Optimal Control of Completely Unknown Nonlinear Systems Based on SDRE Method

Abstract

This paper proposes a novel online iterative algorithm for optimizing the control of nonlinear systems, enabling optimization of continuous nonlinear systems with unknown dynamics. The method builds upon traditional state-dependent Riccati equation (SDRE) concepts, segmentally approximating and linearizing the nonlinear system, transforming the Hamilton–Jacobi–Bellman (HJB) equation into a solvable SDRE problem. By applying an arbitrary stable control and utilizing real-time data, this method eliminates the need for system matrices A and B, directly solving the optimal control problem through a data-driven approach. Strategy iteration is employed to approximate the solution of the Riccati equation for each linearized system segment, which is then applied in real-time without requiring prior knowledge of the system’s dynamics. Unlike conventional SDRE-based algorithms that rely on accurate system modeling, the proposed method remains effective even when the system model changes, addressing a key limitation of traditional approaches. The paper also presents a convergence proof for the recursive algorithm and validates its effectiveness through simulations on second-order affine nonlinear continuous systems. Compared to traditional SDRE control methods, the proposed approach offers substantial advantages in adaptability and performance.