New Results on Cooperative Optimal Consensus Control of Multiagents Using LPV Approach for Lipschitz Nonlinear Systems Under Digraphs

This article addresses the distributed cooperative protocol for nonlinear agents with the aim of attaining the optimal leader-following consensus. The main challenges encountered when deriving the cooperative optimal protocol are caused due to the conservatism of Lipschitz nonlinear dynamics, uncertainties, disturbances, and coupling of agents. Until now, the consensus optimal protocols for Lipschitz nonlinear agents are provided in the existing literature, which is conservative and has limited applications. To tackle these issues, a cooperative protocol is provided for intelligent nonlinear systems that are optimal for the performance index and robust against uncertainties and disturbances. The performance index of the optimal protocol depends on the Lipschitz nonlinearities is converted into linear parameter-varying (LPV) form. The LPV approach reduces the conservatism of the existing methods for Lipschitz nonlinearities that improves the scope of the design approach and is applicable to practical applications of nonlinear multiagents. The optimal solution is obtained by solving the algebraic Riccati equation. The proposed optimal scheme increases the region of the feasibility of the Lipschitz constant by extracting precise information about nonlinearities. Moreover, a robust cooperative optimal protocol is designed that has ensured optimal consensus for the nonlinear agents and eliminated the negative effects of parameter uncertainties and disturbances. Finally, the results are verified through a simulation example of multiple nonlinear robotic manipulators.