ABSTRACT
In Chapters 3 and 4, we developed ADP-based controllers for linear and nonlinear systems in the event-triggered control framework. In both these chapters, we have seen that the event-triggering conditions can be derived using Lyapunov stability analysis. Contrarily, in this chapter, we shall see that the design of event-triggering condition can be coupled with the control synthesis by utilizing game-theoretic techniqes. To this end, this chapter presents an event- and a self-triggered sampling and regulation scheme for continuous-time linear and nonlinear dynamic systems, as well as tracking control problems. We shall develop these schemes based on a zero-sum game formulation, wherein the control policy is treated as the first player, and the threshold for control input error due to aperiodic dynamic feedback is treated as the second player. The optimal control policy and sampling intervals are generated using the saddle point or Nash equilibrium solution, which is obtained from the corresponding game algebraic Riccati equation. The event- and self-triggering control schemes presented in this chapter are based on the work by \textit{Sahoo et al., 2018, 2017a} and the second part of the chapter dealing with nonlinear systems are based on the work in \textit{Narayanan et al., 2018}. The last part of this chapter on tracking controllers are based on the work presented in \textit{Sahoo and Narayanan, 2019}.
