| Summary: | This article investigates the optimal sliding mode control approach for consensus of nonlinear discrete-time high-order multi-agent systems (MASs). First, the nonlinearity and communication delay in the MAS is solved by designing a distributed discrete-time integral sliding mode control law, together with a proof of reachability of the sliding mode surface, as well as a proof that the chattering of the system is attenuated. In addition, the optimal controller is designed based on the model obtained after the distributed sliding mode control law is applied to the system. The merits of the proposed distributed sliding mode controller with the fusion of optimal control are that it can reduce the chattering of the MASs and their existence of quasi-sliding modes, as well as tolerate the negative impact caused by communication delay among agents. The MASs can achieve consensus quickly with the combined action of the sliding mode controller and the optimal controller. Finally, two examples are given to verify the effectiveness of the control method proposed in this paper.
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