Sequential Action Control: Closed-Form Optimal Control for Nonlinear Systems
نویسندگان
چکیده
This paper presents a means to compute predictive optimal controls on-line and in closed loop for broad classes of differentiable nonlinear systems. Rather than iteratively optimize control sequences to minimize an objective, we derive a closedform expression for the control actions at each instant that optimally improve a tracking objective. As a special case, optimal actions are shown to reduce to LQ regulators with defined local stability properties. Globally, derivations prove the optimal actions are solutions to a well-studied class of Tikhonov regularization problems and so inherit guarantees for existence and uniqueness. To sequence actions, an algorithm is presented that forms a (piecewise) continuous min-max constrained response to state that avoids the overhead typically required to impose control saturation constraints. Benchmark examples included in this paper show that the approach can outperform both traditional optimal controllers and recently published, case-specific methods from literature in terms of tracking performance, and at computational speeds many orders of magnitude faster that traditionally achievable for nonlinear closed-loop predictive control.
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تاریخ انتشار 2014