Stochastic Feedback Control of Systems with Unknown Nonlinear Dynamics

TL;DR

This paper introduces a method for stochastic optimal control of systems with unknown nonlinear dynamics by combining trajectory optimization, system identification from experimental data, and LQG control design to maintain system states near optimal trajectories.

Contribution

It presents a novel approach that integrates trajectory optimization, data-driven system identification, and LQG control for unknown nonlinear systems under stochastic disturbances.

Findings

Effective control performance demonstrated in a computational example.

System states remain close to the optimal trajectory under small noise.

Method handles unknown nonlinear dynamics without explicit system models.

Abstract

This paper studies the stochastic optimal control problem for systems with unknown dynamics. First, an open-loop deterministic trajectory optimization problem is solved without knowing the explicit form of the dynamical system. Next, a Linear Quadratic Gaussian (LQG) controller is designed for the nominal trajectory-dependent linearized system, such that under a small noise assumption, the actual states remain close to the optimal trajectory. The trajectory-dependent linearized system is identified using input-output experimental data consisting of the impulse responses of the nominal system. A computational example is given to illustrate the performance of the proposed approach.