Robust adaptive control problem for linear systems with unknown parameters

Formulates a robust adaptive control problem for uncertain linear systems. For complete linear systems with a quadratic performance index, a minimax controller is easily obtained. The class of systems under consideration has a bilinear structure. Although it allows a finite dimensional estimator, the problem still remains more difficult than the linear-quadratic problem. For these class of systems, the minimax dynamic programming problem is formulated with the estimator equation and its associated Riccati equation as state variables. It is then shown that a saddle point controller is equivalent to a minimax controller by using the Hamilton-Jacobi-Isaacs equation. Since the saddle point optimal return function satisfies the minimax dynamic programming equation, restrictive assumptions on the uniqueness of the worst case state are not required. The authors finally show that with additional assumptions the problem can be extended to the infinite-time problem