The Open-Loop Linear Quadratic Differential Game for Index One Descriptor Systems

In this paper we consider the linear quadratic differential game for descriptor systems that have index one. We derive both necessary and sufficient conditions for existence of an open-loop Nash equilibrium.Linear quadratic differential games;open-loop information structure;descriptor systems

The Open-Loop Discounted Linear Quadratic Differential Game for Regular Higher Order Index Descriptor Systems

In this paper we consider the discounted linear quadratic differential game for descriptor systems that have an index larger than one. We derive both necessary and sufficient conditions for existence of an open-loop Nash (OLN) equilibrium. In a small macro-economic stabilization game we illustrate that the corresponding optimal response is generically cyclic.linear quadratic differential games;open-loop information structure;descriptor systems

The Open-Loop Linear Quadratic Differential Game for Index One Descriptor Systems

In this paper we consider the linear quadratic differential game for descriptor systems that have index one. We derive both necessary and sufficient conditions for existence of an open-loop Nash equilibrium.

Feedback Nash Equilibria for Linear Quadratic Descriptor Differential Games

In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a Nash equilibrium.linear-quadratic games;linear feedback Nash equilibrium;affine systems;solvability conditions;Riccati equations

Feedback saddle point equilibria for soft-constrained zero-sum linear quadratic descriptor differential game

In this paper the feedback saddle point equilibria of soft-constrained zero-sum linear quadratic differential games for descriptor systems that have index one will be studied for a finite and infinite planning horizon. Both necessary and sufficient conditions for the existence of a feedback saddle point equilibrium are considere

Feedback Nash Equilibria for Descriptor Differential Games Using Matrix Projectors

In this article we address the problem of finding feedback Nash equilibria for linear quadratic differential games defined on descriptor systems. First, we decouple the dynamic and algebraic parts of a descriptor system using canonical projectors. We discuss the effects of feedback on the behavior of the descriptor system. We derive necessary and sufficient conditions for the existence of the feedback Nash equilibria for index 1 descriptor systems and show that there exist many informationally non-unique equilibria corresponding to a single solution of the game. Further, for descriptor systems with index greater than 1, we give a regularization based approach and discuss the associated drawbacks.

The Optimal Linear Quadratic Feedback State Regulator Problem for Index One Descriptor Systems

In this note we present both necessary and sufficient conditions for the existence of a linear static state feedback controller if the system is described by an index one descriptor system. A priori no definiteness restrictions are made w.r.t. the quadratic performance criterium. It is shown that in general the set of solutions that solve the problem constitutes a manifold. This feedback formulation of the optimization problem is natural in the context of differential games and we provide a characterization of feedback Nash equilibria in a deterministic context.

The Zero-Sum Discrete-Time Feedback Linear Quadratic Dynamic Game: From Two-Player Case to Multi-Player Case

The two-person zero-sum discrete-time feedback linear quadratic dynamic game is considered. A method that provides a saddle-point for the zero-sum discrete dynamic game is developed to derive a necessary and sufficient condition under which the game has a feedback saddle-point solution. Existence solutions, which are described in terms of a sequence of nonnegative definite algebraic Riccati matrices, are constructed. Next, a generalization of such a game to a multi-player case is studied. Using the results in a two-person case, the characterization of a feedback saddle-point solution for the multi-player game is derived