Optimal Output Regulation for General Linear Systems via Adaptive Dynamic Programming

In this article, we consider an adaptive optimal output regulation problem for general linear systems. The purpose of the optimal output regulation problem is to guarantee the stability of the closed-loop system and disturbance rejection, as well by minimizing some predefined performance indices. It can be realized by using an optimal controller, in which both optimal feedback control gain and optimal feedforward control gain are included. First, an adaptive dynamic programming (ADP) technique is used to solve the optimal feedback control gain. Next, the unknown system matrices of the plant are explicitly computed. In addition, based on the property of the minimal polynomial, the coefficient of the exogenous disturbance in the expression of the regulated output can also be calculated. Finally, according to the regulator equation, an extra cost function is given, which aims to obtain the optimal feedforward control gain. The linear vector space optimization methods are used to solve the optimal problem. As a result, the linear optimal output regulation problem can be solved by the approximately optimal feedback and feedforward control gains.