We investigate the problem of optimal state reduction under minimization of the angle between system behaviors. The angle is defined in a worst-case sense, as the largest angle that can occur between a system trajectory and its optimal approximation in the reduced order model. This problem is...

We study a class of discounted autonomous infinite horizon optimal control problems where the state dynamics may undergo discontinuous changes when the state crosses from one region of the state space to another. Assuming the state and control space are one-dimensional, we provide structural...

Maxmin or minmax optimization problems arise in many applications. There is a classical connection between these problems and zero-sum games. This paper shows that, under certain conditions, maxmin solutions also arise from Nash equilibria of population games as studied in evolutionary game...

In this note we present as well necessary as sufficient conditions for existence of a Pareto optimum for general non-convex differential games. The obtained results are used to analyze the non-convex regular indefinite linear quadratic differential game. For the scalar case an algorithm is...

In this article we derive necessary and sufficient conditions for the existence of Pareto optimal solutions for an N player cooperative infinite horizon differential game. Firstly, we write the problem of finding Pareto candidates as solving N constrained optimal control subproblems. We derive...