Optimal Codesign of Control Input and Triggering Instants for Networked Control Systems Using Adaptive Dynamic Programming

The problem of codesign or simultaneous synthesis of triggering and input policies is investigated. The policies are synthesized to minimize a cost function incorporating a data transmission cost. This is unlike the common practice of utilizing an a priori-designed stabilizing control policy and designing a triggering policy, which retains stability. Initially, a finite-horizon cost function that penalizes the state, the control input, and each data transmission is selected. The optimal actions comprised of the control input and the triggering decision, under the operation choice of zero-order hold (ZOH), are approximately obtained in a feedback form, using adaptive dynamic programming. Afterward, the design is extended to the case of generalized ZOH, where the last transmitted state information is updated using a possibly imperfect model. Extension to infinite-horizon cost functions is presented. After analysis of convergence and optimality, the performance of the method is demonstrated through some numerical examples.