摘要：

研究具有全状态约束的不确定非线性系统的预设性能优化跟踪控制问题, 提出由自适应控制与最优补偿相结合的控制方案。首先, 利用基于障碍函数的非线性映射技术, 将受约束的状态和跟踪误差映射为非约束变量, 从而将全状态受约束问题和预设性能跟踪优化问题转化成非约束变量的收敛性问题; 其次, 构造与非约束变量相关的误差系统, 采用反步法和滤波技术设计自适应控制器, 并通过最小化成本函数的策略迭代得到最优补偿控制器; 然后, 利用李雅普诺夫稳定性理论证明了闭环误差系统的半全局一致最终有界性; 最后, 通过理论分析和数值仿真, 验证了提出的控制方案不仅能保证系统输出以良好的暂稳态性能在预设时间内实现对参考信号的跟踪, 而且可以保障系统状态始终不违反约束。

关键词: 不确定非线性系统, 强化学习, 预设性能控制, 全状态约束, 最优控制

Abstract:

In this study, the prescribed performance optimization tracking control problem of uncertain nonlinear systems with full-state constraints is addressed, and a control scheme combining adaptive control and optimal compensation is proposed. First, by using barrier function-based nonlinear mapping techniques, the constrained states and tracking error are mapped to unconstrained variables. This results in a convergence problem of unconstrained variables, which replaces the problem of full-state constraints and prescribed performance tracking control. Second, an error system related to the unconstrained variables is constructed, an adaptive controller is designed using backstepping and filtering techniques, and the optimal compensation controller is obtained via policy iteration by minimizing the cost function. Subsequently, the semiglobal uniform ultimate boundedness of the closed-loop error system is proven using the Lyapunov stability theory. Finally, theoretical analysis and numerical simulation are used to verify that the proposed control scheme ensures that the system output tracks the reference signal with good transient stability performance within the preset time and that the system state does not violate constraints.

Key words: uncertain nonlinear systems, reinforcement learning, prescribed performance control, full-state constraints, optimal control