Nonlinear MPC defines implicit regional optimal control laws

Mönnigmann, Martin; Otten, Jonas; Jost, Michael

doi:10.1016/j.ifacol.2015.11.274

Cited by 14 publications

(18 citation statements)

References 10 publications

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“…Now n ě 2 implies 3888mn´5256m ě 0 and 1296n 24 86n´1742 ě 0 for all m. Adding these two inequalities to 1328m 2 ě 0, which also holds for all m, shows that condition (20) holds. Case (iii) can be shown by noting that (18) can equivalently be stated as…”

Section: Computational Effort Of Approach A1mentioning

confidence: 90%

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: Computational Effort Of Approach A1mentioning

confidence: 90%

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

Berner

Mönnigmann

2020

IEEE Trans. Contr. Syst. Technol.

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“…which provides (11). It follows that under the stated assumptions the active constraints Ã define the optimal feedback law u(0).…”

Section: Proposition 3 Consider An Arbitrary Active Setmentioning

confidence: 91%

“…Regions defined by active sets with the same subset Ã are then united and for each of those unions, the optimal feedback law u ⋆ is determined with (11). Further, each union is underestimated by one or more ellipsoids E of the form…”

Section: Implementational Aspectsmentioning

confidence: 99%

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State space sets with common optimal feedback laws for nonlinear MPC

Mitze¹,

Dyrska²,

König³

et al. 2020

Preprint

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In model predictive control (MPC), an optimal control problem (OCP) is solved for the current state and the first input of the solution, the optimal feedback law, is applied to the system. This procedure requires to solve the OCP in every time step. Recently, a new approach was suggested for linear MPC. The parametric solution of a linear quadratic OCP is a piecewise-affine feedback law. The solution at a point in state space provides an optimal feedback law and a domain on which this law is the optimal solution. As long as the system remains in the domain, the law can be reused and the calculation of an OCP is avoided. In some domains the optimal feedback laws are identical. By uniting the corresponding domains, bigger domains are achieved and the optimal feedback law can be reused more often. In the present paper, we investigate in how far this approach can be extended from linear to nonlinear MPC, we propose an algorithm and we illustrate the achieved savings with an example.

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“…Nonlinear MPC (NMPC) is more challenging, since a lot of assumptions and helpful properties such as convexity do no longer hold, and solving a nonlinear program (NLP) may be very expensive [1,14]. There exist some extensions of explicit methods for linear systems to the nonlinear case [9,19,17,18], but none of them are as comprehensive as in the linear case.…”

Section: Introductionmentioning

confidence: 99%

Accelerated Nonlinear Model Predictive Control by Exploiting Saturation

Dyrska,

Mitze,

Mönnigmann

2020

Preprint

Self Cite

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We present an approach for accelerating nonlinear model predictive control. If the current optimal input signal is saturated, also the optimal signals in subsequent time steps often are. We propose to use the open-loop optimal input signals whenever the first and some subsequent input signals are saturated. We only solve the next optimal control problem, when a non-saturated signal is encountered, or the end of the horizon is reached. In this way, we can save a significant number of NLPs to be solved while on the other hand keep the performance loss small. Furthermore, the NMPC is reactivated in time when it comes to controlling the system safely to its reference.

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Nonlinear MPC defines implicit regional optimal control laws

Cited by 14 publications

References 10 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

State space sets with common optimal feedback laws for nonlinear MPC

Accelerated Nonlinear Model Predictive Control by Exploiting Saturation

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