A Distributed Adaptive Model Predictive Control Framework for Interconnected Systems with Parametric Uncertainty

핵심 개념

A distributed adaptive model predictive control (DAMPC) framework is proposed to efficiently control interconnected systems with parametric uncertainty in a distributed manner without a central unit.

초록

The paper presents a distributed adaptive model predictive control (DAMPC) framework for controlling interconnected systems with parametric uncertainty. The key contributions are:

Imposing structured design on the control matrices and sets to enable distributed optimization of the MPC problem, reducing the computational complexity compared to a centralized approach.
Proposing decentralized and distributed set-membership identification schemes to update the parameter bounds in a distributed manner without a central unit.
Proving that the DAMPC algorithm ensures robust constraint satisfaction, recursive feasibility, and finite gain L2 stability of the closed-loop system.
Demonstrating the performance improvements of the DAMPC approach over a distributed robust MPC scheme, especially when the model uncertainty is large, through simulations on an interconnected mass-spring-damper system.

The distributed structure is achieved by:

Designing a structured control gain matrix K and state tube matrix Hx, where each agent's control input and state tube depend only on its neighbors' states.
Structuring the parameter matrix Hθ such that constraints affecting multiple agents use shared Lagrange multipliers.
Formulating the MPC optimization problem in a distributed consensus form that can be solved using the Alternating Direction Method of Multipliers (ADMM).
The decentralized identification scheme updates each agent's parameter bounds using only its own and its neighbors' state measurements. The distributed identification scheme further improves performance by also sharing the parameter bounds between neighbors.
The proposed DAMPC framework enables efficient distributed control of interconnected systems with parametric uncertainty, outperforming a distributed robust MPC approach, especially when the model uncertainty is large.

통계

The average closed-loop cost of the DAMPC scheme with distributed identification is 15.1% lower than the distributed robust MPC scheme when the model uncertainty scaling parameter κ = 1.0.

인용구

"The relative improvement in performance is higher when the model uncertainty is large. Moreover, distributed identification yields markedly larger cost reductions."

핵심 통찰 요약

A distributed framework for linear adaptive MPC

by Anilkumar Pa... 게시일 arxiv.org 04-17-2024

https://arxiv.org/pdf/2109.05777.pdf

더 깊은 질문

How can the structured design of the control matrices and sets be further optimized to improve the performance of the DAMPC framework

To further optimize the structured design of the control matrices and sets in the DAMPC framework, several strategies can be employed. Firstly, refining the parameterization of the state tube matrices can lead to improved performance. By adjusting the structure of the state tube matrices to better capture the dynamics and constraints of each agent in the interconnected system, the optimization problem can be more effectively solved. Additionally, enhancing the distributed identification algorithms to provide more accurate and timely updates to the parameter sets can lead to tighter bounds on the uncertain parameters, resulting in better control performance. Moreover, exploring advanced optimization techniques, such as incorporating machine learning algorithms for adaptive learning and optimization, can further enhance the efficiency and effectiveness of the DAMPC framework.

What are the potential challenges and limitations in applying the DAMPC approach to large-scale interconnected systems with complex network topologies

Applying the DAMPC approach to large-scale interconnected systems with complex network topologies may pose several challenges and limitations. One major challenge is the computational complexity associated with solving the distributed optimization problem in real-time for a large number of interconnected agents. As the size of the network increases, communication and coordination between agents become more challenging, potentially leading to delays and inefficiencies in the control process. Moreover, ensuring robust constraint satisfaction and stability in highly interconnected systems with complex dynamics and constraints can be more difficult, requiring sophisticated control strategies and coordination mechanisms. Additionally, scalability issues may arise when extending the DAMPC framework to large-scale systems, as the computational and communication overheads could increase significantly with the number of agents and network complexity.

Could the DAMPC framework be extended to handle time-varying parametric uncertainties or nonlinear system dynamics in interconnected systems

Extending the DAMPC framework to handle time-varying parametric uncertainties or nonlinear system dynamics in interconnected systems is a promising direction for future research. To address time-varying uncertainties, adaptive identification algorithms can be integrated into the framework to continuously update the parameter sets based on real-time measurements and feedback. This adaptive approach allows the system to adapt to changing uncertainties and maintain robustness in the face of dynamic variations. Additionally, incorporating nonlinear system dynamics into the DAMPC framework can be achieved by employing nonlinear model predictive control techniques or adaptive control strategies tailored for nonlinear systems. By integrating these advanced control methods, the DAMPC framework can effectively handle time-varying uncertainties and nonlinear dynamics in interconnected systems, enhancing its applicability to a wider range of complex control scenarios.