完全非线性近似逆及其在轨迹跟踪中的应用

非线性系统输出跟踪问题在理论和实际中都具有十分重要的意义。人们对此问题进行了大量地研究和广泛地应用。但是所有的研究对象一般都要求仿射型非线性系统，以便容易解出相应的控制输入。对于一般的完全非线性系统，由于没有控制输入的显性表达式，很难得到相应的结果。本文讨论了完全非线性系统的输出跟踪问题，在理论上研究了完全非线性系统逆的存在性。利用神经网络可逼近任意 Ｌ２ 函数的特性，提出了求解完全非线性系统逆近似控制律的方法，并由此研究了完全非线性飞机模型的轨迹跟踪问题。通过对飞机轨迹跟踪问题的仿真，表明该方法是切实可行的。

Full Nonlinear Approximate Inversion and Application to Trajectory Tracking

Output tracking problem for nonlinear systems is of importance to theoretical and practical applications. There are many approaches and applications in this field. But all the methods require that the system is affine in the control so as to express tracking control law conveniently. There is little result for general nonlinear systems in which the control do not linearly appear because the control input can not be directly solved. In this paper, the output tracking for general nonlinear systems is discussed. Existence of the full nonlinear inversion is proved. With the property that neural networks are able to approximate any L 2 function uniformly, a technique to approximate nonlinear inverse is presented. Trajectory tracking of a full aircraft model is simulated and satisfactory results are obtained.