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