In this study, a decentralised output learning control strategy for a class of nonlinear intercon... more In this study, a decentralised output learning control strategy for a class of nonlinear interconnected systems is studied. Based on Takagi-Sugeno fuzzy (TS) model to approximate the considered interconnected nonlinear systems, a decentralised observer-based control scheme is designed to override the external disturbances such that the H ∞ performance is achieved. The appealing attributes of this approach include: (1) the closed-loop system exhibits a robustness against nonlinear interconnections and external disturbance, (2) by one-step procedure, the gain matrices of observer and controller are obtained on a single step. In simulation results, the controller design is evaluated on the steering stability of a car where the nonlinear model describes the side slip, roll and yaw motions of the automotive vehicle equipped with four-wheel-steering and active suspension.
In this article, a new approach regarding H∞ and non-fragile stability analysis and observer-base... more In this article, a new approach regarding H∞ and non-fragile stability analysis and observer-based controller synthesis problem for a class of discrete-time fuzzy systems is investigated. The multiplicative gain variations under consideration are contained in both the controller gain and observer gain. By defining a basis-dependent Lyapunov function and introducing some additional matrix variables, new sufficient conditions are derived to
This paper investigates the problem of multiobjective control for a class of uncertain discrete-t... more This paper investigates the problem of multiobjective control for a class of uncertain discrete-time fuzzy systems. The state-space Takagi-Sugeno T-S fuzzy model with linear fractional parameter uncertainties is adopted. Based on a linear matrix inequality approach and via so-called dynamic parallel distributed compensation, a fuzzy full-order dynamic output feedback controller is developed such that the L 2 gain performance from the exogenous input signals to the controlled output is less than or equal to some prescribed value and, for all admissible uncertainties, the closed-loop poles of each local system are within a pre-specified sub-region of complex plane. Two numerical examples are provided to illustrate the effectiveness of the proposed design method. Keywords T-S fuzzy model Á H ? performance Á Pole-placement Á Output feedback Á Robust control Á Linear matrix inequalities (LMIs) Communicated by Y. Jin
This paper is concerned with the problem of robust discrete-time sliding-mode control for a class... more This paper is concerned with the problem of robust discrete-time sliding-mode control for a class of uncertain descriptor systems with time-varying delay and external disturbance. A new sliding function is proposed and sufficient conditions are derived to guarantee that the sliding mode dynamics is robustly admissible. Moreover, a quasi-sliding mode controller is established to satisfy the reaching condition. The developed results are tested on a representative example to illustrate the theoretical developments.
Optimal Control Applications & Methods, Oct 9, 2018
SummaryThis paper investigates the problem of control design for a class of uncertain switched si... more SummaryThis paper investigates the problem of control design for a class of uncertain switched singular systems with time‐varying delay. Under mode‐dependent average dwell time and using an appropriate Lyapunov‐Krasovskii functional, the exponential admissibility of the system is analyzed. In order to obtain less conservative conditions, the delay partitioning technique is adopted as well as the improved reciprocally convex approach. By means of the developed admissibility condition, a static output feedback controller is then designed using linear matrix inequality approach. Moreover, by solving an optimization convex problem with constraints, the switched controller is developed to ensure simultaneously the stability of the closed‐loop system and satisfy an optimized upper bound of both the linear quadratic guaranteed cost and the H∞ norm. Numerical examples are proposed to verify the efficiency and the merits of the method proposed.
The computation of the time-varying matrix pseudoinverse has become crucial in recent years for s... more The computation of the time-varying matrix pseudoinverse has become crucial in recent years for solving time-varying problems in engineering and science domains. This paper investigates the issue of calculating the time-varying pseudoinverse based on full-rank decomposition (FRD) using the zeroing neural network (ZNN) method, which is currently considered to be a cutting edge method for calculating the time-varying matrix pseudoinverse. As a consequence, for the first time in the literature, a new ZNN model called ZNNFRDP is introduced for time-varying pseudoinversion and it is based on FRD. Five numerical experiments investigate and confirm that the ZNNFRDP model performs as well as, if not better than, other well-performing ZNN models in the calculation of the time-varying pseudoinverse. Additionally, theoretical analysis and numerical findings have both supported the effectiveness of the proposed model.
International Journal of Adaptive Control and Signal Processing
This article deals with the problem of robust output feedback control design for a class of switc... more This article deals with the problem of robust output feedback control design for a class of switched systems with uncertainties and random time‐varying delay. Our purpose is focused on designing a full order dynamic output feedback controller and an appropriate switching rule to ensure the exponential mean square stability of the resulting closed‐loop switching system with an l2−l∞ performance level. The appealing aspects of the proposed control scheme include: (a) the development of LMI based delay‐dependent sufficient conditions for the exponential stability analysis of the stochastic hybrid systems using the appropriate choice of the augmented Lyapunov–Krasovskii functional, the partitioning technique and the average dwell time, (b) conservatism reduction of the unified design conditions, and (c) the controller designed exhibiting robustness with l2−l∞ performance against uncertainties and external disturbance. Finally, representative examples are given to demonstrate the validity and the merit of the proposed design technique.
Fuzzy theory is widely studied and applied. This article introduces an adaptive control scheme fo... more Fuzzy theory is widely studied and applied. This article introduces an adaptive control scheme for a class of non-linear systems with Markov jump switching. The introduced scheme supposes that the system is submitted to external disturbances under imperfect premise matching. By using discrete-time Takagi–Sugeno fuzzy models, a sliding mode observer-based control scheme is utilized to estimate unmeasured states of the system. We build two fuzzy switching manifolds for the disturbance and sliding mode observer systems. Then, a linear matrix inequality-based criterion is developed using slack matrices. This criterion proves that the sliding mode dynamics are robustly admissible under an H-infinity performance often used in control theory. Hence, new adaptive sliding mode controllers are synthesized for the disturbance and sliding mode observer systems. This allows the reachability of pre-designed sliding surfaces to be guaranteed. Finally, experimental numerical illustrations on a bio-...
2017 18th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA), 2017
This study involves problem of state feedback controller (SFC) design for switched systems with t... more This study involves problem of state feedback controller (SFC) design for switched systems with time varying delay. The essential objective is to create a state feedback controller with a switching rule assuring the robust exponential stability and guarantee an H∞ performance of the resulting closed loop hybrid system. Applying Average Dwell Time (ADT) approaches and using appropriate Lyapunov Krasovskii functional (LKf), LMI-based criterion is developed to deal with problem H∞ analysis and synthesis. Simulation examples including the comparisons are relevant to expose the merit of the designed technique.
In this study, we consider eight stages per step family of explicit Runge-Kutta-Nyström pai·rs of... more In this study, we consider eight stages per step family of explicit Runge-Kutta-Nyström pai·rs of orders eight and six. The pairs from this family effectively use eight stages for each step. The coefficients p·rovided by such a method are much less than the number of non linear o·rder conditions requi·red to be solved. Thus, we t·raditionally apply various simplified assumptions in o·rder to address this drawback. The assumptions taken in the family we consider he·re deliver a subsystem where all the coefficients are evaluated successively and explicitly with respect to five f·ree parameters. We t·rain (adjust) these f·ree parameters in o·rder to derive a certain pair that outperforms other similar pai·rs of orders 8(6) in Keplerian type o·rbits, e.g., Kepler, pe·rturbed Kepler, A·renstorf o·rbit, or Pleiades. Diffe·rential evolution technique is used for the training. The pair that we finally present offe·rs about an additional digit of accu·racy in a va·riety of orbits.
2016 17th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA), 2016
This work investigates the problem of state controller synthesis of switched system with time-var... more This work investigates the problem of state controller synthesis of switched system with time-varying delay. Based on Lyapunov-krasovskii technique and the average dwell time approach (ADTA), a switched state feedback controller is created such that the system is exponentially stable and a weighted La-gain is accomplished. By solving a set of linear matrix inequalities (LMIs), controller parameters and the tolerable switching sequence, subject to the disposed average dwell time, can be taken. Two illustrative examples are proposed to demonstrate validity of the introduced method.
2018 Annual American Control Conference (ACC), 2018
This work investigates the problem of state feedback control design for a class of switched singu... more This work investigates the problem of state feedback control design for a class of switched singular systems with time-varying delay. Under Mode-Dependent Average Dwell Time (MDADT), the exponential admissibility of the system is analyzed by considering an appropriate Lyapunov-Krasovskii and the improved reciprocally convex combination approach. By mean of developed admissibility conditions, the existence of stabilizing switching signals and the state feedback controllers are introduced in terms of linear matrix inequalities. A numerical example is simulated to verify the efficiency and the merits of the proposed method.
In this study, we investigate the H∞ fault-tolerant control problem for a discrete-time singular ... more In this study, we investigate the H∞ fault-tolerant control problem for a discrete-time singular system which is subject to external disturbances, actuator faults, and sensor saturation. By assuming that the state variable of the system is unavailable for measurement, and the actuator fault can be described by a Markovian jump process, attention is mainly focused on designing a reliable dynamic output-feedback (DOF) controller able to compensate for the effects of the aforementioned factors on the system stability and performance. Based on the sector non-linear approach to handle the sensor saturation, a new criterion is established to ensure that the closed-loop system is stochastically admissible with a γ level of the H∞ disturbance rejection performance. The main aim of this work is to develop a procedure for synthesizing the controller gains without any model transformation or decomposition of the output matrix. Therefore, by introducing a slack variable, the H∞ admissibility cr...
2018 7th International Conference on Systems and Control (ICSC), 2018
This paper is concerned with the problems of state estimation and sliding mode control for non-li... more This paper is concerned with the problems of state estimation and sliding mode control for non-linear descriptor systems described by (TS) fuzzy models. In fact, using an appropriate fuzzy observer to estimate the system states, an integral sliding mode surface and an adaptive observer-based sliding mode controller will be designed to guarantee the closed-loop fuzzy descriptor system to be robustly stable with H∞ performances, insensitive to all admissible uncertainties and satisfies the reaching condition. The developed results are tested on a representative example to confirm the effectiveness of the theoretical developments.
In this study, a decentralised output learning control strategy for a class of nonlinear intercon... more In this study, a decentralised output learning control strategy for a class of nonlinear interconnected systems is studied. Based on Takagi-Sugeno fuzzy (TS) model to approximate the considered interconnected nonlinear systems, a decentralised observer-based control scheme is designed to override the external disturbances such that the H ∞ performance is achieved. The appealing attributes of this approach include: (1) the closed-loop system exhibits a robustness against nonlinear interconnections and external disturbance, (2) by one-step procedure, the gain matrices of observer and controller are obtained on a single step. In simulation results, the controller design is evaluated on the steering stability of a car where the nonlinear model describes the side slip, roll and yaw motions of the automotive vehicle equipped with four-wheel-steering and active suspension.
In this article, a new approach regarding H∞ and non-fragile stability analysis and observer-base... more In this article, a new approach regarding H∞ and non-fragile stability analysis and observer-based controller synthesis problem for a class of discrete-time fuzzy systems is investigated. The multiplicative gain variations under consideration are contained in both the controller gain and observer gain. By defining a basis-dependent Lyapunov function and introducing some additional matrix variables, new sufficient conditions are derived to
This paper investigates the problem of multiobjective control for a class of uncertain discrete-t... more This paper investigates the problem of multiobjective control for a class of uncertain discrete-time fuzzy systems. The state-space Takagi-Sugeno T-S fuzzy model with linear fractional parameter uncertainties is adopted. Based on a linear matrix inequality approach and via so-called dynamic parallel distributed compensation, a fuzzy full-order dynamic output feedback controller is developed such that the L 2 gain performance from the exogenous input signals to the controlled output is less than or equal to some prescribed value and, for all admissible uncertainties, the closed-loop poles of each local system are within a pre-specified sub-region of complex plane. Two numerical examples are provided to illustrate the effectiveness of the proposed design method. Keywords T-S fuzzy model Á H ? performance Á Pole-placement Á Output feedback Á Robust control Á Linear matrix inequalities (LMIs) Communicated by Y. Jin
This paper is concerned with the problem of robust discrete-time sliding-mode control for a class... more This paper is concerned with the problem of robust discrete-time sliding-mode control for a class of uncertain descriptor systems with time-varying delay and external disturbance. A new sliding function is proposed and sufficient conditions are derived to guarantee that the sliding mode dynamics is robustly admissible. Moreover, a quasi-sliding mode controller is established to satisfy the reaching condition. The developed results are tested on a representative example to illustrate the theoretical developments.
Optimal Control Applications & Methods, Oct 9, 2018
SummaryThis paper investigates the problem of control design for a class of uncertain switched si... more SummaryThis paper investigates the problem of control design for a class of uncertain switched singular systems with time‐varying delay. Under mode‐dependent average dwell time and using an appropriate Lyapunov‐Krasovskii functional, the exponential admissibility of the system is analyzed. In order to obtain less conservative conditions, the delay partitioning technique is adopted as well as the improved reciprocally convex approach. By means of the developed admissibility condition, a static output feedback controller is then designed using linear matrix inequality approach. Moreover, by solving an optimization convex problem with constraints, the switched controller is developed to ensure simultaneously the stability of the closed‐loop system and satisfy an optimized upper bound of both the linear quadratic guaranteed cost and the H∞ norm. Numerical examples are proposed to verify the efficiency and the merits of the method proposed.
The computation of the time-varying matrix pseudoinverse has become crucial in recent years for s... more The computation of the time-varying matrix pseudoinverse has become crucial in recent years for solving time-varying problems in engineering and science domains. This paper investigates the issue of calculating the time-varying pseudoinverse based on full-rank decomposition (FRD) using the zeroing neural network (ZNN) method, which is currently considered to be a cutting edge method for calculating the time-varying matrix pseudoinverse. As a consequence, for the first time in the literature, a new ZNN model called ZNNFRDP is introduced for time-varying pseudoinversion and it is based on FRD. Five numerical experiments investigate and confirm that the ZNNFRDP model performs as well as, if not better than, other well-performing ZNN models in the calculation of the time-varying pseudoinverse. Additionally, theoretical analysis and numerical findings have both supported the effectiveness of the proposed model.
International Journal of Adaptive Control and Signal Processing
This article deals with the problem of robust output feedback control design for a class of switc... more This article deals with the problem of robust output feedback control design for a class of switched systems with uncertainties and random time‐varying delay. Our purpose is focused on designing a full order dynamic output feedback controller and an appropriate switching rule to ensure the exponential mean square stability of the resulting closed‐loop switching system with an l2−l∞ performance level. The appealing aspects of the proposed control scheme include: (a) the development of LMI based delay‐dependent sufficient conditions for the exponential stability analysis of the stochastic hybrid systems using the appropriate choice of the augmented Lyapunov–Krasovskii functional, the partitioning technique and the average dwell time, (b) conservatism reduction of the unified design conditions, and (c) the controller designed exhibiting robustness with l2−l∞ performance against uncertainties and external disturbance. Finally, representative examples are given to demonstrate the validity and the merit of the proposed design technique.
Fuzzy theory is widely studied and applied. This article introduces an adaptive control scheme fo... more Fuzzy theory is widely studied and applied. This article introduces an adaptive control scheme for a class of non-linear systems with Markov jump switching. The introduced scheme supposes that the system is submitted to external disturbances under imperfect premise matching. By using discrete-time Takagi–Sugeno fuzzy models, a sliding mode observer-based control scheme is utilized to estimate unmeasured states of the system. We build two fuzzy switching manifolds for the disturbance and sliding mode observer systems. Then, a linear matrix inequality-based criterion is developed using slack matrices. This criterion proves that the sliding mode dynamics are robustly admissible under an H-infinity performance often used in control theory. Hence, new adaptive sliding mode controllers are synthesized for the disturbance and sliding mode observer systems. This allows the reachability of pre-designed sliding surfaces to be guaranteed. Finally, experimental numerical illustrations on a bio-...
2017 18th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA), 2017
This study involves problem of state feedback controller (SFC) design for switched systems with t... more This study involves problem of state feedback controller (SFC) design for switched systems with time varying delay. The essential objective is to create a state feedback controller with a switching rule assuring the robust exponential stability and guarantee an H∞ performance of the resulting closed loop hybrid system. Applying Average Dwell Time (ADT) approaches and using appropriate Lyapunov Krasovskii functional (LKf), LMI-based criterion is developed to deal with problem H∞ analysis and synthesis. Simulation examples including the comparisons are relevant to expose the merit of the designed technique.
In this study, we consider eight stages per step family of explicit Runge-Kutta-Nyström pai·rs of... more In this study, we consider eight stages per step family of explicit Runge-Kutta-Nyström pai·rs of orders eight and six. The pairs from this family effectively use eight stages for each step. The coefficients p·rovided by such a method are much less than the number of non linear o·rder conditions requi·red to be solved. Thus, we t·raditionally apply various simplified assumptions in o·rder to address this drawback. The assumptions taken in the family we consider he·re deliver a subsystem where all the coefficients are evaluated successively and explicitly with respect to five f·ree parameters. We t·rain (adjust) these f·ree parameters in o·rder to derive a certain pair that outperforms other similar pai·rs of orders 8(6) in Keplerian type o·rbits, e.g., Kepler, pe·rturbed Kepler, A·renstorf o·rbit, or Pleiades. Diffe·rential evolution technique is used for the training. The pair that we finally present offe·rs about an additional digit of accu·racy in a va·riety of orbits.
2016 17th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA), 2016
This work investigates the problem of state controller synthesis of switched system with time-var... more This work investigates the problem of state controller synthesis of switched system with time-varying delay. Based on Lyapunov-krasovskii technique and the average dwell time approach (ADTA), a switched state feedback controller is created such that the system is exponentially stable and a weighted La-gain is accomplished. By solving a set of linear matrix inequalities (LMIs), controller parameters and the tolerable switching sequence, subject to the disposed average dwell time, can be taken. Two illustrative examples are proposed to demonstrate validity of the introduced method.
2018 Annual American Control Conference (ACC), 2018
This work investigates the problem of state feedback control design for a class of switched singu... more This work investigates the problem of state feedback control design for a class of switched singular systems with time-varying delay. Under Mode-Dependent Average Dwell Time (MDADT), the exponential admissibility of the system is analyzed by considering an appropriate Lyapunov-Krasovskii and the improved reciprocally convex combination approach. By mean of developed admissibility conditions, the existence of stabilizing switching signals and the state feedback controllers are introduced in terms of linear matrix inequalities. A numerical example is simulated to verify the efficiency and the merits of the proposed method.
In this study, we investigate the H∞ fault-tolerant control problem for a discrete-time singular ... more In this study, we investigate the H∞ fault-tolerant control problem for a discrete-time singular system which is subject to external disturbances, actuator faults, and sensor saturation. By assuming that the state variable of the system is unavailable for measurement, and the actuator fault can be described by a Markovian jump process, attention is mainly focused on designing a reliable dynamic output-feedback (DOF) controller able to compensate for the effects of the aforementioned factors on the system stability and performance. Based on the sector non-linear approach to handle the sensor saturation, a new criterion is established to ensure that the closed-loop system is stochastically admissible with a γ level of the H∞ disturbance rejection performance. The main aim of this work is to develop a procedure for synthesizing the controller gains without any model transformation or decomposition of the output matrix. Therefore, by introducing a slack variable, the H∞ admissibility cr...
2018 7th International Conference on Systems and Control (ICSC), 2018
This paper is concerned with the problems of state estimation and sliding mode control for non-li... more This paper is concerned with the problems of state estimation and sliding mode control for non-linear descriptor systems described by (TS) fuzzy models. In fact, using an appropriate fuzzy observer to estimate the system states, an integral sliding mode surface and an adaptive observer-based sliding mode controller will be designed to guarantee the closed-loop fuzzy descriptor system to be robustly stable with H∞ performances, insensitive to all admissible uncertainties and satisfies the reaching condition. The developed results are tested on a representative example to confirm the effectiveness of the theoretical developments.
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Papers by Mourad Kchaou