Unified neuroadaptive fault-tolerant control of fractional-order systems with or without state constraints

The problem of controlling fractional-order nonlinear systems remains interesting and challenging due to the powerful and hereditary memory features of such systems. In this paper, we investigate the adaptive tracking control problem for a class of fractional-order nonlinear systems with or without state constraints. The tan-type barrier Lyapunov function (BLF) is adopted for the first time in fractional Lyapunov direct method. Such technique allows for the accommodation of the situations with and without state constraints in a unified framework. Moreover, neural network (NN) is utilized to reconstruct the sophisticated nonlinear functions arising from the fractional-order differentiation of the virtual controller, resulting in a neuroadaptive fault-tolerant control scheme. It is shown that, with the proposed unified control, all the closed-loop signals are semiglobally ultimately uniformly bounded whether state constraints are imposed or not. Both theoretical analysis and numerical simulation confirm the effectiveness of the developed approach.