Towards a solution of mean-field control problems using model predictive control

Borzì, Alfio; Grüne, Lars

doi:10.1016/j.ifacol.2020.12.1086

Cited by 5 publications

(5 citation statements)

References 16 publications

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“…2). Also, we remark that the error dynamics becomes globally asymptotically convergent to 0 if the control input in (13) includes the extra term − [e(x, t)V e (x, t)] x , which is a nonlinear (quadratic) function of the mismatch. In this case, (15) simplifies to e t (x, t) = −K p e(x, t).…”

Section: B Macroscopic Control Designmentioning

confidence: 98%

Continuification Control of Large-Scale Multiagent Systems in a Ring

Maffettone

Boldini

Bernardo

et al. 2023

IEEE Control Syst. Lett.

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In this paper, we propose a method to control large-scale multiagent systems swarming in a ring. Specifically, we use a continuification-based approach that transforms the microscopic, agent-level description of the system dynamics into a macroscopic, continuum-level representation, which we employ to synthesize a control action towards a desired distribution of the agents. The continuum-level control action is then discretized at the agent-level in order to practically implement it. To confirm the effectiveness and the robustness of the proposed approach, we complement theoretical derivations with a series of numerical simulations.

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Section: B Macroscopic Control Designmentioning

confidence: 98%

Continuification Control of Large-Scale Multiagent Systems in a Ring

Maffettone

Boldini

Bernardo

et al. 2023

IEEE Control Syst. Lett.

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“…Here, the density of the particles is obtained as the number of particles tends to infinity [9, 15-17, 21, 30, 31, 33-35]. Of particular interest is therefore the design of controls in the mean-field control approaches [7,[22][23][24].…”

Section: Introductionmentioning

confidence: 99%

The turnpike property for mean-field optimal control problems

Gugat,

Herty,

Segala

2024

Eur. J. Appl. Math

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We study the turnpike phenomenon for optimal control problems with mean-field dynamics that are obtained as the limit $N\rightarrow \infty$ of systems governed by a large number $N$ of ordinary differential equations. We show that the optimal control problems with large time horizons give rise to a turnpike structure of the optimal state and the optimal control. For the proof, we use the fact that the turnpike structure for the problems on the level of ordinary differential equations is preserved under the corresponding mean-field limit.

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Section: Introductionmentioning

confidence: 99%

“…Kwon first proposed the method of receding horizon control in [22, 23] and studied the stabilization problem of the system. Because this strategy is easy to calculate and has good tracking performance, it is also partially applied in mean‐field systems [24–27]. In [25], the MPC scheme was applied to the controlled Fokker‐Planck equation, and the approximate optimal solution was obtained.…”

Section: Introductionmentioning

confidence: 99%

“…Because this strategy is easy to calculate and has good tracking performance, it is also partially applied in mean‐field systems [24–27]. In [25], the MPC scheme was applied to the controlled Fokker‐Planck equation, and the approximate optimal solution was obtained. [26] introduced the relationship between the proposed method and the chance‐constrained control technique and illustrated the performance of the proposed control based on stochastic optimization.…”

Section: Introductionmentioning

confidence: 99%

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Receding horizon control for continuous‐time mean‐field systems

Gao,

Liu,

Zhang

et al. 2023

Asian Journal of Control

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In this paper, we study the receding horizon control (RHC) stabilization of continuous‐time mean‐field system. An explicit RHC controller is obtained by introducing a cost function with two terminal matrices and the conditions that make the system stable are also obtained; that is, when two coupled Lyapunov inequalities are satisfied, the system controlled by RHC is stabilized. Finally, a simulation example is given to verify the effectiveness of the proposed strategy.

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Towards a solution of mean-field control problems using model predictive control

Cited by 5 publications

References 16 publications

Continuification Control of Large-Scale Multiagent Systems in a Ring

Continuification Control of Large-Scale Multiagent Systems in a Ring

The turnpike property for mean-field optimal control problems

Receding horizon control for continuous‐time mean‐field systems

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