Fault-tolerant Control and Diagnosis for Integer and Fractional-order Systems

When a nonlinear system develops a fault, the challenge is not only to detect it but to estimate its effects and keep the system operating safely. Fault-tolerant Control and Diagnosis for Integer and Fractional-order Systems develops mathematical and observer-based approaches to that challenge, bringing differential algebra together with the calculus of non-integer-order dynamics.

Across nine chapters, the authors move from core mathematical tools to methods for diagnosis, estimation, and control. The treatment covers both conventional integer-order models and fractional-order systems, with simulations and application examples connecting the theory to engineering problems.

From differential algebra to fault diagnosis

The opening chapters establish the differential-algebra foundations used throughout the book. The authors then apply these ideas to fault diagnosis in nonlinear systems, including invariant observers, reduced-order observers, observability, and diagnosability. The emphasis is on how available input-output measurements can reveal faults and system states.

Control strategies for integer-order systems

For integer-order systems, the book develops multi-fault-tolerant control methods and examines the observer and controller designs behind them. Applications include an academic example and a three-tank system, offering concrete contexts for the diagnostic and control ideas.

Working with fractional-order dynamics

A dedicated foundation in fractional calculus introduces fractional integrals and derivatives, along with concepts used to describe and assess fractional-order dynamical systems. Subsequent chapters extend observer-based fault diagnosis and fault-tolerant control to these models, including methods for estimating multiple faults and state variables.

Observers, synchronization, and applications

The later material explores fractional reduced-order observers, synchronization and anti-synchronization in fractional chaotic systems, and a robust observer-based controller for uncertain systems with bounded disturbances. Examples include fractional Lorenz and Rössler systems, the Van der Pol oscillator, and a DC motor. Simulation studies help readers follow how the proposed approaches are evaluated.

For readers of nonlinear control and applied mathematics

Written for engineers, mathematicians, physicists, researchers, and postgraduate students with a working knowledge of calculus, this book combines introductory mathematical material with advanced research topics. It is especially relevant to readers interested in fault diagnosis, state estimation, nonlinear control, and the expanding study of fractional-order systems.