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

This paper presents a new model-based algorithm that computes predictive optimal controls online and in a 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 optimizing 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 online, in receding horizon fashion, the proposed controller provides a min-max constrained response to a state that avoids the overhead typically required to impose control constraints. Benchmark examples show that the approach can avoid local minima and outperform nonlinear optimal controllers and recent case-specific methods in terms of tracking performance and at speeds that are orders of magnitude faster than traditionally achievable ones.