Sequential Action Control: Closed-Form Optimal Control for Nonlinear and Nonsmooth Systems

TL;DR

This paper introduces Sequential Action Control, a novel closed-form optimal control method for nonlinear and nonsmooth systems, enabling fast, stable, and constraint-aware control in real-time applications.

Contribution

It derives a closed-form expression for control actions that can be sequenced online, improving efficiency and robustness over traditional iterative methods.

Findings

Achieves real-time control for complex nonlinear systems

Outperforms existing nonlinear optimal controllers in tracking accuracy

Provides stability analysis and parameter tuning framework

Abstract

This paper presents a new model-based algorithm that computes predictive optimal controls on-line and in closed loop for traditionally challenging nonlinear systems. Examples demonstrate the same algorithm controlling hybrid impulsive, underactuated, and constrained systems using only high-level models and trajectory goals. Rather than iteratively optimize finite horizon control sequences to minimize an objective, this paper derives a closed-form expression for individual control actions, i.e., control values that can be applied for short duration, that optimally improve a tracking objective over a long time horizon. Under mild assumptions, actions become linear feedback laws near equilibria that permit stability analysis and performance-based parameter selection. Globally, optimal actions are guaranteed existence and uniqueness. By sequencing these actions on-line, in receding horizon fashion, the proposed controller provides a min-max constrained response to state that avoids the overhead typically required to impose control constraints. Benchmark examples show the approach can avoid local minima and outperform nonlinear optimal controllers and recent, case-specific methods in terms of tracking performance, and at speeds orders of magnitude faster than traditionally achievable.