作者:孟桂芝 ， 吕 岩
Authors:MENG Guizhi, Lü Yan摘要:针对 一 类带有未知参数向量和外界扰动的非线性系统 ,研究了其在线性外系统驱动下的逆最优输出 调节问题 。首先依据调节器方程是可解的条件 ,得到调节器方程的解 ,再通过坐标变换 ,将不确定非线性系统的输 出调节问题转化为镇定问题 。接着对增广系统建立与内模相关的辅助系统 ,然后结合逆最优增益配置定理 ,设计 了与辅助系统相关的内模和状态反馈逆最优自适应控制器 ,并提出了与控制器和辅助系统相关的新的目标泛函。 新设计的控制器不仅使得闭环系统中的全部信号都是半全局最终 一致有界 ,而且还能够保证新提出的目标泛函达 到最小 。最后通过仿真算例验证了所设计控制器的可行性 ,与已有的文献进行对比 ,可以发现采用逆优化方法所 得出的跟踪误差收敛更快。
Abstract:For a class of nonlinear systems with unknown parameter vector and disturbance, the inverse optimal output regulation problem driven by a linear exosystem is researched. In the first place, on account of the condition that the regulator equation is solvable, one can get the solution of the regulator equation. Afterwards the output regulation problem of the uncertain nonlinear systems is turned into a nonlinear stabilization problem by the state transformation and the internal model. Then an auxiliary system is constructed for the augmented system and the auxiliary system is connected with the internal model. Furthermore, by combining the inverse optimal gain assignment theorem, a new internal model and state feedback inverse optimal controller which are connected with the auxiliary system are designed, and based on the auxiliary system and the controller a new cost function is proposed. The novel control scheme we have raised in this work can not only make all of the signals in the closed loop systems be semi-global uniformly ultimately bounded, but also minimize the proposed cost function. Finally, a simulation case is raised to testify the reasonability of the new raised controller. The tracking error is smaller than the existing references by employing the inverse optimal method.

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