Linear quadratic performance with worst case disturbance rejection

The Lagrange multiplier method and maximum principle are proposed for the design of "LQR" controllers with the worst case disturbance rejection for a linear time-varying (LTV) plant on a finite horizon. The disturbance is bounded by either the windowed /spl Lscr//sup 2/-norm or the windowed /spl Lscr//sup /spl infin//-norm or both. In the case of the windowed /spl Lscr//sup 2/-norm, uncertain but norm bounded initial conditions are also considered. Certain necessary and sufficient conditions for the existence of a linear controller are derived. The results are extended to the steady state ones for the linear time-invariant (LTIV) plant on the infinite horizon. In the case of the windowed /spl Lscr//sup /spl infin//-norm, the solution for the worst case disturbance turns out to be of switching (or bang-bang) type. Finally, some comparison to different problem settings in the windowed /spl Lscr//sup 2/-norm case and an alternative approach are presented.