Neural network controller design for fractional-order systems with input nonlinearities and asymmetric time-varying Pseudo-state constraints

This article considers the neural adaptive control issues of a category of non-integer-order non-square plants with actuator Nonlinearities and Asymmetric Time-Varying pseudo-State Constraints. First, the original non-square non-affine system with input nonlinearities is transformed into an equivalent affine-in-control square model by defining a set of auxiliary variables and by employing the mean-value theorem. Second, Neural networks and Nussbaum functions are exploited to obviate the requirement of a complete knowledge of the system dynamics and the control directions, respectively. Third, a novel adaptive dynamic surface control method based on Caputo fractional derivative definitions and fractional order filters is developed to overcome the “explosion of complexity” problem in the traditional backstepping design process and to determine the parameter update laws and control signals, concurrently. Then, Asymmetric Barrier Lyapunov Functions with error variables are adopted to ensure the uniform stability of the closed-loop system and to prevent the violation of the full pseudo-State constraints. The novelties and contributions of this article are: (1) through the introduction of new technical Lemmas and corollaries, existing control design and stability theories linked to integer-order square systems are developed and extended to non-square non-integer-order ones. (2) all signals, including variables and errors in the closed-loop system are semi-global practical finite-time stability whereas the the tracking errors are asymptotically driven to zero without transgression of the constraints. Finally, the effectiveness and potential of the proposed control approach are substantiated by two example simulations.