Adaptive Fixed-Time Optimized Control for Nonlinear Systems With Given Transient Performance and State Constraints

This article focuses on addressing adaptive fixed-time optimal control problem for state-constrained nonlinear systems with uncertain dynamics. First, new barrier optimal cost functions are constructed for subsystems to achieve optimal control performance. To achieve this, actor-critic structures are proposed to acquire the optimal fixed-time controller, utilizing universal approximator (e.g., neural networks) to estimate unknown system nonlinearities. Then, a method ensuring tracking error to converge to a prescribed region is formulated under certain bound condition (i.e., full-state constraints are not violated). The implementation of this method is through integrating prescribed exponential function into barrier Lyapunov functions. Moreover, it is worth noting that the proposed optimal control scheme can guarantee that all closed-loop signals are bounded in fixed time and that the convergence precision of tracking error can be prescribed a priori. Finally, one numerical example is provided to show the effectiveness of the proposed optimal fixed-time control approach.