Linear-quadratic Optimal Control with Integral Quadratic Constraints

Abstract

We derive closed-form solutions for the linear-quadratic (LQ) optimal control problem subject to integral quadratic constraints. The optimal control is a non-linear function of the current state and the initial state. Furthermore, the optimal control is easily calculated by solving an unconstrained LQ control problem together with an optimal parameter selection problem. Gradient formulae for the cost functional of the optimal parameter selection problem is derived. Application to minimax problems is given. The method is illustrated in a numerical example. Show more