Robust Design of Nonlinear Control Systems

在这一年里，我们得到了以下结果：1.研究了非线性非标准H^*控制问题。在本研究中，涉及两种情况：(A)从输入到输出的直通项不是满秩项；(B)从扰动到测量输出的直通项不是满秩项的情况。在这些情况下，平方补不能用通常的方法进行，因此，Hamilton-Jacobi-Issas偏微分不等式不是很好地定义的。为了解决这一困难，在耗散不等式中加入了包含待定函数的项，使得直通项具有满秩性。函数确定为相加项等于零，并将待定函数代入Hamilton-Jacobi-Isacs偏微分不等式中。从而得到了(A)和(B)两种情形的充分条件。2.研究了含有不确定参数的线性系统的稳定性条件。将映射定理推广到关于不确定参数的单调性假设成立的情况，而原映射定理假定为多重线性。利用推广的映射定理，给出了系统稳定的充分条件。在矢量相对度未知的多输入多输出非线性系统中，定义了鲁棒矢量相对度。为了在计算机上运行上述控制律，提出了一种新的非线性数字再设计方法，保证了三阶精度。

In this year, we have obtained the following results.1.The nonlinear non-standard H^* control problem is studied. In this research, two cases are concerned with : (a) the case in which the direct-through term from the input to the output does not have full-rank, and (b) the case in which the direct-through term from the disturbance to the measurement output does not have full-rank. In these cases, the square compliment cannot be carried out with the usual method, and thus the Hamilton-Jacobi-Issacs partial differential inequality is not well-defined. To resolve this difficulty, the term includes undecided function is added to the dissipative inequality, which makes the direct-through term have full-rank. The function is determined as the added term is equal to zero, and substitutes the undecided function in the Hamilton-Jacobi-Issacs partial differential inequality. Therefore the sufficient conditions for the cases (a) and (b) are obtained.2.The stability condition of the linear systems which includes uncertain parameters nonlinearly is studied. The mapping theorem is extended to the case that the assumption of the monotonicity with respect to the uncertain parameters holds, while the original mapping theorem assumes the multi-linearity. By means of the extended mapping theorem the sufficient condition of stability is derived. Also the sufficient condition of monotonicity is obtained.3.In the MIMO nonlinear system of which the vector relative degree cannot be defined, the robust vector relative degree is defined. The control law is derived using the robust vector relative degree, and it achieves BIBS stability of the control system.4.To run the above control laws on computers, a new nonlinear digital-redesign method is developed, which ensures the precision of third order with respect to the sampling interval.