Sequential Action Control: Closed-Form Optimal Control for Nonlinear and Nonsmooth Systems
This provides a more efficient solution for controlling hybrid, underactuated, and constrained systems, which is incremental but offers practical speed improvements.
The paper tackles optimal control for challenging nonlinear systems by deriving a closed-form expression for individual control actions that optimally improve tracking objectives, enabling on-line computation without iterative optimization. Benchmark results show the approach outperforms existing methods in tracking performance and achieves speeds orders of magnitude faster.
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.