[Paper Review] Fully Distributed Adaptive Controllers for Cooperative Output Regulation of Heterogeneous Linear Multi-agent Systems with Directed Graphs

Zhongkui Li, Michael Z. Q. Chen+1 more|arXiv (Cornell University)|Nov 26, 2014

Distributed Control Multi-Agent Systems32 references3 citations

TL;DR

This paper proposes fully distributed adaptive controllers for cooperative output regulation in heterogeneous linear multi-agent systems with directed communication graphs, where only a subset of agents access the exosystem signal. By combining distributed adaptive observers with the internal model principle, the controllers enable each agent to estimate the exogenous signal and regulate outputs to zero without relying on global graph information, achieving robust regulation even under system uncertainties.

ABSTRACT

This paper considers the cooperative output regulation problem for linear multi-agent systems with a directed communication graph, heterogeneous linear subsystems, and an exosystem whose output is available to only a subset of subsystems. Both the cases with nominal and uncertain linear subsystems are studied. For the case with nominal linear subsystems, a distributed adaptive observer-based controller is designed, where the distributed adaptive observer is implemented for the subsystems to estimate the exogenous signal. For the case with uncertain linear subsystems, the proposed distributed observer and the internal model principle are combined to solve the robust cooperative output regulation problem. Compared with the existing works, one main contribution of this paper is that the proposed control schemes can be designed and implemented by each subsystem in a fully distributed fashion for general directed graphs. For the special case with undirected graphs, a distributed output feedback control law is further presented.

Motivation & Objective

• Address the challenge of achieving cooperative output regulation in heterogeneous linear multi-agent systems with directed communication graphs, where global graph information is unavailable to individual agents.
• Overcome the limitation of existing controllers that require knowledge of nonzero Laplacian eigenvalues (global information), enabling fully distributed design.
• Extend fully distributed control to systems with uncertain subsystems using adaptive observers and the internal model principle.
• Provide a distributed output feedback control law for the special case of undirected graphs, reducing communication burden.
• Ensure robustness to parametric uncertainties in agent dynamics while maintaining fully distributed implementation.

Proposed method

• Design a distributed adaptive observer that enables each agent to estimate the exogenous signal using only local and neighbor information, without requiring global graph knowledge.
• Implement adaptive laws for coupling weights between agents to achieve distributed learning of the exosystem dynamics.
• Integrate the internal model principle with the distributed observer to handle uncertain linear subsystems and ensure robust regulation.
• Construct a state-space controller using augmented dynamics that include the internal model and observer states, ensuring stability via Lyapunov analysis.
• Use a transformation matrix to decouple the closed-loop system into stable subsystems, proving Hurwitz stability of the overall system matrix.
• For undirected graphs, propose an output feedback control law that reduces communication cost by relying only on output measurements.

Experimental results

Research questions

• RQ1 Can fully distributed adaptive controllers be designed for cooperative output regulation in heterogeneous linear multi-agent systems with general directed graphs?
• RQ2 How can agents estimate the exogenous signal when only a subset has access to it, without using global graph information?
• RQ3 Can robust cooperative output regulation be achieved when agent dynamics are uncertain, using only local and neighbor information?
• RQ4 What control structure enables both distributed implementation and robustness to parametric uncertainties in the presence of directed communication graphs?
• RQ5 Is it possible to design a distributed output feedback controller for undirected graphs that reduces communication cost while maintaining regulation performance?

Key findings

• The proposed controllers are fully distributed and do not require knowledge of any global graph properties, such as nonzero Laplacian eigenvalues.
• For nominal systems, the distributed adaptive observer enables asymptotic estimation of the exogenous signal, leading to zero regulated output error.
• For uncertain systems, the combination of the distributed observer and internal model principle ensures robust cooperative output regulation despite parametric uncertainties.
• The closed-loop system is proven to be asymptotically stable under the proposed control laws, with all regulated outputs converging to zero.
• In the special case of undirected graphs, the proposed output feedback controller reduces communication cost while maintaining performance.
• Simulation results confirm that all regulated outputs $ e_i $ asymptotically converge to zero, validating the theoretical claims.