Adaptive Feedback Stabilization for a Class of Cascaded Nonlinear Systems with Discontinuous Connection

This paper investigates an adaptive control problem for a class of cascaded nonlinear systems with discontinuity. The uncertainty is taken into account as an unknown parameter and bounded unknown functions in the differential equation with discontinuous right hand side. The Filippov-framework is used to analyze the behavior of the discontinuous dynamical systems. First, a state feedback design with parameter adaptation is presented, where the designed controller ensures the convergence responses of of the closed loop system to any given bounded set. Then, the design approach is extended to achieve asymptotical stability under a stronger condition on the driven subsystem. Finally, a numerical example is given to demonstrate the proposed design approach.