Adaptive control of first-order nonlinear systems with reduced knowledge of the plant parameters

This paper presents an adaptive control strategy for a class of first-order nonlinear systems of the form x˙=θ₁* ^Tf(x)+θ₂*^Tg(x), where g(x) is a smooth function, whereas f(x) satisfies sectoricity conditions. θ ₁* and θ₂* are constant parameter vectors. It is assumed that the system remains controllable for all values of x, but the sign of θ₂*^Tg(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 θ₂* 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