Linear Quadratic Differential Games: Saddle Point and Riccati Differential Equation
Michel C. Delfour · SIAM Journal on Control and Optimization · 2007
Zhang [SIAM J. Control Optim., 43 (2005), pp. 2157–2165] recently established the equivalence between the finiteness of the open loop value of a two-player zero-sum linear quadratic (LQ) game and the finiteness of its open loop lower and upper values. In this paper we complete and sharpen the results of Zhang for the finiteness of the lower value of the game by providing a set of necessary and sufficient conditions that emphasizes the feasibility condition: $(0,0)$ is a solution of the open loop lower value of the game for the zero initial state. Then we show that, under the assumption of an open loop saddle point in the time horizon $[0,T]$ for all initial states, there is an open loop saddle point in the time horizon $[s,T]$ for all initial times s, $0\le s