Robust Adaptive Model Predictive Control for Tracking in Interconnected Systems via Distributed Optimization

This study presents a novel Distributed Robust Adaptive Model Predictive Control (DRAMPC) for tracking in multi-agent systems. The framework is designed to work with dynamically coupled subsystems and limited communication, which is restricted to local neighborhoods. The proposed approach explicitly accounts for parametric uncertainties and additive disturbances by employing a tube-based formulation to bound the system response for any possible uncertainty realizations. To ensure recursive feasibility and asymptotic stability, contractivity properties for the terminal cross-section are derived alongside a structured stabilizing gain for the closed-loop dynamics. The conservativeness of the tube-based formulation is relaxed by exploiting a distributed set membership via recursive identification of the parameter uncertainty set. The control problem is formulated by leveraging the Artificial Reference method for piecewise reference signals to ensure feasibility even when the desired reference is not directly reachable. The consensus ADMM algorithm is employed to solve the distributed optimization problem efficiently while maintaining scalability as the number of agents increases. Furthermore, the artificial reference formulation is extended to trajectory tracking, allowing the controller to track time-varying references while preserving feasibility. The effectiveness of the proposed method is demonstrated through illustrative examples, highlighting its capability to achieve accurate and robust tracking in multi-agent uncertain systems.