A multi-agent system consisting of N agents is considered. The problem of steering each agent from its initial position to a desired goal while avoiding collisions with obstacles and other agents is studied. This problem, referred to as the multi-agent collision avoidance problem, is formulated as a differential game. Dynamic feedback strategies which approximate the feedback Nash equilibrium solutions of the differential game are constructed and it is shown that, provided certain assumptions are satisfied, these guarantee that the agents reach their targets while avoiding collisions.

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An identification-free control design strategy for discrete-time linear time-varying systems with unknown dynamics is introduced. The closed-loop system (under state feedback) is parametrised with data-dependent matrices obtained from an ensemble of input-state trajectories collected offline. This data-driven system representation is used to classify control laws yielding trajectories which satisfy a certain bound and to solve the linear quadratic regulator problem -both using data-dependent linear matrix inequalities only. The results are illustrated by means of a numerical example.

With the aim of designing controllers to simultaneously ensure robustness and optimality properties, the mixed H 2 /H ∞ control problem is considered. A class of inputaffine nonlinear systems is considered and the problem is formulated as a nonzero-sum differential game, similar to what has been done earlier by Limebeer et al. for linear systems. A heuristic algorithm for obtaining solutions for the coupled algebraic Riccati equations which are characteristic of the linear quadratic problem is provided together with a systematic method for constructing approximate solutions for the general, nonlinear problem. A few numerical examples are provided.

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