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Cooperative nonlinear distributed model predictive control with dissimilar control horizons

Paula Chanfreut, José M. Maestre, Quanyan Zhu, W. P. M. H. Heemels

TL;DR

A nonlinear distributed model predictive control algorithm is introduced, which allows for dissimilar and time-varying control horizons among agents, thereby addressing a common limitation in current DMPC schemes.

Abstract

In this paper, we introduce a nonlinear distributed model predictive control (DMPC) algorithm, which allows for dissimilar and time-varying control horizons among agents, thereby addressing a common limitation in current DMPC schemes. We consider cooperative agents with varying computational capabilities and operational objectives, each willing to manage varying numbers of optimization variables at each time step. Recursive feasibility and a non-increasing evolution of the optimal cost are proven for the proposed algorithm. Through numerical simulations on systems with three agents, we show that our approach effectively approximates the performance of traditional DMPC, while reducing the number of variables to be optimized. This advancement paves the way for a more decentralized yet coordinated control strategy in various applications, including power systems and traffic management.

Cooperative nonlinear distributed model predictive control with dissimilar control horizons

TL;DR

A nonlinear distributed model predictive control algorithm is introduced, which allows for dissimilar and time-varying control horizons among agents, thereby addressing a common limitation in current DMPC schemes.

Abstract

In this paper, we introduce a nonlinear distributed model predictive control (DMPC) algorithm, which allows for dissimilar and time-varying control horizons among agents, thereby addressing a common limitation in current DMPC schemes. We consider cooperative agents with varying computational capabilities and operational objectives, each willing to manage varying numbers of optimization variables at each time step. Recursive feasibility and a non-increasing evolution of the optimal cost are proven for the proposed algorithm. Through numerical simulations on systems with three agents, we show that our approach effectively approximates the performance of traditional DMPC, while reducing the number of variables to be optimized. This advancement paves the way for a more decentralized yet coordinated control strategy in various applications, including power systems and traffic management.

Paper Structure

This paper contains 11 sections, 2 theorems, 17 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem setting
  3. System description
  4. Multi-agent control architecture
  5. Main goal
  6. Nonlinear DMPC with dissimilar control horizons
  7. Control algorithm
  8. Properties
  9. Extension to dynamic control horizons
  10. Simulation results
  11. Conclusions

Key Result

Theorem 1

If the initial sequences $[\mathbf{u}_i^0(0)]_{i\in\mathcal{N}}$ are globally feasible, then problems eq:Dist_MPC for all agents $i\in\mathcal{N}$ and problem eq:coord_problem will be recursively feasible.

Figures (5)

  • Figure 1: Distributed system with 4 subsystems managed by MPC agents.
  • Figure 2: Heat-map with the values of index $J_\mathrm{cc}$ for different combinations of $N_{\mathrm{c},2}$ and $N_{\mathrm{c},3}$.
  • Figure 3: Box chart with the time required to solve problem \ref{['eq:Dist_MPC']} with different values of horizon $N_{\mathrm{c},i}$.
  • Figure 4: System state and input over time for $N_{\mathrm{c},2}=8$ and $N_{\mathrm{c},3}=20$.
  • Figure 5: Evolution of $N_{\mathrm{c},i}$ for $i\in \{1,2,3\}$ over the iterations implemented in the first 12 time steps.

Theorems & Definitions (6)

  • Remark 1
  • Remark 2
  • Theorem 1: Recursive feasibility
  • proof
  • Theorem 2: Non-increasing objective function
  • proof