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 L² -norm or the windowed L^∞-norm or both. In the case of the windowed L²-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 L^∞-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 L²-norm case and an alternative approach are presented