the simulations and physical implementation, the system successfully maintained the SBR’s balance. In conclusion, the use of the inverted pendulum mathematical model and the implementation of LQR control successfully produced a stable and effective control system for SBR balance. By testing various values of the LQR parameters, optimal robot control parameters can be obtained.

In this paper, we construct new array patterns of regulator re-optimization algorithms using the duality relations between the two Riccati Difference Equations (RDE), that are at the heart of Linear Quadratic Gaussian Estimator (LQG-E) on the one part, and Linear Quadratic Regulator (LQR) on the other. By doing so, we advocate steps to integrate the best computational LQG-E solutions which have come into practice over the preceding decades, into the LQR re-design, in which a stepwise solution for the backward RDE has primary importance. Array-based algorithmic templates developed in this paper offer customization flexibility, together with the utmost brevity, to both users and application programmers, and ensure the independence of a specific program language.

This paper presents the design and performance evaluation of a terrain following controller for modelscale helicopters. The methodology used to develop the tracking controller amounts to augmenting the discrete state space model of the plant with terrain preview data. The terrain information is obtained by applying a 2D reconstruction technique to the measurements taken by a forward looking laser range scanner. The resulting control problem is solved using the discrete time Stochastic Linear Quadratic Regulator where the particular structure of the augmented system is explored to simplify the computation of the feedforward gain matrix. Simulation results obtained with the full nonlinear dynamic model of the Vario X-Treme acrobatic helicopter and the preview controller are presented and discussed.

In this paper we study the open-loop zero-sum linear quadratic differential game for descriptor systems that have index one. We present both necessary and sufficient conditions for the existence of an open-loop Nash equilibrium. We also relate the existence of an open-loop Nash equilibrium with the theory of invariant subspaces.

For autonomous vehicles, safety is most important. Thus, it is desired to know how the vehicle will behave given e.g. a steering input. Additionally, it is important to predict how the vehicle would behave given some perturbation. Therefore, this thesis investigates which analytical methods can be used to quantify the robustness, performance, and stability properties of the system. To ensure safety, how limits can be derived regarding disturbances or uncertainties is also considered. To investigate these matters, linear vehicle models augmented with uncertain parameters and adapted to the behavior of a more complex nonlinear model are used as tools for analysis and controller synthesis. In both the time and the frequency domain, specifications regarding the desired performance and the system uncertainty are created. PID, LQ, and H ∞ control are then used and compared. Optimization of controllers, given system behavior objectives, is also performed. Uncertainty analysis gives a trustworthy range of system behavior for the linear model. Adapting this model to the nonlinear model behavior results mostly in similar system responses, making the argument that analytical results can be carried over from the linear to the nonlinear model easier for these cases. Most of the optimized controllers result in the wanted system behavior. The analytical methods successfully quantified system behavior. However, some methods proved more useful than others. Uncertainty and disturbance limits are both computed through simulation, with an analytical verification of the frequency domain uncertainty.

This article discusses a new robust control technique that enables the DC-DC boost converter driving a permanent magnet direct current (PMDC) motor to operate in high static and dynamic performances. The new technique is based on the design of a both linear quadratic regulator (LQR) and linear quadratic regulator-proportional integral (LQR-PI) type controllers, which have the advantage of eliminating oscillations, overshoots and fluctuations on different characteristics in steady-state system operation. In order to increase the output voltage, the LQR regulator is combined with a first-order system represented in the form of a closed-loop transfer function, the latter raising the output voltage to 24 volts, this voltage is enough to drive the permanent magnet direct current motor. The contribution of this paper is the creation of a robust control system represented in the form of a hybrid corrector able to regulate steadystate and transient disturbances and oscillations as well as to increase DC-DC boost converter output voltage for the PMDC motor to operate at rated voltage. The results of the three control techniques are validated by MATLAB Simulink.

In recent years, specially designed patches containing beta emitters have been developed for contact brachytherapy of skin lesions. The aim of the present work was to evaluate the biological effects of the 32 P-patch on the skin of Sencar mice as a result of a brachytherapy treatment. For this purpose, a 32 Ppatch was prepared with Chromic 32 P-phosphate and silicone and the classical model of two-stage skin carcinogenesis was reproduced in Sencar mice. Animals were divided in six groups. Four groups received the contact brachytherapy treatments using a scheme of a single session of 40 and 60 Gy (SD40 and SD60) and a scheme of two sessions of 40 and 60 Gy each (FD40 and FD60). The other two groups were used as controls of the single (CSD) and the fractionated (CFD) treatments. Radiation doses were estimated with equations derived from the MIRD DOSE scheme, and biologically effective doses (BED) were calculated according to equations derived from the linear-quadratic model. The endpoint to evaluate the treatments effects was tumor size after a follow-up period of 44 days. Finally, animals were sacrificed in order to get samples of all tumors for histological analysis and PCNA staining. Erythema, dermatitis and skin ulceration developed in almost all treated animals, but they gradually healed with regeneration of tissue during the follow-up period. Radiation effects on the skin of SD40, SD60, FD40 and FD60 showed a significant reduction of the tumor size with regard to controls, independently of the scheme and the radiation dose considered. PCNA staining scores of control groups were higher than for treated groups, independently of the scheme and the radiation dose considered. This radioactive 32 Psilicone-patch which is easy to prepare and use in the treatment of skin diseases, seems promising as a radioactive device for clinical use.

The United States trucking industry is immense. Employing over three million drivers and traveling to every city in the country. Semi-Trucks travel millions of miles each week and encompass roads that civilians travel on. These vehicles should be safe and allow efficient travel for all. Autonomous vehicles have been discussed in controls for many decades. Now fleets of autonomous vehicles are beginning their integration into society. The ability to create an autonomous system requires domain and system specific knowledge. Approaches to implement a fully autonomous vehicle have been developed using different techniques in control systems such as Kalman Filters, Neural Networks, Model Predictive Control, and Adaptive Control. However some of these control techniques require superb models, immense computing power, and terabytes of storage. One way to circumvent these issues is by the use of an adaptive control scheme. Adaptive control systems allow for an existing control system to self-tune its performance for unknown variables i.e. when an environment changes. In this thesis a LQR error state control system is derived and shown to maintain a magnitude of 15 cm of steady state error from the center-line of the road. In addition a proposed LQR-MRAC controller is used to test the robustness of a lane-keeping control system. The LQR-MRAC controller was able to improve its transient response peak error from the center-line of the road of the tractor and the trailer by 9.47 [cm] and 7.27 [cm]. The LQR-MRAC controller increased tractor steady state error by 0.4 [cm] and decreased trailer steady state error by 1 [cm]. The LQR-MRAC controller was able to outperform modern control techniques and can be used to improve the response of the tractor-trailer system to handle mass changes in its environment.

The United States trucking industry is immense. Employing over three million drivers and traveling to every city in the country. Semi-Trucks travel millions of miles each week and encompass roads that civilians travel on. These vehicles should be safe and allow efficient travel for all. Autonomous vehicles have been discussed in controls for many decades. Now fleets of autonomous vehicles are beginning their integration into society. The ability to create an autonomous system requires domain and system specific knowledge. Approaches to implement a fully autonomous vehicle have been developed using different techniques in control systems such as Kalman Filters, Neural Networks, Model Predictive Control, and Adaptive Control. However some of these control techniques require superb models, immense computing power, and terabytes of storage. One way to circumvent these issues is by the use of an adaptive control scheme. Adaptive control systems allow for an existing control system to self-tune its performance for unknown variables i.e. when an environment changes. In this thesis a LQR error state control system is derived and shown to maintain a magnitude of 15 cm of steady state error from the center-line of the road. In addition a proposed LQR-MRAC controller is used to test the robustness of a lane-keeping control system. The LQR-MRAC controller was able to improve its transient response peak error from the center-line of the road of the tractor and the trailer by 9.47 [cm] and 7.27 [cm]. The LQR-MRAC controller increased tractor steady state error by 0.4 [cm] and decreased trailer steady state error by 1 [cm]. The LQR-MRAC controller was able to outperform modern control techniques and can be used to improve the response of the tractor-trailer system to handle mass changes in its environment.

The crucial role of shunt active power filter (SAPF) is to compensate for reactive power, balances unbalanced currents and counteract harmonics produced due to non-linear loads, by injecting phase-opposed compensation current by designing an appropriate controller. In this work, a combined controller-observer state and disturbances estimation scheme for a SAPF is proposed. To avoid the requirement of full-state feedback, unknown input observers (UIO) is designed. This is conducted in OPAL-RT OP4510 environment. Real-time simulations are used to show how successful the suggested controller-observer architecture for SAPF is; wherein the estimated states from the observer are fed back to the controller, and finally, the disturbance is also estimated. UIO is designed for SAPF to deal with nominal conditions and in the presence of sinusoidal disturbance.The OPAL-RT results clearly show that LO introduces steady state error between the reference input and the estimated state of SAPF in the presence of disturbances. This steady state error is completely eliminated in presence of all disturbances using UIO. The results also show that UIO perfectly tracks the reference input in the presence of disturbances. Further, disturbances are also estimated perfectly with UIO.

An iterative algorithm to solve Algebraic Riccati Equations with an indefinite quadratic term is proposed. The global convergence and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given. Numerical examples are also provided to demonstrate the superior effectiveness of the proposed algorithm when compared with methods based on finding stable invariant subspaces of Hamiltonian matrices. A game theoretic interpretation of the algorithm is also provided.

An iterative algorithm to solve periodic Riccati differential equations (PRDE) with an indefinite quadratic term is proposed. In our algorithm, we replace the problem of solving a PRDE with an indefinite quadratic term by the problem of solving a sequence of PRDEs with a negative semidefinite quadratic term which can be solved by existing methods. The global convergence is guaranteed and a proof is given.

In 1995, Mayor and Queloz [a] detected for the first time a planet orbiting a nearby star (15.4 parsecs). Since then, the interest in the detection of extra-solar planets, in order to learn about the origin, evolution, and composition of planetary systems, has grown tremendously and ...

The use of a constant discount rate to study long-lived environmental problems such as global warming has two disadvantages: the prescribed policy is sensitive to the discount rate, and with moderate discount rates, large future damages have almost no effect on current decisions. Time-consistent quasihyperbolic discounting alleviates both of these modeling problems, and is a plausible description of how people think about the future. We analyze the time-consistent Markov Perfect equilibrium in a general model with a stock pollutant. The solution to the linear-quadratic specialization illustrates the role of hyperbolic discounting in a model of global warming.

Non-strategic firms with rational expectations make investment and emissions decisions. The investment rule depends on firms' beliefs about future emissions policies. We compare emissions taxes and quotas when the (strategic) regulator and (nonstrategic) firms have asymmetric information about abatement costs, and all agents use Markov Perfect decision rules. Emissions taxes create a secondary distortion at the investment stage, unless a particular condition holds; emissions quotas do not create a secondary distortion. We solve a linear-quadratic model calibrated to represent the problem of controlling greenhouse gasses. The endogeneity of abatement capital favors taxes, and it increases abatement.

In this paper an optimal control strategy based on the linear quadratic regulator (LQR) method for static synchr onous compensator (ST A TCOM) is introduced. Simulations results verify the performance of the controller in improvc the damping of the power systems.

An inverted pendulum is a pendulum - a free body hung from a fix point and can swing freely in all directions – that has its center of mass above its pivot point. Unlike regular pendulum which is inherently stable, an inverted pendulum is inherently unstable and must be actively balanced in order to remain upright by applying some force at the pivot point, thus moving the pivot point horizontally as a feedback system. The pivot point is moved using a simple vehicle consisting of two wheels that moves freely in one direction. The feedback control to move the pivot point horizontally is a sensor system consisting of solid state accelerometer and gyroscope. The accelerometer will detect the angle of the inverted pendulum device and the gyroscope will detect the rate of rate of change of angle and therefore measure the angular velocity. The vehicle robot is a two-wheel vehicle which is controlled independently using two independent DC motor. The DC motors are controlled by a microproces...

This paper presents an optimal transport theoretic formulation to assess the controller robustness for F-16 aircraft. We compare the state regulation performance for a linear quadratic regulator (LQR) and gain scheduled LQR (gsLQR), applied to nonlinear longitudinal open-loop dynamics of F-16, under stochastic initial condition uncertainty. It is shown that both controllers have comparable immediate and asymptotic performance, but gsLQR achieves better transient performance than LQR. Algorithms based on Perron-Frobenius operator, are given for tractable computation. Numerical results from the proposed method, are in unison with Monte Carlo simulations.

Robots have been used in many applications in the past few decades. Moreover, due to high nonlinearity behavior of these systems, an optimal and robust control design approaches have been considered to stabilize and improve their performance and robustness. The uncertainties of the time delay on the output states of the mobile robot system have a significant influence on the system nominal performance. As a result, the work becomes here to address the influence of these uncertainties on the robot system performance. In order to achieve this objective, the nonlinear controller via sliding mode control (SMC) is designed by selecting a suitable sliding surface dynamics in which the considered robot displacement and tilt angle are sliding on. The lyapunov function is considered here to accomplish  the design of the sliding control signals for robot stabilization. Furthermore, the stability of the considered system is guaranteed due to convergence of  the lyapunov functions into zero whe...

In this paper, a new local measure of linear controller performance is introduced for linear controllers operating on a nonlinear plant. The measure, called the performance sensitivity measure, quantifies the departures from optimality of a locally linear quadratic regulators. The measure applies to nonlinear systems that admit a controllable and observable linearization. It is shown that the measure can be related to standard minimum variance benchmarking techniques and can therefore be assessed using closed-loop process data in an operating region of interest.

The following faculty members have examined the final copy of the thesis for form and content, and recommend that it be accepted in partial fulfillment of the requirement for the degree of Master of Science with major in Electrical Engineering. John M. Watkins, Committee Chair __________________________________ M. Edwin Sawan, Committee Member __________________________________ Esra Buyuktahtakin, Committee Member iv DEDICATION To my professors Dr. John Watkins, M. Edwin Sawan for his immense support, my Colleagues in Born Inc, for their understanding and encouragement to do this research and my family for their continued support v ACKNOWLEDGEMENTS It is my privilege and pleasure to express my profound sense of respect, gratitude to my advisor Dr. John Watkins, Dr. Edwin Sawan, Professor Emeritus, Wichita State University for his valuable inputs, guidance and constant motivation throughout this research and even before that. I wish to express my deep gratitude to my company CEO Dr. Sidney Born, my vice president Mr. Vijay K Rachakonda, my colleagues Ms. Glory Srivastava and Mr. Dhananjay Dhane for their support and their constructive criticism which led the successful completion of this thesis. I would like to thank all the staff, friends and family for their good wishes and their motivation which led the successful completion of the thesis. Finally, I thank all those who directly and indirectly helped me in this regard. vi

The contribution of this paper is to present and compare two state-feedback design methods for the automatic control of the Neuromuscular Blockade Level (NMB) based on optimal control. For this purpose a parsimoniously parameterized model is used to describe the patient's response to a muscle relaxant. Due to clinical restrictions the controller action begins when the patient recovers after an initial drug bolus. The NMB control problem, typically consisting of tracking a constant NMB reference level, can be associated with an optimal control problem (OCP) with a positivity constraint in the input signal. Due to the complexity associated with the introduction of a positivity constraint in the input, approximate solutions to this OCP will be found in this paper using two methods. In the first method, the optimal control problem is relaxed into a Semi-Definite Program (SDP) using a change of variables, whereas in the second method the OCP is approximated by an infinite horizon constrained Linear Quadratic Regulator (LQR) problem. These two controllers are compared with a classical PI controller in simulation. The PI exhibits a slightly worse performance in terms of the control magnitude but it was not optimized taking this magnitude into account. The simulation results show that the SDP relaxation

In the money demand literature the Linear Quadratic Adjustment Cost (LQAC) model is often considered to explain the observed slow adjustment in agents' money holdings. In this paper we propose a new method of estimating and testing the LQAC model of money demand. In an empirical application to U.K. money demand, we reject the LQAC model defined from a loss function expressed in terms of real money balances. This is in sharp contrast to the results obtained by Cuthbertson and Taylor (1990) in a previous article in this journal using similar techniques on an equivalent data set. In order to explain the discrepancies we point out some pitfalls in the empirical methodology adopted by Cuthbertson and Taylor. We also consider a specification of the LQAC model in terms of nominal money and, despite statistical rejection, we find that if the LQAC model should have any empirical content such a specification should be preferred to the real money specification.

This survey provides a detailed description of some of the recent theoretical and empirical literature on rational expectations econometrics. The survey pays special attention to non–stationarity of the data, and to the various methods for evaluating rational expectations models that have been developed as alternatives to the classical statistical approach of testing overidentifying restrictions. These methods have become very popular and widely used in empirical research. We provide an illustration using Danish stock market data, and we summarize the many results obtained recently using these measures in areas as diverse as stock prices, the term structure of interest rates, exchange rates, consumption and saving, the balance of payments, tax–smoothing, hyperinflation, and linear quadratic adjustment cost models for inventories, labour demand, and money demand.

This paper derives a method for estimating and testing the Linear Quadratic Adjustment Cost (LQAC) model when the target variable and some of the forcing variables follow I(2) processes. Based on a forward-looking error-correction formulation of the model it is shown how to obtain strongly consistent estimates of the structural long-run parameters and the adjustment cost parameter from both a linear and a non-linear cointegrating regression, where first-differences of the I(2) variables are included as regressors (multicointegration). Further, based on the estimated parameter values, it is shown how to test and evaluate the LQAC model using a VAR approach. In an empirical application using UK money demand data, the non-linear multicointegrating regression delivers an economically plausible estimate of the adjustment cost parameter. However, the exact restrictions implied by the LQAC model under rational expectations are strongly rejected.

In this paper we demonstrate a new way of testing the linear quadratic adjustment cost (LQAC) model under rational expectations. We illustrate how the parameter restrictions arising from this model can be formally specified and we use these restrictions to extent the technique of Campbell and Shiller (1987) to a wider class of models based on present value relations. Potentially the demand for labour is an area in which the LQAC model can find applicability in practice and subsequently we analyse sectoral labour demand in Danish manufacturing. We find, however, that for our data set the quadratic adjustment cost model under rational expectations can be rejected.

In this paper we characterize the controllers and the disturbances which are possible solutions of a certain linear quadratic minimax control problem. The necessary and sufficient conditions for minimaxity are given which involve a frequency domain inequality. It is then shown that this inequality implies good robustness properties of the closed-loop system.

A state‐space model for representing the non‐linear material deformation and an optimal control scheme for obtaining desired process conditions in the deforming material are presented in this paper. The formulation is general for various metal‐forming processes including forging and extrusion operations. The state variables selected in the formulation are the die/billet contact nodal velocities and the nodal velocities of the critical finite elements of the billet. The control input is the ram velocity, which is determined by using the linear quadratic regulator (LQR) theory to maintain desired strain rates within the selected finite elements. The influence of an optimally designed ram velocity on the deforming material is studied using performance measures. This paper includes the development of the state‐space model from non‐linear finite element formulation, optimal control strategy and numerical example cases with discussions.

Load balancing is widely used in computing systems as a way to optimize performance by equalizing loads to reduce delays, such as adjusting the size of memory pools to balance resource demands in a database management system. Load balancing is generally approached as a nonlinear constrained optimization in which dynamics are ignored. We approach load balancing differently - as a feedback controller design problem using a multiple input multiple output linear quadratic regulator (LQR) that achieves the constrained optimization objective. Such an approach allows us to exploit well-established techniques for handling disturbances (e.g., due to changes in workloads) and to incorporate the cost of control (e.g., throughput reductions due to resizing buffer pools) by properly selecting the LQR Q and R matrices. From studies of DB2 Universal Database Server using industry standard benchmarks, we show that the controller obtains a factor of three increases in throughput for an OLTP workload...

Load balancing is widely used in computing systems as a way to optimize performance by reducing bottleneck utilizations, such as adjusting the size of buffer pools to balance resource demands in a database management system. Load balancing is generally approached as a constrained optimization problem in which only the benefits of load balancing are considered. However, the costs of control are important as well. Herein, we study the value of including in controller design the trade-off between the cost of transient imbalances in resource utilizations and the cost of changing resource allocations. An example of the latter are actions such as resizing buffer pools that can reduce throughputs. This is because requests for data in pools whose memory is reduced immediately have longer access times whereas requests for data in pools whose memory is increased must fill this memory with data from disk before accessed times are reduced. We frame our study of control costs in terms of the widely used linear quadratic regulator (LQR). We develop a cost model that allows us to specify the LQR É and Ê matrices based on the impact on system performance of changing resource allocations and transient load imbalances. Our studies of a DB2 Universal Database Server using benchmarks for online transaction processing and decision support workloads show that incorporating our cost model into the MIMO LQR controller results in a 14% improvement in performance beyond that achieved by dynamically allocating the size of buffers without properly considering the cost of control.

Nowadays, Two Wheeled Inverted Pendulum Mobile Robots (TWIPMR) are being used widely in many different applications. It's very important to ensure that the robot is able to stabilize itself when it moves forward and backward. Stabilization and the trajectory tracking of the robot has gained extensive momentum and become increasingly popular with researchers around the world. In addition, the robot must regulate the steering angle when it turns left or right must be considered in control design and analysis beside stability and the trajectory tracking. To achieve these, two decoupling optimal controllers based on Linear Quadratic Regulator (LQR) design method are proposed in this paper to robustly balance the robot platform and to generate the required optimal control signals under any external disturbances. The simulation results are provided to show the effectiveness of the proposed designed control method to get an accurate tracking signal of the desired trajectory. Furthermore, the 3D representation of the simulation and a visualization model to observe robot behavior in different scenarios is included

Nowadays, Two Wheeled Inverted Pendulum Mobile Robots (TWIPMR) are being used widely in many different applications. It’s very important to ensure that the robot is able to stabilize itself when it moves forward and backward. Stabilization and the trajectory tracking of the robot has gained extensive momentum and become increasingly popular with researchers around the world. In addition, the robot must regulate the steering angle when it turns left or right must be considered in control design and analysis beside stability and the trajectory tracking. To achieve these, two decoupling optimal controllers based on Linear Quadratic Regulator (LQR) design method are proposed in this paper to robustly balance the robot platform and to generate the required optimal control signals under any external disturbances. The simulation results are provided to show the effectiveness of the proposed designed control method to get an accurate tracking signal of the desired trajectory. Furthermore, t...

Smart grid, equipped with modern communication infrastructures, is subject to possible cyber attacks. Particularly, false report attacks which replace the sensor reports with fraud ones may cause the instability of the whole power grid or even result in a large area blackout. In this paper, a trustiness system is introduced to the controller, who computes the trustiness of different sensors by comparing its prediction, obtained from Kalman filtering, on the system state with the reports from sensor. The trustiness mechanism is discussed and analyzed for the Linear Quadratic Regulation (LQR) controller. Numerical simulations show that the trustiness system can effectively combat the cyber attacks to smart grid.