Contributions to fractional-order fault-tolerant control of nonlinear systems.

Abstract

The primary aim of this thesis is to develop adaptive control strategies tailored for specific categories of uncertain single-input single-output (SISO) and interconnected multi-input multi-output (MIMO) fractional-order nonlinear systems. The investigation includes the analysis of the effect of saturation on the control inputs along with the external disturbances on the dynamics of systems. In all the proposed methodologies, neural networks or fuzzy logic systems serve as universal approximators to estimate the unknown nonlinear dynamics of the systems. The architectures of the proposed controllers address the well-known challenges associated with complexity explosion while circumventing the conventional back-stepping technique thanks to the introduction of a new fractional systems transformation into the controllable Bronovsky form. By using the implicit function theorem and the strictly positive real (SPR) property, output feedback approaches become feasible. Compared to similar approaches, the proposed adaptive neural/fuzzy controllers exhibit minimal online learning parameters. Furthermore, the integration of the Eventtriggered mechanism optimizes resource utilization by updating control actions only when necessary, thereby reducing computational burden and communication overhead. Additionally, stability analysis of all control loops is conducted using the Lyapunov method, and simulation results are provided for each scheme to demonstrate its efficacy.