Moment-Driven Predictive Control of Mean-Field Collective Dynamics

Abstract

Feedback control synthesis for large-scale particle systems is reviewed in the framework of model predictive control (MPC). The high-dimensional character of collective dynamics hampers the performance of traditional MPC algorithms based on fast online dynamic optimization at every time step. Two alternatives to MPC are proposed. First, the use of supervised learning techniques for the offline approximation of optimal feedback laws is discussed. Then, a procedure based on sequential linearization of the dynamics based on macroscopic quantities of the particle ensemble is reviewed. Both approaches circumvent the online solution of optimal control problems enabling fast, real-time, feedback synthesis for large-scale particle systems. Numerical experiments assess the performance of the proposed algorithms.

Crowd Dynamics: Modeling and Control of Multiagent Systems

“…A further alternative (86) is to synthesize suboptimal feedback-type controls by linearizing the interaction kernel and solving the resulting linear-quadratic optimal control problem through a Riccati equation (all based on the corresponding mean-field equations, similarly to the approach used in References 48 and 79) and use this control in the nonlinear dynamics. This approach also avoids the limitations associated with the synthesis of optimal feedback laws for high-dimensional nonlinear dynamics via the Hamilton-Jacobi-Bellman partial differential equation (87,88).…”

Receding horizon control for continuous‐time mean‐field systems

“…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][25][26][27].…”

“…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.…”

“…[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. In [27], the performance and robustness of the system were improved by using the linearization method to calculate the suboptimal control. It can be seen that there were few studies on the stabilization of mean‐field system using RHC strategy and little progress had been made.…”