Aperiodic Sampling Artificial-Actual $H_{\infty}$ Optimal Control for Interconnected Constrained Systems

This paper analyzes decentralized/centralized event/ self-triggered schemes respectively according to a large-scale interconnected system with state limitation and uncertain interference, and devises a set of parallel controllers for the control input and the worst disturbance. Firstly, the system with asymmetric state constraints is transformed into an auxiliary system by means of coordinate transformation. And then, the physical and artificial systems are integrated to establish a parallel control structure to improve the performance of the system. Next, an aperiodic sampling robust
$H_{\infty}$
optimization method to save communication resources is proposed through zero-sum game (ZSG) theory, and the control pair sequence is obtained by solving the event-triggered Hamilton-Jacobi-Isaacs equation (ET-HJIE) via heuristic dynamic programming (HDP). Based on decentralized ET control (DETC), centralized ETC (CETC), decentralized self-triggered control (DSTC) and centralized STC (CSTC) are further proposed. In addition, the stability of the system under these four modes is proved, and the Zeno phenomenon is discussed. In the end, a simulation model is used to verify the control sequences within four trigger schemes, and satisfactory results are obtained
Note to Practitioners
—Inspired by the large scale, interrelated terms, unavoidable disturbances, and nonlinear constraints of practical engineering systems, an aperiodic sampling HDP algorithm based on artificial-actual interaction is presented to handle with
$H_{\infty}$
optimization of nonlinear interconnected systems with state constraints. The four kinds of aperiodic sampling control methods including DETC, CETC, DSTC and CSTC are proposed in turn, which can greatly reduce data transmission while ensuring the control performance. Moreover, the advantages and characteristics of the four trigger mechanisms are summarized based on simulation, which has certain reference significance for physical systems with different control requirements.