Convex Formulations and Algebraic Solutions for Linear Quadratic Inverse Optimal Control Problems

Abstract

This paper presents convex formulations for inverse optimal control problems for linear systems to infer cost function matrices of a quadratic cost from both optimal and non-optimal closed-loop gains. It introduces an optimality measure which enables a formulation of the problem as a convex semidefinite program for the general case and a linear program for several special cases. We derive an explicit algebraic expression for general objective function matrices as well as conditions under which the solution to the inverse optimal control problem is unique. The result is derived by means of a vectorization and parametrization of the algebraic Riccati equation. A simulation example highlights the robust performance in the presence of noise on the measured closed-loop gain and the computational efficiency of the proposed problem formulations.