Robust controller design for linear, time-varying systems

This dissertation examines the design of controllers for linear, time-varying systems. In particular, a design procedure is presented that incorporates performance and robustness objectives into existing optimal control methods.; In the first part of this dissertation, descriptions of a time-varying system in the time and frequency domains are presented. Specifically, the concepts of poles and zeros are extended to time-varying systems and several analogues of the transfer function are examined. These analogues are based on a general system transformation known as the {dollar}{lcub}cal W{rcub}{dollar}-transform and are functions of both frequency and time. It is shown that a single frequency component of an input to a time-varying system influences each frequency component of the output to some extent. Furthermore, a correlation is established between the transmission of power across frequencies and the time-variation of a system using several measures of time-variation.; In the second part, the design procedure is developed using these descriptions and the solution of the analogue to the {dollar}{lcub}cal H{rcub}sb{lcub}infty{rcub}{dollar} optimal control problem for time-varying systems. In particular, design guidelines are derived for several basic performance and robustness objectives. These guidelines reflect the time dependence of the frequency response of a time-varying system while retaining the frequency domain intuition of the time-invariant case. This procedure is analogous to the loop shaping design procedure of McFarlane and Glover for time-invariant systems.; For time-varying systems, the amount of computation required in the synthesis of an optimal controller is formidable. Moreover, frequency domain analysis of a time-varying system is computationally intensive. To remedy this situation, a special class of state space realizations is introduced that provide a linear, time-varying representation of a physical system with a finite amount of data. For systems admitting this type of realization, the {dollar}{lcub}cal H{rcub}sb{lcub}infty{rcub}{dollar} controller synthesis problem is shown to be computationally tractable permitting effective implementation of the design procedure. As an illustration of the procedure, the design of a steering controller for an automated highway vehicle is presented.