Observer-based adaptive control for fractional-order strict-feedback nonlinear systems with state quantisation and input quantisation

This paper investigates the adaptive control problems of fractional-order strict-feedback nonlinear systems with state quantisation and input quantisation. Both Caputo and Riemann-Liouville derivative definitions are considered. Based on these two definitions, two fractional-order state observers are constructed to smooth the discontinuous quantised states, respectively. Then, new error variables and the dynamic filters are introduced to facilitate the design of the adaptive quantised controller. It is shown that the designed controller is valid for fractional-order strict-feedback nonlinear systems under both Caputo derivative definition and Riemann-Liouville derivative definition. Finally, three examples are given to demonstrate the effectiveness of the proposed method.