Output-regulated distributed time-varying optimal control design of high-order nonlinear strict-feedback multi-agent systems under cooperative-competitive graphs

In this paper, for the time-varying distributed optimisation problems(DOPs) under the cooperation-competition graph, we introduce a novel optimal control strategy for high-order nonlinear strict-feedback multi-agent systems(MASs). By employing an ‘estimation-tracking’ hierarchical architecture, this strategy ensures that the decision variables of the two adversarial camps converge to the optimal solutions corresponding to their respective groups. Initially, combining a well-designed subnet clustering consensus algorithm and the dynamics of exosystems, an optimal solution estimator based on output regulation theory is proposed, which accurately estimates the time-varying optimal solutions for the two competing camps. Then, a backstepping-based bilateral consensus controller makes use of the estimator's output to achieve asymptotic tracking. The dual mechanism of estimation and control guarantees the asymptotic convergence of the MASs' decision variables to the optimal solutions. Finally, the effectiveness of the proposed optimal control strategy is verified through two simulation cases.