Learning-Based Predictive Control for Discrete-Time Nonlinear Systems With Stochastic Disturbances.

Area of Science:

• Control Systems Engineering
• Machine Learning
• Nonlinear Dynamics

Background:

• Conventional model predictive control (MPC) often relies on open-loop optimization or simplified closed-loop methods.
• Existing reinforcement learning (RL) and adaptive dynamic programming (ADP) methods can face high computational costs for infinite-horizon problems.

Purpose of the Study:

• To propose a learning-based predictive control (LPC) scheme for adaptive optimal control of discrete-time nonlinear systems with stochastic disturbances.
• To develop a finite-horizon iterative reinforcement learning (RL) algorithm for solving closed-loop nonlinear optimal control problems within each prediction horizon.
• To reduce computational costs and improve learning efficiency compared to existing methods.

Main Methods:

• Formulating the control task as a closed-loop nonlinear optimal control problem within each horizon.
• Developing a finite-horizon iterative reinforcement learning (RL) algorithm.
• Decomposing infinite-horizon problems into a series of finite-horizon problems.
• Utilizing successive policy updates between adjoint time horizons.

Main Results:

• The proposed LPC scheme effectively handles stochastic disturbances in discrete-time nonlinear systems.
• Convergence of the RL algorithm and Lyapunov stability of the closed-loop system are mathematically proven.
• LPC demonstrates lower computational costs than conventional nonlinear MPC and ADP.

Conclusions:

• The learning-based predictive control (LPC) scheme offers superior performance in policy optimality and computational efficiency.
• LPC represents a new class of closed-loop learning-based optimization techniques for nonlinear predictive control.
• The method successfully balances control performance with reduced computational burden.