分数阶线性系统P-型迭代学习控制在L^p范数意义下的收敛性

Convergence of P-type Iterative Learning Control for Fractional-Order Linear System in the Sense of Lp Norm

针对一类分数阶线性时不变系统,讨论P-型迭代学习控制律(ILC)的单调收敛性.首先,在Lebesgue-p(L^p)范数意义下,利用卷积的推广Young不等式,推导一、二阶P-型控制律单调收敛的充分条件,并推广到N阶控制律的情形;然后,比较分析一、二阶控制律的收敛速度.研究结果表明控制律的收敛条件取决于控制律的学习增益以及系统本身的属性.数值仿真验证了理论的正确性和控制律的可行性.

The convergence of P-type iterative learning control（ILC）for some fractional-order linear time-invariant system is studied in this paper.The sufficient conditions for the monotone convergence of the first and second order P-type control laws are firstly deduced and generalized to the case of the Nth order control law under the Lebesgue-p（L^p）norm through the extended Young inequality.Then the convergence speed of first and second-order P-type ILC are compared and analyzed.The results show that the sufficient conditions of control algorithm is determined by the learning gains and the attributes of the system itself.Numerical simulation verifies the correctness of the theory and the feasibility of this algorithm.