A comparison of four variants of event-triggered networked MPC

Berner, Patrik Simon; Mönnigmann, Martin

doi:10.1109/cca.2016.7588016

Cited by 11 publications

(17 citation statements)

References 20 publications

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“…Since bandwidth and computational resources are limited, it is crucial to investigate alternatives to sending the feedback law and polytope (i.e., real matrices and vectors) across the network. The present paper extends earlier theoretical results [5] by new results on the computa-tional and bandwidth requirements of the alternatives (Propositions 4-6), by details on the implementation (Section 4), and by a validation with an actual implementation on industrial hardware (Section 5).…”

Section: Introductionsupporting

confidence: 72%

“…It suffices to send much less data, however. This is stated more precisely in Lemma 2, which was proved in [5].…”

Section: Trade-off Between Transmitted Data and Local Calculationsmentioning

confidence: 92%

“…Therefore, the same closed-loop optimal system behavior is obtained as solving (2) or (3) in every time step [16]. The claim about (9b) in Lemma 2 holds, because U ‹ defines Apxq according to (5) and A defines K ‹ M , b ‹ M , T ‹, d ‹ and thus the law and polytope according to (6).…”

Section: Lemma 2 Letmentioning

confidence: 94%

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A Complexity Analysis of Event-Triggered Model Predictive Control on Industrial Hardware

Berner

Mönnigmann

2020

IEEE Trans. Contr. Syst. Technol.

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We implement a recently proposed event-triggered networked MPC approach on industrial hardware to analyze its practical relevance. There exist several alternatives for such an implementation that differ with respect to the distribution of computational load between local and central nodes, and with respect to network bandwidth requirements. These alternatives have been analyzed theoretically before, but when implemented it becomes evident that their usefulness cannot be predicted based on theoretical considerations alone. It is the purpose of the present paper to account for both practical and theoretical aspects in determining which alternative is most appropriate for an implementation on industrial hardware. The smallest possible bandwidth is known to result for a variant in which only the active set of constraints is transmitted from the central to the local nodes. Since local nodes must determine the control law from the active set in this case, which requires matrix inversions, an unattractive computational cost results at first sight. Somewhat surprisingly, the computational cost scales practically linearly in the problem size when implemented. We confirm this result with a more detailed theoretical complexity analysis than given in previous papers. All results are illustrated with data obtained with an implementation on industrial hardware components.

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Section: Introductionsupporting

confidence: 72%

“…It suffices to send much less data, however. This is stated more precisely in Lemma 2, which was proved in [5].…”

Section: Trade-off Between Transmitted Data and Local Calculationsmentioning

confidence: 92%

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A Complexity Analysis of Event-Triggered Model Predictive Control on Industrial Hardware

Berner

Mönnigmann

2020

IEEE Trans. Contr. Syst. Technol.

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“…We claim without giving details that the computational effort for calculating the matrices in ( 6) and ( 8) is smaller than for solving a QP (2) (see Berner and Mönnigmann [2] for details).…”

Section: Regional Predictive Controlmentioning

confidence: 99%

“…We use Corollary 2 as follows: First we determine the active set A for a given state x P X f by solving QP (2). If G A has full row rank, we determine Ã " AXt1, .…”

Section: Proof 4 First Note That the Inverse Of G A H ´1gmentioning

confidence: 99%

Accelerating MPC by online detection of state space sets with common optimal feedback laws

König,

Mönnigmann

2020

Preprint

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Model predictive control (MPC) samples a generally unknown and complicated feedback law point by point. The solution for the current state x contains, however, more information than only the optimal signal u for this particular state. In fact, it provides an optimal affine feedback law x Ñ upxq on a polytope Π Ă R n , i.e., on a full-dimensional state space set. It is an obvious idea to reuse this affine feedback law as long as possible. Reusing it on its polytope Π is too conservative, however, because any Π is a state space set with a common affine law x Ñ pu 1 0 pxq, . . . , u 1 N ´1pxqq1 P R N m for the entire horizon N . We show a simple criterion exists for identifying the polytopes that have a common x Ñ u 0 pxq, but may differ with respect to u 1 pxq, . . . , u N ´1pxq. Because this criterion is too computationally expensive for an online use, we introduce a simple heuristics for the fast construction of a subset of the polytopes of interest. Computational examples show (i) a considerable fraction of QPs can be avoided (10 % to 40 %) and (ii) the heuristics results in a reduction very close to the maximum one that could be achieved if the explicit solution was available. We stress the proposed approach is intended for use in online MPC and it does not require the explicit solution.

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Output-Based Event-Triggered Model Predictive Control for Networked Control Systems

et al. 2017

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A comparison of four variants of event-triggered networked MPC

Cited by 11 publications

References 20 publications

A Complexity Analysis of Event-Triggered Model Predictive Control on Industrial Hardware

A Complexity Analysis of Event-Triggered Model Predictive Control on Industrial Hardware

Accelerating MPC by online detection of state space sets with common optimal feedback laws

Output-Based Event-Triggered Model Predictive Control for Networked Control Systems

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