Abstract
This paper proposes a method to compute the verified solution of LQ control problem using floating point arithmetic. To this end, we propose a guaranteed accuracy algorithm to solve Riccati equation, and define a verification problem of LQ controller. The algorithm computes the basis of the eigenspace of the Hamilton matrix using verified numerical computation. Krawczyk method which is known as an interval version of Newton's method is also used to obtain a sharp interval. In the verification problem of LQ controller, the verification conditions which validate whether the numerical solution satisfies the requirements of LQ controller are proposed. Furthermore, we describe a method which finds the numerical solution of LQ control problem which minimizes an evaluation function for the design specification among the set of the verified solutions. Numerical examples are shown to demonstrate the effectivity of the proposed method.
