Linear Quadratic Two-Person Zero-Sum Differential Games

Part of the Systems & Control: Foundations & Applications book series (SCFA)


In this chapter we broaden the general perspective of the book and consider two-player zero-sum games with linear dynamics and a quadratic utility function over a finite time horizon. They can be viewed as a natural extension of the single player linear quadratic optimal control problem. In particular they illustrate the occurrence of symmetrical solutions to the matrix Riccati differential equation that are not necessarily positive semi-definite. It also connects with the glimpse of H-theory given in the previous chapter.


Utility Function Nash Equilibrium Saddle Point Closed Loop System Couple System 
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© Birkhäuser Boston 2007

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