LMI-Based Model Predictive Control for Linear Discrete-Time Periodic Systems

Böhm, Christoph; Raff, Tobias; Reble, Marcus; Allgöwer, Frank

doi:10.1007/978-3-642-01094-1_8

Cited by 11 publications

(17 citation statements)

References 14 publications

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“…Thus, x(k) ∈ X for all k ∈ Z + and Problem IV.4 is feasible for all k ∈ Z + for any x(0) ∈ X. This implies that X is a positively invariant set for (10). Then, any {u(…”

Section: Assumption Iv2 There Exist Functionsᾱmentioning

confidence: 99%

“…Both Lemma V.1 and Lemma V.2 can be employed to calculate a tdPCLF along with a corresponding input sequence by solving a single SDP online. Compared to the RHC scheme [10], in both approaches the SDP is significantly less complex, besides being less restrictive due to the relaxed stability conditions. Furthermore, [10] requires the calculation of a global CLF at each time instant, whereas in Lemma V.1 and Lemma V.2 the tdPCLF depends on the actual trajectory.…”

Section: Implementation Via Sdpmentioning

confidence: 99%

“…This further reduces conservativeness. Concerning constraint handling, [10] requires the calculation of invariant ellipsoids lying in the interior of polytopic constraint sets. Here, we consider more general constraint formulations, see (17f) and (21d), which leads to a less conservative set-up.…”

Section: Implementation Via Sdpmentioning

confidence: 99%

“…Recently, there has been an increasing interest towards designing stabilizing RHC schemes for periodic systems. For example, the linear matrix inequalities (LMIs) based RHC approach of [9] for uncertain linear systems was extended to periodic systems in [10] and periodic systems with uncertainty in [11]. Further extensions were discussed in [12].…”

Section: Introductionmentioning

confidence: 99%

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A relaxation of Lyapunov conditions and controller synthesis for discrete-time periodic systems

Böhm

Lazăr

Allgöwer

2010

49th IEEE Conference on Decision and Control (CDC)

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Citation for published version (APA):Böhm, C., Lazar, M., & Allgöwer, F. (2010). A relaxation of Lyapunov conditions and controller synthesis for discrete-time periodic systems. In Proc. 49th IEEE Conference on Decision and Control (CDC), 15-17 December 2010, Atlanta, Georgia (pp. 3277-3282 Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at:openaccess@tue.nl providing details and we will investigate your claim. Abstract-This paper proposes a novel approach to stability analysis and controller synthesis for discrete-time periodically time-varying systems. Firstly, a relaxation of standard Lyapunov conditions is derived. This leads to a less conservative Lyapunov function that is required to decrease at every period, rather than at each time instant. Secondly, several solutions for synthesizing such periodic control Lyapunov functions are presented. These solutions make use of on-line optimization and can be formulated as a semi-definite program for constrained linear periodic systems. An example illustrates the effectiveness of the developed method.

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“…Thus, x(k) ∈ X for all k ∈ Z + and Problem IV.4 is feasible for all k ∈ Z + for any x(0) ∈ X. This implies that X is a positively invariant set for (10). Then, any {u(…”

Section: Assumption Iv2 There Exist Functionsᾱmentioning

confidence: 99%

Section: Implementation Via Sdpmentioning

confidence: 99%

Section: Implementation Via Sdpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A relaxation of Lyapunov conditions and controller synthesis for discrete-time periodic systems

Böhm

Lazăr

Allgöwer

2010

49th IEEE Conference on Decision and Control (CDC)

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“…The reader is referred to [6,7,20,21,23]/ [7,28] on MPC of periodic linear/nonlinear systems. A main objective of this paper is to demonstrate the power and flexibility of periodic MPC problem formulations via the example of building climate control.…”

Section: Introductionmentioning

confidence: 99%

Least-restrictive robust MPC of periodic affine systems with application to building climate control

Linares

Oldewurtel

Jones

2010

49th IEEE Conference on Decision and Control (CDC)

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Abstract-Robust state-feedback model predictive control (MPC) of discrete-time periodic affine systems is considered. States and inputs are subject to periodically time-dependent, hard, convex, polyhedral constraints. Disturbances are additive, bounded and subject to periodically time-dependent bounds. The control objective is given in terms of periodically timedependent costs. First, maximum robust periodic controlled invariant sets are formally characterized and subsequently employed in the design of least-restrictive robustly strongly feasible periodic MPC problems. Finally, the proposed methods are applied to controlling room temperatures in buildings.

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Constrained control of discrete-time linear periodic system

Nguyen

Bourdais

2014

2014 American Control Conference

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The aim of this paper is twofold. In the first part, we provide a method for constructing invariant sets for discrete-time linear periodic systems with state and input constraints. The main advantage of the method is that it generates invariant sets at any step of the underlying set iteration. In the second part a novel interpolating controller between a local unconstrained optimal control law and a global maximum state contractive controller is proposed. At each time instant, two linear programming problems are solved on-line. Proofs of recursive feasibility and asymptotic stability are given.

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LMI-Based Model Predictive Control for Linear Discrete-Time Periodic Systems

Cited by 11 publications

References 14 publications

A relaxation of Lyapunov conditions and controller synthesis for discrete-time periodic systems

A relaxation of Lyapunov conditions and controller synthesis for discrete-time periodic systems

Least-restrictive robust MPC of periodic affine systems with application to building climate control

Constrained control of discrete-time linear periodic system

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