Distributed Cooperative and Competitive Optimisation Over Networks

Abstract

Multi-agent systems have received a significant amount of research attention during the last three decades. As one of the most important problems, distributed optimisation for multi-agent systems has been actively studied in recent years, owing to its wide applications in engineering, social and economic networks. In this thesis, two different types of optimisation problems are considered: the cooperative and competitive optimisation. In network cooperation, the agents aim to optimise the summation of all local objectives. A distributed algorithm is proposed to deal with the multi-objective resource allocation problem with affine constraints. The framework encompasses a group of distributed decision makers in the subagents, where each of them possesses a local preference index. Novel distributed algorithms are proposed to solve such a problem in a distributed manner. The weighted L_p preference index is utilised in each agent since it can provide a robust Pareto solution to the problem. By using distributed fixed-time optimisation methods, the L_p preference index is constructed online without specifying the unknown parameters.Furthermore, consensus-based fixed-time algorithms are deployed to solve time-varying optimisation problems. Since the cost functions and their derivatives are usually impossible to be expressed by explicit functions due to the complexity of modern systems, function calls have to be performed to obtain those values. Therefore, a surrogate-assisted method is proposed to approximate the true functions and to optimise the black-box functions. A balanced infill strategy for exploration and exploitation is designed to optimise the current model and to improve the surrogate fitting. Distributed algorithms are further employed to solve this surrogate-based optimisation problem, and convergence of those algorithms are analysed. Seeking a Nash equilibrium is the ultimate goal for distributed competitive games. The agents are not assumed to have direct access of other agents’ states, and instead, they estimate other agents' states by communicating with their neighbours. Advanced consensus algorithms are implemented for such purposes, and consequently the game is decentralised into a set of subsystems interacting over a communication network. Affine constraints are introduced in the problem settings such that local decision vectors are coupled. Fixed-gain design and adaptive design are developed to search the generalised Nash equilibrium. Moreover, to speed up the convergence, fixed-time algorithms are designed to obtain the Nash equilibrium within a bounded time.

Date of Award	31 Dec 2021
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Zhirun Hu (Supervisor) & Zhengtao Ding (Supervisor)