针对含全状态约束的非线性系统固定时间控制问题,引入一种新型的非线性映射来处理系统状态存在约束的问题,并且利用此非线性映射提出一种固定时间控制设计方法。首先,建立具有全状态约束非线性系统的数学模型;其次,结合时变状态约束条件采用非线性映射技术将原本存在约束的系统转换为相应的无约束系统;然后,利用径向基函数神经网络设计基于反步法的固定时间控制律;最终,采用Lyapunov理论证明系统的稳定性,并结合具体仿真算例验证了所提控制方法的有效性和可行性。
A novel nonlinear mapping is introduced to address the fixed-time control problem of nonlinear systems with full state constraints, and a fixed-time control design method is proposed using the nonlinear mapping method. Firstly, We establish a mathematical model of a nonlinear system with full state constraints; Secondly, by combining time-varying state constraints and using nonlinear mapping techniques, the system with existing constraints is transformed into a corresponding unconstrained system; Then, a fixed-time control law based on backstepping is designed using a radial basis function neural network; Finally, the stability of the system is demonstrated using Lyapunov theory, and the effectiveness and feasibility of the proposed control method are verified through specific simulation examples.
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