We consider the multi-agent collision avoidance problem for a team of wheeled mobile robots. Recently, a local solution to this problem, based on a game theoretic formulation, has been provided and validated via numerical simulations. Due to its local nature the result is not well-suited for online application. In this paper we propose a novel hybrid implementation of the control inputs that yields a control strategy suited for the online navigation of mobile robots. Moreover, subject to a certain dwell time condition, the resulting trajectories are globally convergent. The control design is demonstrated both via simulations and experiments.

Motivated by the challenges arising in the field of multi-agent systems (MAS) control, we consider linear heterogenous MAS subject to local communication and investigate the problem of designing distributed controllers for such systems. We provide a game theoretic framework for systematically designing distributed controllers, taking into account individual objectives of the agents and their possibly incomplete knowledge of the MAS. Linear statefeedback control laws are obtained via the introduction of a distributed differential game, namely the combination of local non-cooperative differential games, which are solved in a decentralised fashion. Conditions for stability of the MAS are provided for the special cases of acyclic and strongly connected communication graph topologies. These results are then exploited to provide stability conditions for general graph topologies. The proposed framework is demonstrated on a tracking synchronisation problem associated with the design of a distributed secondary voltage controller for microgrids and on a numerical example.

It is well known that finding Nash equilibrium solutions of nonzero-sum differential games is a challenging task. Focusing on a class of linear quadratic differential games, we consider three notions of approximate feedback Nash equilibrium solutions and provide a characterisation of these in terms of matrix inequalities which constitute quadratic feasibility problems. These feasibility problems are then recast first as bilinear feasibility problems and finally as rank constrained optimisation problems, i.e. a class of static problems frequently encountered in control theory.

A multi-agent system consisting of heterogeneous agents, described by nonlinear dynamics and with inter-agent communication characterised by a directed acyclic graph, is considered in this paper. A framework for designing distributed control strategies obtained via the combination of local non-cooperative differential games is provided. The resulting dynamic (local) state-feedback control laws can be computed offline and in a decentralised manner. Conditions for ensuring stability of the overall closed-loop system are provided, before the proposed game theoretic framework is applied to a formation control problem.

A multi-agent system consisting of linear heterogeneous agents is considered in this paper. Distributed control laws for each agent are designed through the formulation of linear quadratic differential games with partial information. Exact and approximate solutions for the differential games are provided before the problem of formation control with limited communication is considered. A numerical example is provided to illustrate the theory.