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A Lyapunov-based MPC for Distributed Multi Agent Systems with Time Delays and Packet Dropouts using Hidden Markov Models

Loaie Solyman, Aamir Ahmad, Ayman El-Badawy

TL;DR

The paper tackles consensus control for multi-agent systems facing time delays, packet dropouts, and varying communication topologies. It introduces SCHMM-LMPC, combining a Semi-Continuous Hidden Markov Model for network prediction with Lyapunov-based Model Predictive Control and LMIs to guarantee stability and consensus. A novel incremental EM algorithm enables online adaptation of SCHMM parameters to topology changes, while an online Viterbi-based predictor forecasts delays. Numerical results in centralized and distributed topologies demonstrate robust consensus under network imperfections and topology dynamics, highlighting the approach's scalability and practical relevance.

Abstract

We propose a SCHMM LMPC framework, integrating Semi Continuous Hidden Markov Models with Lyapunov based Model Predictive Control, for distributed optimal control of multi agent systems under network imperfections. The SCHMM captures the stochastic network behavior in real time, while LMPC ensures consensus and optimality via Linear Matrix Inequalities LMIs. The developed optimal control problem simultaneously minimizes three elements. First, the control effort is reduced to avoid aggressive inputs and second, the network induced error caused by time delays and packet dropouts. Third, the topology-induced error, as the distributed graph restricts agents access to global information. This error is inherent to the communication graph and cannot be addressed through offline learning. To overcome this, the study also introduces the incremental Expectation Maximization EM algorithm, enabling online learning of the SCHMM. This adaptation allows the framework to mitigate both network and topology errors while maintaining optimality through MPC. Simulations validate the effectiveness of the proposed SCHMM LMPC, demonstrating adaptability in multi agent systems with diverse topologies.

A Lyapunov-based MPC for Distributed Multi Agent Systems with Time Delays and Packet Dropouts using Hidden Markov Models

TL;DR

The paper tackles consensus control for multi-agent systems facing time delays, packet dropouts, and varying communication topologies. It introduces SCHMM-LMPC, combining a Semi-Continuous Hidden Markov Model for network prediction with Lyapunov-based Model Predictive Control and LMIs to guarantee stability and consensus. A novel incremental EM algorithm enables online adaptation of SCHMM parameters to topology changes, while an online Viterbi-based predictor forecasts delays. Numerical results in centralized and distributed topologies demonstrate robust consensus under network imperfections and topology dynamics, highlighting the approach's scalability and practical relevance.

Abstract

We propose a SCHMM LMPC framework, integrating Semi Continuous Hidden Markov Models with Lyapunov based Model Predictive Control, for distributed optimal control of multi agent systems under network imperfections. The SCHMM captures the stochastic network behavior in real time, while LMPC ensures consensus and optimality via Linear Matrix Inequalities LMIs. The developed optimal control problem simultaneously minimizes three elements. First, the control effort is reduced to avoid aggressive inputs and second, the network induced error caused by time delays and packet dropouts. Third, the topology-induced error, as the distributed graph restricts agents access to global information. This error is inherent to the communication graph and cannot be addressed through offline learning. To overcome this, the study also introduces the incremental Expectation Maximization EM algorithm, enabling online learning of the SCHMM. This adaptation allows the framework to mitigate both network and topology errors while maintaining optimality through MPC. Simulations validate the effectiveness of the proposed SCHMM LMPC, demonstrating adaptability in multi agent systems with diverse topologies.

Paper Structure

This paper contains 14 sections, 43 equations, 12 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Formulation
  4. Methodology
  5. Grouping
  6. Compact Form
  7. Network Imperfections
  8. Theoretical Analysis
  9. Adapted SCHMM using Incremental Expectation Maximization Algorithm
  10. LMPC
  11. Numerical Simulations
  12. SCHMM Training
  13. SCHMM-LMPC
  14. Conclusion

Figures (12)

  • Figure 1: SCHMM-LMPC framework for agent $i$ describing the data flow of the received delayed information to drive agent $i$ towards global consensus.
  • Figure 2: Example Multi Agent System with three agents.
  • Figure 3: Example Multi Agent System with five agents (starting top-left) showing local consensus points to scale computed using \ref{['eq81']} and propagation directions of the agents achieving global consensus.
  • Figure 4: Internal structure of the Semi Continuous Hidden Markov Model.
  • Figure 5: Gaussian distributions corresponding to time delays measured in ms and Dirac-delta function corresponding to packet dropouts masked with the value $10^5$ms.
  • ...and 7 more figures