Towards multiobjective optimization and control of smart grids

Sauerteig, Philipp; Worthmann, Karl

doi:10.1002/oca.2532

Cited by 17 publications

(8 citation statements)

References 38 publications

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“…Within this work we will reach this aim by introducing upper bounds on the possible choices steered by the selected efficient solution in the first step. Note that we do not rely on scalarization approaches like a weighted sum of the objective functions as done in [23], as this would require pre-knowledge for instance about the preferred weights, which is in general not available. For a discussion on the advantage of direct methods compared to scalarization based approaches we refer to [12].…”

Section: Introductionmentioning

confidence: 99%

Relaxed dissipativity assumptions and a simplified algorithm for multiobjective MPC

et al. 2022

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We consider nonlinear model predictive control (MPC) with multiple competing cost functions. In each step of the scheme, a multiobjective optimal control problem with a nonlinear system and terminal conditions is solved. We propose an algorithm and give performance guarantees for the resulting MPC closed loop system. Thereby, we significantly simplify the assumptions made in the literature so far by assuming strict dissipativity and the existence of a compatible terminal cost for one of the competing objective functions only. We give conditions which ensure asymptotic stability of the closed loop and, what is more, obtain performance estimates for all cost criteria. Numerical simulations on various instances illustrate our findings. The proposed algorithm requires the selection of an efficient solution in each iteration, thus we examine several selection rules and their impact on the results. and we also examine numerically how different selection rules impact the results

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Section: Introductionmentioning

confidence: 99%

Relaxed dissipativity assumptions and a simplified algorithm for multiobjective MPC

et al. 2022

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show abstract

“…Within this work we will reach this aim by introducing upper bounds on the possible choices steered by the selected efficient solution in the first step. Note that we do not rely on scalarization approaches like a weighted sum of the objective functions as done in [22], as this would require preknowledge for instance about the preferred weights, which is in general not available. For a discussion on the advantage of direct methods compared to scalarization based approaches we refer to [12].…”

Section: Introductionmentioning

confidence: 99%

Relaxed dissipativity assumptions and a simplified algorithm for multiobjective MPC

Eichfelder¹,

Grüne²,

Krügel³

et al. 2022

Preprint

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We consider nonlinear model predictive control (MPC) with multiple competing cost functions. In each step of the scheme, a multiobjective optimal control problem with a nonlinear system and terminal conditions is solved. We propose an algorithm and give performance guarantees for the resulting MPC closed loop system. Thereby, we significantly simplify the assumptions made in the literature so far by assuming strict dissipativity and the existence of a compatible terminal cost for one of the competing objective functions only. We give conditions which ensure asymptotic stability of the closed loop and, what is more, obtain performance estimates for all cost criteria. Numerical simulations on various instances illustrate our findings. The proposed algorithm requires the selection of an efficient solution in each iteration and we also examine numerically how different selection rules impact the results.

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“…Recently, the distributed optimization problem has important applications in many scenarios, such as consensus control, [1][2][3][4][5][6] task optimization, 7,8 and smart grid. 9 In these literatures, Qin et al 3 proposed a novel framework to prove the attractiveness of the synchronization mainfold for the dynamical systems which can be of generic linear or Lipschitz nonlinear type. Qin et al 4 designed the method for complex dynamical networks and the method can not only provide the convergence analysis more concisely but also supply the convergence rate explicitly.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the distributed optimization problem has important applications in many scenarios, such as consensus control, 1‐6 task optimization, 7,8 and smart grid 9 . In these literatures, Qin et al 3 proposed a novel framework to prove the attractiveness of the synchronization mainfold for the dynamical systems which can be of generic linear or Lipschitz nonlinear type.…”

Section: Introductionmentioning

confidence: 99%

Distributed time‐varying convex optimal consensus control for multi‐agent system with/without chattering restrain

Zhu

Zhao

et al. 2022

Optim Control Appl Methods

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In this article, the consensus, collision avoidance, and distributed convex optimization problems of a class of multi-agent systems with a time-varying objective function are studied. Moreover, the proposed method in this article can reduce the chattering problem of the controller input caused by the sign function. First, the sign function is used to design the controller to improve the convergence rate of the system, on this basis, the optimization item is designed for the more complex time-varying objective function to ensure that the value of the objective function is the smallest when the system achieves the speed consensus. Second, considering the chattering problem caused by the sign function, the designed controller is improved to reduce the chattering phenomenon.Third, two novel Lyapunov functions are constructed to verify the stability of the system and the distributed optimization objective. Due to the controller is designed for the time-varying objective function, moreover, the tasks of the formation and collision avoidance are needed to take into account, therefore, the designed Lyapunov functions in this article are more difficult. Finally, the formation function is designed to ensure that the multi-agent system achieves the desired formation configuration. The simulation results show the correctness of the theoretical design of this article and the superiority in extending the running time of the system.

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Towards multiobjective optimization and control of smart grids

Cited by 17 publications

References 38 publications

Relaxed dissipativity assumptions and a simplified algorithm for multiobjective MPC

Relaxed dissipativity assumptions and a simplified algorithm for multiobjective MPC

Relaxed dissipativity assumptions and a simplified algorithm for multiobjective MPC

Distributed time‐varying convex optimal consensus control for multi‐agent system with/without chattering restrain

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