Optimal sampling and regulation of uncertain interconnected linear continuous time systems

This paper presents a co-design approach for optimizing both the sampling period and the control policy of uncertain isolated and interconnected linear continuous time systems. The simultaneous optimization of event-based aperiodic sampling instants and control policy is formulated as a min-max problem and a saddle point solution is generated. An adaptive solution to the min-max control problem is obtained using a two player zero-sum game based Q-leaning approach. Novel update laws, both for flow period and jump instants, for updating the Q-function parameters are proposed in an impulsive system framework. Asymptotic regulation of the system states and Q-function parameters are guaranteed for both the isolated and interconnected systems, under the assumption of persistence of excitation (PE) condition. It is demonstrated that the resulting sampled data implementation of the controllers for both the isolated and interconnected systems do not exhibit Zeno behavior. Numerical results are included to substantiate the claims.