I&I based command filtered back-stepping of pure-feedback systems in presence of non-linearly parameterized uncertainty

An Immersion and Invariance-based command filtered back-stepping control, is addressed for non-linearly parameterized pure-feedback systems, which avoids the complicate analytic derivatives in traditional back-stepping design. In the underlying control scheme, integral sliding-mode filters are designed to approximate the virtual control derivatives, to solve the "circular construction problem" and the problem of "explosion of complexity" in pure feedback system. The resulting closed-loop system consists of controller-filter pair, which both satisfy the input-to-state stability(ISS) property, providing the celebrated small-gain theorem can be exploited to guarantee the stability of closed-loop system. Referring to the issue of non-linearly parameterized uncertainty, adaptive laws are derived via Immersion and Invariance technique. Numerical simulations are included to illustrate the effectiveness of proposed control scheme.