Near-optimal control with adaptive receding horizon for discrete-time piecewise affine systems

Conference paper (2017)

Authors

J. Xu Team Bart De Schutter - Mechanical, Maritime and Materials Engineering
Lucían Busoniu Technical University of Cluj-Napoca
B.H.K. De Schutter Team Bart De Schutter - Mechanical, Maritime and Materials Engineering
Research Group
Team Bart De Schutter (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2017 J. Xu, Lucian Buşoniu, B.H.K. De Schutter
DOI: https://doi.org/10.1016/j.ifacol.2017.08.806
Piecewise affine systems Near-optimality analysis Nonlinear predictive control Optimistic planning
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Published Date

2017

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Bart De Schutter

Abstract

We consider the infinite-horizon optimal control of discrete-time, Lipschitz continuous piecewise affine systems with a single input. Stage costs are discounted, bounded, and use a 1 or ∞-norm. Rather than using the usual fixed-horizon approach from model-predictive control, we tailor an adaptive-horizon method called optimistic planning for continuous actions (OPC) to solve the piecewise affine control problem in receding horizon. The main advantage is the ability to solve problems requiring arbitrarily long horizons. Furthermore, we introduce a novel extension that provides guarantees on the closed-loop performance, by reusing data (“learning”) across different steps. This extension is general and works for a large class of nonlinear dynamics. In experiments with piecewise affine systems, OPC improves performance compared to a fixed-horizon approach, while the data-reuse approach yields further improvements.