Fixed-Time Distributed Output Optimization for Heterogeneous Linear Multiagent Systems: Introducing Distributed Piecewise Protocols

This article is devoted to fixed-time (FXT) output optimization for heterogeneous linear multiagent systems (MASs) by proposing distributed piecewise protocols. By introducing an auxiliary variable for each agent, a state-based control scheme is designed and a distributed piecewise algorithm is developed for each auxiliary state. It is revealed that the FXT output optimization is successfully solved through three steps: accurately reaching the auxiliary state, realizing local optimization, and achieving global output optimization. To avoid the inaccessibility dilemma of state information, an output-based control protocol is further developed and an output-based distributed algorithm is proposed to realize output optimization in a fixed time. Finally, the proposed optimization algorithms are further illustrated via numerical results.