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

Alexander R. Ansari, Todd D. Murphey

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1196-1214
Number of pages19
JournalIEEE Transactions on Robotics
Issue number5
StatePublished - Oct 2016


  • Closed-loop systems
  • hybrid systems
  • impacting systems
  • nonlinear control systems
  • real-time optimal control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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