Optimized Formation Control of Nonlinear Systems with Full-State Constraints Using Adaptive Fixed-Time Techniques

This paper proposes an approach for fixed-time (FxT) adaptive optimized formation control of nonlinear multi-agent systems (MASs) with unknown nonlinear dynamics and full-state constraints. To address system uncertainty and state constraints while achieving optimality in FxT settings, the paper presents a novel adaptive estimation and analysis. The proposed approach first introduces a tan-type nonlinear mapping to handle state constraints, eliminating the feasibility condition of the conventional barrier Lyapunov function method. Next, the actual optimal controller is iteratively designed using the identifier-actor-critic structure and optimized backstepping method, with neural approximators used to learn system uncertainty. Finally, a monotonically decreasing function is constructed to prove that the designed actor-critic update laws have an upper bound, which is essential for stability analysis. The proposed scheme can ensure that the formation is realized at a fixed time while optimizing a given performance index and meeting the constraint requirements. The simulation results verify the effectiveness of the proposed approach. Note to Practitioners - There are inevitable system constraints and model uncertainties in actual physical systems, which may degrade the operational performance of the system. In addition, for practical requirements, designers are eager for multiple agents to achieve the required formation performance at a fast convergence speed. While meeting the requirements of system constraints, it is of practical and theoretical significance to improve the convergence speed and robustness of MASs formation and ensure optimal performance. For this reason, this paper focuses on proposing an effective adaptive FxT-optimized formation control scheme to enhance system performance and convergence speed, which combines nonlinear mapping to address full-state constraints. To achieve optimality under FxT settings, an optimal controller with learning laws is first designed using an identifier-actor-critic structure, in which the identifier is used to learn uncertainty. Then, by constructing a quadratic function, it is proved that the estimation error of the learning law is bounded, thereby forming a new adaptive estimation and analysis scheme.