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Explicit Distributed MPC: Reducing Computation and Communication Load by Exploiting Facet Properties

Parth R. Brahmbhatt, Hari S. Ganesh, Styliani Avraamidou

Abstract

Classical Distributed Model Predictive Control (DiMPC) requires multiple iterations to achieve convergence, leading to high computational and communication burdens. This work focuses on the improvement of an iteration-free distributed MPC methodology that minimizes computational effort and communication load. The aforementioned methodology leverages multiparametric programming to compute explicit control laws offline for each subsystem, enabling real-time control without iterative data exchanges between subsystems. Extending our previous work on iteration-free DiMPC, here we introduce a FAcet-based Critical region Exploration Technique for iteration-free DiMPC (FACET-DiMPC) that further reduces computational complexity by leveraging facet properties to do targeted critical region exploration. Simulation results demonstrate that the developed method achieves comparable control performance to centralized methods, while significantly reducing communication overhead and computation time. In particular, the proposed methodology offers substantial efficiency gains in terms of the average computation time reduction of 98% compared to classic iterative DiMPC methods and 42% compared to iteration-free DiMPC methods, making it well-suited for real-time control applications with tight latency and computation constraints.

Explicit Distributed MPC: Reducing Computation and Communication Load by Exploiting Facet Properties

Abstract

Classical Distributed Model Predictive Control (DiMPC) requires multiple iterations to achieve convergence, leading to high computational and communication burdens. This work focuses on the improvement of an iteration-free distributed MPC methodology that minimizes computational effort and communication load. The aforementioned methodology leverages multiparametric programming to compute explicit control laws offline for each subsystem, enabling real-time control without iterative data exchanges between subsystems. Extending our previous work on iteration-free DiMPC, here we introduce a FAcet-based Critical region Exploration Technique for iteration-free DiMPC (FACET-DiMPC) that further reduces computational complexity by leveraging facet properties to do targeted critical region exploration. Simulation results demonstrate that the developed method achieves comparable control performance to centralized methods, while significantly reducing communication overhead and computation time. In particular, the proposed methodology offers substantial efficiency gains in terms of the average computation time reduction of 98% compared to classic iterative DiMPC methods and 42% compared to iteration-free DiMPC methods, making it well-suited for real-time control applications with tight latency and computation constraints.

Paper Structure

This paper contains 12 sections, 16 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background on Iterative & Iteration-Free DiMPC using Multi-Parametric Programming
  3. Multi-Parametric (mp) MPC (Explicit-MPC)
  4. Iterative Explicit DiMPC (I-mpDiMPC)
  5. Iteration-Free Explicit DiMPC (IF-mpDiMPC)
  6. FACET-DiMPC
  7. Results and Discussion
  8. Case Studies
  9. Control Performance
  10. Communication Burden
  11. Computation Time
  12. Conclusions

Figures (7)

  • Figure C1: Possibilities exist for regions $R1$ and $R2$ sharing a common hyperplane $H1$.
  • Figure D1: Number of critical regions for different subsystems.
  • Figure D2: Controller performance for 2 subsystems. (a) Subsystem outputs. (b) Controller outputs. The black lines represent two random runs for visualization.
  • Figure D3: Number of data transfer instances for different DiMPC controllers during the entire simulation.
  • Figure D4: Average computation time (sec) of DiMPC control architectures over 100 plants. (Log-Scale)
  • ...and 2 more figures