Distributed Optimal Coordination of Multiple Dynamical Systems over Unbalanced Directed Networks


Student thesis: Doctoral Thesis

View graph of relations


Related Research Unit(s)


Awarding Institution
  • Haibo Ji (External person) (External Supervisor)
  • Lu LIU (Supervisor)
Award date26 Oct 2022


Distributed optimal coordination entails the development of distributed control strategies to drive a team of networked agents towards an optimal solution that minimizes the sum of the local cost functions assigned to individual agents. A networked multiple dynamical system composed of interacting agents is also called a multi-agent system. It has experienced significant advances in recent years because of its great potential in a wide range of applications, such as source-seeking with networked multi-robot systems, formations of unmanned ground/aerial vehicles, and the coordination of distributed energy resources in power systems. Most existing works on distributed optimal coordination assume that communication network topologies among agents are undirected graphs or, at most, balanced digraphs. Moreover, most control strategies for this topic rely on certain global information about network connectivity and/or cost functions and are thus not fully distributed. However, communication network topologies among agents in practical scenarios are often unbalanced digraphs, and the required global information is often not available. In addition, existing control strategies usually assume that the agents have access to their internal states, and admit strongly convex local cost functions with global Lipschitz gradients. Nevertheless, these stringent requirements cannot be satisfied in engineering practice.

This thesis aims to develop distributed control strategies for the distributed optimal coordination of multiple networked dynamical systems under some forms of practical constraints. The main results of this thesis consist of two parts. In the first part, control strategies are developed to address the distributed optimal coordination problem of multi-agent systems with linear/nonlinear agent dynamics over unbalanced digraphs. In the second part, the developed control strategies are applied to deal with the cooperative source-seeking with multiple mobile robotic vehicles and the coordination of distributed energy resources in power systems without using any global information. The main challenges of these problems lie in the imbalance of the communication topologies, the lack of global information, the complexity of general agent dynamics as well as other physical constraints, including unavailability of agent states, absence of convexity of cost functions or global Lipschitz continuity of gradients.

The main results of this thesis can be summarized as follows.

1. The distributed optimal coordination problem of heterogeneous linear multi-agent systems over unbalanced directed networks is investigated. This thesis considers the more general unbalanced digraph, while the linear dynamics are allowed to be non-minimum phases. A distributed state feedback controller and a distributed output feedback controller are proposed to steer all the agent outputs to the global minimizer.

2. The distributed optimal coordination problem of second-order uncertain nonlinear multi-agent systems over unbalanced directed networks is considered. It is assumed that the nonlinear dynamics have parameter uncertainties and external disturbances. By exploiting the adaptive control approach, a novel distributed dynamic state feedback controller is developed such that the problem is addressed while no prior knowledge of the uncertainties or disturbances is required.

3. The distributed optimal coordination problem of uncertain nonlinear multi-agent systems in the normal form over unbalanced directed networks is studied. A high-gain observer is exploited in the controller design to estimate the agent states in the presence of uncertainties and disturbances so that the proposed controller relies only on agent outputs. The semi-global convergence of the agent outputs towards the optimal solution that minimizes the sum of all local cost functions is proved under standard assumptions.

4. The cooperative source-seeking problem of multiple Euler\textendash{}Lagrange systems is investigated. Based on the topology balancing technique and the adaptive control approach, a fully distributed controller, which is dependent on neither prior global information concerning network connectivity nor the convexity of local cost functions, is developed so that the multiple mobile robotic vehicles over unbalanced directed networks simultaneously approach the source position.

5. The distributed optimal resource allocation problem of multi-agent systems under the relaxed condition that the gradients of local cost functions are locally Lipschitz is addressed. The input-to-state stability with a vanishing input of the closed-loop system under the proposed fully distributed controller is first established, and the convergence towards the optimal solution of the decision variables while remaining within their respective local feasibility constraints is then presented.

    Research areas

  • Distributed optimal coordination, Multi-agent system, Directed network topology, Linear systems, Nonlinear systems, Global information, Adaptive control, Cooperative source-seeking, Distributed resource allocation