OPTIMALITY AND ROBUSTNESS OF LINEAR QUADRATIC CONTROL FOR NONLINEAR-SYSTEMS

The paper is concerned with an inverse optimal control problem, which is to find the conditions for optimality of a nonlinear time-varying plant driven by a Linear Quadratic (LQ) control. The control law is obtained by the standard quadratic optimization of the linear part of the plant. Once optimality of the nonlinear closed-loop system is established, the robustness of stability with respect to bounded variation in open-loop dynamics is assured in terms of the gain and phase margins. Of particular interest are the extensions of the optimality and robustness results of unconstrained feedback to LQ control of large systems with decentralized information structure constraints. In particular, we will show that optimality of decentralized LQ control guarantees gain and phase margins at each control input channel, as well as tolerance to nonlinear time-varying distortions of the feedback control laws. © 1990.