Optimal Tracking for Nonlinear Interconnected Dynamic Systems using State Dependent Riccati Equation

Abstract

This paper considers the problem of optimal control of nonlinear single and multiple interconnected dynamic systems using state dependent Riccati equation (SDRE). SDRE method mimics the classical LQR method of optimal linear control for a large class of nonlinear systems. It relies on a non-unique factorization of nonlinear systems known as the state dependent coefficient (SDC) parametrization. The paper initially provides a comprehensive derivation of SDRE for a single nonlinear system represented by SDC. Then, the necessary equations are given for multiple interconnected dynamic system based on the generalized SDC representation. We show the effectiveness of SDRE method and compare it with the method of control law partitioning or the method of computed-torque control (CTC), which has been used in control of robotics manipulators. Illustrative examples are given to demonstrate the usefulness of SDRE method as applied to single and multiple interconnected inverted pendulum as well as robotic manipulator.