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It is desirable but challenging to fulfill system constraints and reachoptimal performance in consensus protocol design for practical multi-agentsystems (MASs). This paper investigates the optimal consensus problem forgeneral linear MASs subject to control input constraints. Two classes of MASsincluding subsystems with semi-stable and unstable dynamics are considered. Forboth classes of MASs without input constraints, the results on designingoptimal consensus protocols are first developed by inverse optimality approach.Utilizing the optimal consensus protocols, the receding horizon control(RHC)-based consensus strategies are designed for these two classes of MASswith input constraints. The conditions for assigning the cost functionsdistributively are derived, based on which the distributed RHC-based consensusframeworks are formulated. Next, the feasibility and consensus properties ofthe closed-loop systems are analyzed. It is shown that 1) the optimalperformance indices under the inverse optimal consensus protocols are coupledwith the network topologies and the system matrices of subsystems, but they aredifferent for MASs with semi-stable and unstable subsystems; 2) the unstablemodes of subsystems impose more stringent requirements for the parameterdesign; 3) the designed RHC-based consensus strategies can make the controlinput constraints fulfilled and ensure consensus for the closed-loop systems inboth cases. But for MASs with semi-stable subsystems, the {\em convergentconsensus} can be reached. Finally, two examples are provided to verify theeffectiveness of the proposed results.

Receding Horizon Consensus of General Linear Multi-agent Systems with Input Constraints: An Inverse Optimality Approach