This paper presents an adaptive control strategy for a class of first-order nonlinear systems of the form x/spl dot/=/spl theta//sub 1/*/sup T/f(x)+/spl theta//sub 2/*/sup T/g(x), where g(x) is a smooth function, whereas f(x) satisfies sectoricity conditions. /spl theta//sub 1/* and /spl theta//sub 2/* are constant parameter vectors. It is assumed that the system remains controllable for all values of x, but the sign of /spl theta//sub 2/*/sup T/g(x)(x) is unknown. The proposed adaptive scheme extends ideas previously presented the authors (1992) where the term premultiplying the input was supposed to be constant. The standard least-squares estimates of /spl theta//sub 2/* are modified using a hysteresis type switching algorithm that enables us to conclude on existence, uniqueness, boundedness and convergence of the solutions of the adaptive closed-loop system.
展开▼
机译：本文提出了一种形式为x / spl dot / = / spl theta // sub 1 / * / sup T / f（x）+ / spl theta // sub 2形式的一阶非线性系统的自适应控制策略/ * / sup T / g（x），其中g（x）是光滑函数，而f（x）满足扇区性条件。 / spl theta // sub 1 / *和/ spl theta // sub 2 / *是常量参数向量。假定系统对于x的所有值保持可控，但是/ spl theta // sub 2 / * / sup T / g（x）（x）的符号未知。提出的自适应方案扩展了先前在作者（1992年）中提出的思想，其中术语“预乘输入”应该是恒定的。 / spl theta // sub 2 / *的标准最小二乘估计值是使用滞后类型切换算法修改的，该算法使我们能够得出自适应闭环系统解的存在性，唯一性，有界性和收敛性。
展开▼
