Distributed Adaptive Optimization for High-Order Full-State Constrained Multiagent Systems With Unknown Nonidentical Control Directions

This article investigates the distributed optimization problem for nonlinear multiagent systems (MASs) with full-state time-varying constraints and unknown nonidentical control directions (UNCDs). To achieve the optimal objective and guarantee the constraint condition, a two-stage distributed optimization algorithm comprising the optimization layer and local control layer is proposed. First, the optimal signal estimator is designed as the reference signal to transform the optimal problem into a tracking control issue. Due to the unavailability of global information, the estimator only uses the measured gradients of the output states. Second, an adaptive control method is presented in the spirit of the backstepping technique and barrier Lyapunov function, ensuring the agents’ outputs converge to the optimal solution. Novel damping terms are integrated into the backstepping method to address the nonlinear coupling between the agents and the optimization algorithm. Based on the convex analysis and Barbalat’s lemma, the asymptotic stability of the two-stage distributed optimization algorithm is proved, full-state constraints are guaranteed, and all signals of the closed-loop systems are bounded. An interesting extension of the main results to the constrained MASs with time-varying UNCDs (unknown and may multiple reverses) is investigated, and a novel time-elongation Nussbaum function is introduced to deal with the shock chattering issue caused by UNCDs. Finally, numerical examples are provided to show the efficacy of the developed control approach.