Receding Horizon Control: A Suboptimality-based Approach

J. Pannek: Receding Horizon Control: A Suboptimality-based Approach
PhD thesis, Chair of Applied Mathematics, University of Bayreuth, Germany, 2009

Keywords: MPC; prädiktive Regelung; nichtlineare Stabilitätstheorie; Regelgüte; Abtastung; Suboptimalität; Adaptivität; suboptimality; adaptivity
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Within the proposed work we consider analytical, conceptional and implementational issues of so called receding horizon controllers in a sampled-data setting. The principle of such a controller is simple: Given the current state of a system we compute an open-loop control which is optimal for a given costfunctional over a fixed prediction horizon. Then, the control is implemented on the first sampling interval and the basic open-loop optimal control problem is shifted forward in time which allows for a repeated evaluation. The contribution of this thesis is threefold: First, we prove estimates for the performance of a receding horizon control, a concept which we call suboptimality degree. These estimate are online computable and can be applied for stabilizing as well as practically stabilizing receding horizon control laws. Moreover, they not only allow for guaranteeing stability of the closed-loop but also for quantifying the loss of performance of the receding horizon control law compared to the infinite horizon control law. Based on these estimates, we introduce adaptation strategies to modify the underlying receding horizon controller in order to guarantee a certain lower bound on the suboptimality degree while reducing the computing cost/time necessary to solve this problem. Within this analysis, the length of the optimization horizon is the parameter we wish to adapt. To this end, we develop and proof several shortening and prolongation strategies which also allow for an effective implementation. Moreover, extensions of our suboptimality estimates to receding horizon controllers with varying optimization horizon are shown. Last, we present details on our implementation of a receding horizon controller PCC2 ( which is on the one hand computationally efficient but also allows for easily incorporating our theoretical results. Since a full analysis of such a controller would exceed the scope of this work, we focus on the main aspects of this algorithm using different examples. In particular, we concentrate on the impact of certain choices of parameters on the computing time. We also consider interactions between these parameters to give a guideline to effectively implement and solve further examples. Moreover, we show applicability and effectiveness of our theoretical results using simulations of standard problems for receding horizon controllers.

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