In this chapter we present a continuous-time adaptive dynamic programming (ADP) procedure that uses the idea of integral reinforcement learning (IRL) to find online the Nash-equilibrium solution for the two-player zero-sum (ZS) differential game. We consider continuous-time (CT) linear dynamics of the form x= Ax + B₁w + B₂u, where u(t), w(t) are the control actions of the two players, and an infinite-horizon quadratic cost. This work is from Vrabie and Lewis (2010).

Chapter Contents:

• 11.1 Zero-sum games for linear systems
• 11.1.1 Background
• 11.1.2 Offline algorithm to solve the game algebraic Riccati equation
• 11.1.3 Continuous-time HDP algorithm to solve Riccati equation
• 11.2 Online algorithm to solve the zero-sum differential game
• 11.3 Online load-frequency controller design for a power system
• 11.4 Conclusion

Inspec keywords: learning (artificial intelligence); differential games; continuous time systems; dynamic programming

Other keywords: integral reinforcement learning; ADP procedure; infinite-horizon quadratic cost; continuous-time linear dynamics; IRL; continuous-time adaptive dynamic programming procedure; CT linear dynamics; Nash-equilibrium solution; ZS differential game; zero-sum two-player games

Subjects: Optimisation techniques; Game theory; Learning in AI (theory)