Linear quadratic minimax controllers

Abstract

Minimax methods are proposed for the analysis and design of controllers for the best controls with the worst initial conditions, worst parameter changes with specified quadratic norms, and worst disturbances with specified integral-square norms. The worst initial conditions are the only forcing functions; disturbances are regarded as an added set of feedback controls whose magnitudes are limited by negative weights in the performance index. The minimax value of the performance index is easily calculated as the maximum eigenvalue of a steady-state Lyapunov or Riccati matrix. There is a lower bound on the disturbance weights in the performance index; at this bound, the controller design is identical to the //<» controller design. There is also an upper bound on the norm of the parameter changes; at this value, the closed-loop system goes unstable, and the corresponding parameter change vector is almost the same as the corresponding vector obtained by real /* analysis—the only difference being the use of a quadratic norm instead of an infinity norm.