Nonfragile near-optimal control of stochastic time-varying multiagent systems with control- and state-dependent noises

In this paper, the near-optimal nonfragile consensus control design problem is investigated for a class of discrete time-varying multiagent systems (MASs) with control- and state-dependent noises. A decentralized observer-based control protocol is proposed by using the relative output measurements. The gain perturbations/variations of the controller as well as the state- and control-dependent noises are simultaneously taken into consideration, which could better reflect the complexities in reality. The corresponding time-varying observer-based nonfragile near-optimal consensus protocol is designed for the underlying MASs over a finite horizon. To be specific, a certain upper bound is first derived for the associate cost function for the MASs. Then, such an upper bound is minimized by using the completing-the-square technique and Moore-Penrose pseudo inverse. The parameters of the time-varying observer/controller are obtained in terms of the solutions to the Riccati-like recursion. In virtue of the matrix partitioning technique, the explicit expressions of the control/observer parameters are presented. Finally, based on the derived consensus protocol, an upper bound of the associate cost function is provided as time goes to infinity. Some numerical simulations are conducted to demonstrate the validity of the proposed methodology.