Journal of Optimization Theory and Applications, 1991
The design of the control of an aircraft encountering windshear after takeoff is treated as a pro... more The design of the control of an aircraft encountering windshear after takeoff is treated as a problem of stabilizing the climb rate about a desired value of the climb rate. The resulting controller is a feedback one utilizing only climb rate information. Its robustness vis-avis windshear structure and intensity is illustrated via simulations employing four different windshear models.
International Journal of Robust and Nonlinear Control, 1993
The control of an aircraft encountering windshear after takeoff is treated as a problem of stabil... more The control of an aircraft encountering windshear after takeoff is treated as a problem of stabilizing the climb rate about a desired value. An adaptive strategy is developed which uses only climb rate information. Robustness vis h vis windshear structure and intensity is illustrated via simulations employing four different windshear models. KEY WORDS Adaptive control Aircraft guidance Windshear * For a survey of such methods see Reference 21.
Feedback control of uncertain systems: robustness with respect to neglected actuator and sensor dynamics†
International Journal of Control, 1986
... and A7 hold}): A7: AD:lR —> |R""" is continuously differentiable and, for a... more ... and A7 hold}): A7: AD:lR —> |R""" is continuously differentiable and, for all re IR, (ll €K9 ... For example, (i) the (linear) forms of the actuator (1.2) and sensor (1.3) are somewhat special ... of uncertain systems (but 01' reduced order in the context of the present paper), based on similar ...
Uncertain systems: Robustness of ultimate boundedness control with respect to neglected dynamics
Lecture Notes in Control and Information Sciences
Feedback control of a class of imperfectly known dynamical systems is considered. On the basis of... more Feedback control of a class of imperfectly known dynamical systems is considered. On the basis of known functional properties and bounds relating to the uncertain elements of the generic system and initially neglecting actuator and sensor dynamics, a feedback structure is first determined (using established Lyapunov-based techniques [1],[2]) which guarantees uniform ultimate boundedness of all motions of the reduced-order system
We consider dynamical systems with norm-bounded uncertainty in (i) the system parameters (model u... more We consider dynamical systems with norm-bounded uncertainty in (i) the system parameters (model uncertainty) or in (ii) the input (disturbance). For case (i), the nominal (null uncertainty) system is linear with constant matrices. Such systems with norm-bounded control as well as with a control penalty are treated. However, in the former the treatment is restricted to single input systems in companion form, and in the latter to second order systems. Fer case (ii), the system is linear with time-varying matrices and norm-bounded control. Using some results from the theories of differential games and general dynamical systems, we deduce feedback controlswhich render the origin uniformly asymptotically stable in the large for all admissible parameter uncertainties or input disturbances; these may be both time and state dependent. The application of the theory is illustrated by examples.
Degenerate feedback and time consistency in differential games
This paper analyses the time consistency of open-loop equilibria, in the cases of Nash and Stacke... more This paper analyses the time consistency of open-loop equilibria, in the cases of Nash and Stackelberg behaviour. We define a class of games where the strong time-consistency of the open-loop Nash equilibrium associates with the time consistency of the open-loop Stackelberg equilibrium. We label these games as `perfect uncontrollable' and provide two examples based on (i) a model where firms invest so as to increase consumers' reservation prices, based upon Cellini and Lambertini (CEJOR, 2003); and (ii) a model where firms compete to increase their respective market shares, based upon Leit- mann and Schmitendorf (IEEE Transactions on Automatic Control, 1978).
Journal of Optimization Theory and Applications, 1990
We consider a resource management problem in which the management objective is to minimize fluctu... more We consider a resource management problem in which the management objective is to minimize fluctuations in resource economics. Stabilizing management policies consist of memoryless state feedback control strategies for a class of discrete-time resource models which contain unknown but bounded fluctuations. The underlying theory is based on conditions developed for Lyapunov-type stability of sets. The design of the stabilizing policies is illustrated by a simulation example from resource economics. Specifically, employment of fishermen is stabilized by using a subsidizing and taxing policy in an open-access common-property fishery in which the value of the resource and the resource level fluctuate, and where entry and exit dynamics are determined by fluctuating revenues obtained from the fishery.
Controller Design for Uncertain Systems via Lyapunov Functions
1988 American Control Conference, 1988
... 2019 Page 2. 2.2 Proposed Controli Here we present some practically stabilizing controller se... more ... 2019 Page 2. 2.2 Proposed Controli Here we present some practically stabilizing controller sets for the systems csidered in the previous section. ... Havresting problems are reated in (28,60) and river pollution control problems are considered in (18,61,62,73-75). ...
Journal of Optimization Theory and Applications, 2001
Based on an earlier publication (Ref. 1), a coordinate transformation is proposed, which allows t... more Based on an earlier publication (Ref. 1), a coordinate transformation is proposed, which allows the direct global extremization of a class of integrals without the use of comparison methods such as variational or field techniques. This direct method is shown to be applicable to a class of unconstrained optimal control problems. A motivation for the proposed method as well as applications are presented.
We present a controller design methodology for uncertain systems which is based on the constructi... more We present a controller design methodology for uncertain systems which is based on the constructive use of Lyapunov stability theory. The uncertainties, which are deterministic, are characterized by certain structural conditions and known as well as unknown bounds. As a consequence of the Lyapunov approach, the methodology is not restricted to linear or time-invariant systems. The robustness of these controllers in the presence of singular perturbations is considered. The situation in which the full state of the system is not available for measurement is also considered as are other generalizations. Applications of the proposed discussed in the complete version of the paper.
Journal of Optimization Theory and Applications, 1991
The design of the control of an aircraft encountering windshear after takeoff is treated as a pro... more The design of the control of an aircraft encountering windshear after takeoff is treated as a problem of stabilizing the climb rate about a desired value of the climb rate. The resulting controller is a feedback one utilizing only climb rate information. Its robustness vis-avis windshear structure and intensity is illustrated via simulations employing four different windshear models.
International Journal of Robust and Nonlinear Control, 1993
The control of an aircraft encountering windshear after takeoff is treated as a problem of stabil... more The control of an aircraft encountering windshear after takeoff is treated as a problem of stabilizing the climb rate about a desired value. An adaptive strategy is developed which uses only climb rate information. Robustness vis h vis windshear structure and intensity is illustrated via simulations employing four different windshear models. KEY WORDS Adaptive control Aircraft guidance Windshear * For a survey of such methods see Reference 21.
Feedback control of uncertain systems: robustness with respect to neglected actuator and sensor dynamics†
International Journal of Control, 1986
... and A7 hold}): A7: AD:lR —> |R""" is continuously differentiable and, for a... more ... and A7 hold}): A7: AD:lR —> |R""" is continuously differentiable and, for all re IR, (ll €K9 ... For example, (i) the (linear) forms of the actuator (1.2) and sensor (1.3) are somewhat special ... of uncertain systems (but 01' reduced order in the context of the present paper), based on similar ...
Uncertain systems: Robustness of ultimate boundedness control with respect to neglected dynamics
Lecture Notes in Control and Information Sciences
Feedback control of a class of imperfectly known dynamical systems is considered. On the basis of... more Feedback control of a class of imperfectly known dynamical systems is considered. On the basis of known functional properties and bounds relating to the uncertain elements of the generic system and initially neglecting actuator and sensor dynamics, a feedback structure is first determined (using established Lyapunov-based techniques [1],[2]) which guarantees uniform ultimate boundedness of all motions of the reduced-order system
We consider dynamical systems with norm-bounded uncertainty in (i) the system parameters (model u... more We consider dynamical systems with norm-bounded uncertainty in (i) the system parameters (model uncertainty) or in (ii) the input (disturbance). For case (i), the nominal (null uncertainty) system is linear with constant matrices. Such systems with norm-bounded control as well as with a control penalty are treated. However, in the former the treatment is restricted to single input systems in companion form, and in the latter to second order systems. Fer case (ii), the system is linear with time-varying matrices and norm-bounded control. Using some results from the theories of differential games and general dynamical systems, we deduce feedback controlswhich render the origin uniformly asymptotically stable in the large for all admissible parameter uncertainties or input disturbances; these may be both time and state dependent. The application of the theory is illustrated by examples.
Degenerate feedback and time consistency in differential games
This paper analyses the time consistency of open-loop equilibria, in the cases of Nash and Stacke... more This paper analyses the time consistency of open-loop equilibria, in the cases of Nash and Stackelberg behaviour. We define a class of games where the strong time-consistency of the open-loop Nash equilibrium associates with the time consistency of the open-loop Stackelberg equilibrium. We label these games as `perfect uncontrollable' and provide two examples based on (i) a model where firms invest so as to increase consumers' reservation prices, based upon Cellini and Lambertini (CEJOR, 2003); and (ii) a model where firms compete to increase their respective market shares, based upon Leit- mann and Schmitendorf (IEEE Transactions on Automatic Control, 1978).
Journal of Optimization Theory and Applications, 1990
We consider a resource management problem in which the management objective is to minimize fluctu... more We consider a resource management problem in which the management objective is to minimize fluctuations in resource economics. Stabilizing management policies consist of memoryless state feedback control strategies for a class of discrete-time resource models which contain unknown but bounded fluctuations. The underlying theory is based on conditions developed for Lyapunov-type stability of sets. The design of the stabilizing policies is illustrated by a simulation example from resource economics. Specifically, employment of fishermen is stabilized by using a subsidizing and taxing policy in an open-access common-property fishery in which the value of the resource and the resource level fluctuate, and where entry and exit dynamics are determined by fluctuating revenues obtained from the fishery.
Controller Design for Uncertain Systems via Lyapunov Functions
1988 American Control Conference, 1988
... 2019 Page 2. 2.2 Proposed Controli Here we present some practically stabilizing controller se... more ... 2019 Page 2. 2.2 Proposed Controli Here we present some practically stabilizing controller sets for the systems csidered in the previous section. ... Havresting problems are reated in (28,60) and river pollution control problems are considered in (18,61,62,73-75). ...
Journal of Optimization Theory and Applications, 2001
Based on an earlier publication (Ref. 1), a coordinate transformation is proposed, which allows t... more Based on an earlier publication (Ref. 1), a coordinate transformation is proposed, which allows the direct global extremization of a class of integrals without the use of comparison methods such as variational or field techniques. This direct method is shown to be applicable to a class of unconstrained optimal control problems. A motivation for the proposed method as well as applications are presented.
We present a controller design methodology for uncertain systems which is based on the constructi... more We present a controller design methodology for uncertain systems which is based on the constructive use of Lyapunov stability theory. The uncertainties, which are deterministic, are characterized by certain structural conditions and known as well as unknown bounds. As a consequence of the Lyapunov approach, the methodology is not restricted to linear or time-invariant systems. The robustness of these controllers in the presence of singular perturbations is considered. The situation in which the full state of the system is not available for measurement is also considered as are other generalizations. Applications of the proposed discussed in the complete version of the paper.
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Papers by G. Leitmann