A Model-Free Optimal Control Method With Fixed Terminal States and Delay

TL;DR

This paper introduces a novel model-free control algorithm that handles fixed terminal states and delays, overcoming challenges of environment interaction complexity and state constraints in reinforcement learning.

Contribution

It proposes a new model-free control method using basis functions, gradient estimation, and Lagrange multipliers to manage fixed terminal states and delays.

Findings

Effective in handling state-dependent switches

Performs well with time delays

Shows favorable results in multiple examples

Abstract

Model-free algorithms are brought into the control system's research with the emergence of reinforcement learning algorithms. However, there are two practical challenges of reinforcement learning-based methods. First, learning by interacting with the environment is highly complex. Second, constraints on the states (boundary conditions) require additional care since the state trajectory is implicitly defined from the inputs and system dynamics. To address these problems, this paper proposes a new model-free algorithm based on basis functions, gradient estimation, and the Lagrange method. The favorable performance of the proposed algorithm is shown using several examples under state-dependent switches and time delays.