Chee-Fai Yung

H/sup /spl infin// control for more general nonlinear systems

The authors consider the standard H/sup /spl infin//-control problem for more general nonlinear systems modeled by equations in which the penalty output and the measured output are, in general, functions of the state, the exogenous input, and the control input. In particular, we characterize a family of H/sup /spl infin// controllers via output feedback as well as state feedback, solving the problem. The results obtained generalize some recent results in the literature.

Parameterization of nonlinear H ∞ state-feedback controllers

State-space formulas are derived for a family of controllers solving the nonlinear H∞ state-feedback control problem. These controllers are obtained by interconnecting the ‘central controller’ with an asymptotically stable, free system that satisfies one additional cascade condition. All proofs given are simple and clear, and also provide a deeper insight into the synthesis of the corresponding linear H∞ controllers.

Technical Communique: Reduced-order H∞ controller design - an algebraic Riccati equation approach

An algebraic Riccati equation (ARE) approach to the reduced-order H^~ controller design problem is proposed. It is shown that the order of H^~ controller can be reduced to r, where r is the rank of the stabilizing solution W~ to an ARE in W developed in Petersen, Anderson and Jonckheere (1991, International Journal of Robust Nonlinear Control, 1, 171-185). State-space formulas for the reduced-order H^~ controller design are also given in terms of the stabilizing solutions to the two standard H^~ AREs. The development uses only elementarily algebraic ideas, mainly the bounded real lemma, thus the proofs given are simple and clear.

Brief H∞ controller reduction for nonlinear systems

Sufficient conditions are proposed for the existence of reduced-order (fixed-order) controllers solving the standard nonlinear H^~ output feedback control problem. State-space formulas for such reduced-order H^~ controllers are also derived in terms of the solutions of two Hamilton-Jacobi inequalities. The development uses only elementary concepts of dissipativity and differential game, thus the proofs given are simple and clear.

New smooth approximation of variable structure systems with application to tracking control

This paper presents an exponential-type continuous control law that approximates relay-type discontinuous control law in the conventional variable structure control to an arbitrary extent of accuracy by simply adjusting a parameter. This continuous control law allows us to apply a high control authority to obtain a fast response and alleviate chattering at the same time. An exposition is also given to show how to apply the new control law to tracking control problem. Some numerical examples are included to illustrate the proposed method.<<ETX>>

Brief paper: On the geometric and dynamic structures of the H2 optimal and H∞ central controllers

In this paper, the geometric structure of observer-based controllers is investigated in order to characterize the controllable and unobservable subspaces of the H2 optimal and the H~ central controllers. It is shown that the controllable and unobservable subspaces of the H2 optimal and the H~ central controllers can be characterized by the kernel and image subspaces of the solutions of two Lyapunov equations. Under this characterization, the connection between the geometric subspaces and the dynamic behavior of the plant and those of the H2 optimal and H~ controllers is derived. It is also shown that the H2 optimal and the H~ central controllers inherit a certain part of the given plant dynamics in the geometric sense. A numerical example is also given for illustration.

A game theoretic approach to strictly positive real control

This paper investigates the strictly positive real (SPR) control problem. A unified game theoretic approach is used here to derive the stabilizing controllers which render closed-loop system strictly positive real. Both state feedback and output feedback cases are examined. In addition, a parameterization of SPR controllers is also provided.

On the design of reduced-order H/sup /spl infin// controllers for nonaffine nonlinear systems

Sufficient conditions are proposed for the existence of reduced-order (fixed-order) controllers solving the H/sup /spl infin// control problem for nonaffine nonlinear systems. State-space formulas for such reduced-order H/sup /spl infin// controllers are also derived in terms of the solutions to two standard Hamilton-Jacobi-Isaacs inequalities.

H/sup /spl infin// controller reduction for nonlinear systems

Sufficient conditions are proposed for the existence of reduced-order (fixed-order) controllers solving the standard nonlinear H/sup /spl infin// output feedback control problem. State-space formulas for such reduced-order H/sup /spl infin// controllers are also derived in terms of the solutions of two Hamilton-Jacobi inequalities. The development uses only elementary concepts of dissipativity and differential games, thus the proofs given are simple and clear.

Mixed H/sup 2//H/sup /spl infin// control for linear time-varying systems: infinite horizon case

In this paper, a mixed H/sup 2//H/sup /spl infin// control problem of infinite horizon linear time-varying systems is solved via a Nash game approach. Necessary and sufficient conditions for the existence of a solution to the problem are obtained. Both state feedback and static output feedback cases are examined. The results obtained in this paper generalize some recent results in the literature.