Showing papers by "Ian R. Petersen published in 2006"

Minimax lqg control

Abstract: This paper presents an overview of some recent results concerning the emerging theory of minimax LQG control for uncertain systems with a relative entropy constraint uncertainty description. This is an important new robust control system design methodology providing minimax optimal performance in terms of a quadratic cost functional. The paper first considers some standard uncertainty descriptions to motivate the relative entropy constraint uncertainty description. The minimax LQG problem under consideration is further motivated by analysing the basic properties of relative entropy. The paper then presents a solution to a worst case control system performance problem which can be generalized to the minimax LQG problem. The solution to this minimax LQG control problem is found to be closely connected to the problem of risk-sensitive optimal control.

Robust output feedback guaranteed cost control of nonlinear stochastic uncertain systems via an IQC approach

Abstract: This paper presents a new approach to constructive output feedback robust nonlinear controller design based on the use of integral quadratic constraints and minimax LQG control. The approach involves a class of controllers which include copies on the nonlinearities in the controller. The nonlinearities being considered are those which satisfy a certain global Lipschitz condition. The linear part of the controller is synthesized using minimax LQG control theory which is closely related to H/sup /spl infin// control theory and this leads to a nonlinear output feedback controller which gives an upper bound on the closed loop value of a quadratic cost functional.

Robust H ∞ Control of an Uncertain System via a Strict Bounded Real Output Feedback Controller

Abstract: The paper presents a new approach to the robust H∞ control of an uncertain system via an output feedback controller which is both stable and has a H∞ norm strictly less than a specified value. The uncertain systems under consideration contain structured uncertainty described by integral quadratic constraints. The controller is designed to achieve absolute stabilization with a specified level of disturbance attenuation. The main result involves solving a state feedback version of the problem by solving an algebraic Riccati equation dependent on a set of scaling parameters. Then two further algebraic Riccati equations are solved which depend on a further set of scaling parameters. The required controller is constructed from the Riccati solutions.

Decentralized state feedback guaranteed cost control of uncertain systems with uncertainty described by integral quadratic constraints

Abstract: This paper presents a procedure for constructing decentralized state feedback guaranteed cost controllers for a class of uncertain systems in which the uncertainty is described by integral quadratic constraints. The proposed procedure involves solving an algebraic Riccati equation of the H/sup /spl infin// control type which is dependent on a number of scaling parameters. By treating the off-diagonal elements of the full state feedback controller gain matrix as uncertainties, a decentralized controller is obtained by taking the block-diagonal part of the full state feedback controller. This approach to decentralized controller design enables the controller to exploit the coupling between the subsystems of the plant.

H ∞ Control of Linear Quantum Systems

Abstract: The purpose of this paper is to formulate and solve a H∞ controller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology. A quantum version of the Strict Bounded Real Lemma is presented and from this, a quantum version of the two Riccati solution to the H∞ control problem is derived.

Robust H~~ Control of an Uncertain System via a Stable Output Feedback Controller

Abstract: The paper presents a new approach to the robust control of an uncertain system via a stable output feedback controller. The uncertain systems under consideration contain structured uncertainty described by integral quadratic constraints. The controller is designed to achieve absolute stabilization with a specified level of disturbance attenuation. The main result involves solving a state feedback version of the problem by solving an algebraic Riccati equation dependent on a set of scaling parameters. Then two further algebraic Riccati equations are solved which depend on a further set of scaling parameters. The required controller is constructed from the Riccati solutions

Guaranteed Cost Control of Stochastic Uncertain Systems with Slope Bounded Nonlinearities via the use of Dynamic Multipliers

Abstract: This paper presents a new approach to constructive output feedback robust nonlinear controller design. The approach involves a class of controllers which include copies of the slope bounded nonlinearities occurring in the plant. Integral Quadratic Constraints and dynamic multipliers are introduced to exploit these repeated nonlinearities. The linear part of the controller is synthesized using minimax LQG control theory. This leads to a stabilizing nonlinear output feedback controller which gives an upper bound on the closed loop value of a quadratic cost functional.

Robust ISI equalization for uncertain channels via minimax optimal filtering

Abstract: We consider a problem of equalization for intersymbol interference (ISI) occurring during data transmission through an imperfectly known channel. It is shown that this problem can be effectively addressed using the minimax filtering approach developed in the paper. This approach leads to a numerically tractable methodology for robust equalizer design which guarantees an optimal upper bound on the equalization error. Copyright © 2006 John Wiley & Sons, Ltd.