Adaptive Optimal Control for a Class of Nonlinear Systems With Dead Zone Input and Prescribed Performance
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摘要: 针对一类考虑指定性能和带有输入死区约束的严格反馈非线性系统，本文提出了一种自适应模糊最优控制方法.采用模糊逻辑系统逼近系统的未知非线性函数及代价函数，利用backstepping方法及命令滤波技术，设计前馈控制器.针对仿射形式的误差系统，结合自适应动态规划技术，设计最优反馈控制器.采用指定性能控制方法，将系统跟踪误差约束在指定范围内.利用死区斜率信息解决具有死区输入的非线性系统的控制问题.基于Lyapunov稳定性理论，证明闭环系统内所有信号是一致最终有界的.最后仿真结果验证了本文方法的可行性和有效性.
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关键词:
- 自适应模糊最优控制 /
- 自适应动态规划 /
- backstepping方法 /
- 输入死区 /
- 指定性能
Abstract: This paper develops an adaptive fuzzy optimal control method for a class of strict-feedback nonlinear systems with dead zone input and prescribed performance. Fuzzy logic systems are used to approximate unknown nonlinear functions and cost functions. Under the command filtered technique and the backstepping method, the feedforward controller is designed. And an optimal feedback controller is derived to stabilize the tracking error dynamics in the affine form via an adaptive dynamic programming technology. Based on the prescribed performance control method, the tracking error can be limited in a prescribed area. Moreover, the control problem of nonlinear systems with dead zone input can be addressed by utilizing the information of dead zone slopes. All signals in the closed-loop system can be proved to be uniformly ultimately bounded by using the of Lyapunov stability theorem. Finally, the simulation results verify the feasibility and effectiveness of the proposed method.-
Key words:
- Adaptive fuzzy optimal control /
- adaptive dynamic programming /
- backstepping method /
- dead zone input /
- prescribed performance
1) 本文责任编委 刘艳军 -
图 2 $ \tilde z_{1}$的轨迹和指定性能边界曲线
Fig. 2 Trajectories of $ \tilde z_{1}$ and performance bounds
图 3 代价函数权值$\hat{w}_{c i}$ 和哈密顿函数 $\hat{H}\left(Z, \hat{U}^{*}\right)$ 的轨迹(i = 1; 2; 3; 4; 5)
Fig. 3 The trajectories of cost functions weights $\hat w_{ci}$ and Hamiltonian $\hat H(Z, \hat U^ *)$ $(i = 1, 2, 3, 4, 5)$
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