چكيده به لاتين
In fault tolerant control field of research, a great intereset is on the development of existing methods to nonlinear systems considering uncertainties, disturbances and noise. Constraints of existing methods limits it's application. This leads to the development of signal based methods, however these methods have very limited tolearnt capabilities. Viability theory is a mathematical theory that analyse dynamical behavior of the system in different conditions. Defined concepts in this theory overcome shortcomings of existing control methods, but develoing theses concepts in control context is not an easy task.
The purpose of this thesis is to use the viability theory in fault diagnosis in nonlinear systems. To achieve this goal, some preliminaries from the viability theory including viability kernel, invariance kernel and capture basin are introduced. One of the main difficulties with these concepts is how to efficiently compute them in control systems. For using these concepts in nonlinear systems, calculation of them are illustrated. A lagrangian method for computing these concepts in nonlinear LPV systems is introduced. Because of simplicity and efficency, zonotopes have been used for set representation. Then, an algorithm is proposed for safety and performance verification of a control systems using these concepts.
The way that these concepts in conjuction with interval observers can be used in fault detection and isolation are discussed. Fault diagnosis is based on checking for an inconsistency between the measured and predicted behaviors using viability theory concepts and sets. Robustness against disturbances and noise can be achieved in residual generation using interval observers. However, viability theory approaches can be used in residual evaluation for fault detection and isolation in both steady and transient states.
Also, fault tolerance evaluation of a nolinear faulty system is provided with viability theory approaches. Because fault effects and system constraints can be dealth with explicitly, Model Predictive Control (MPC) structure has been investigated. Proposed approaches let us decide wether continue system operation after fault occurence or stop it because it is unable to achieve desired gaols. Applicability of the proposed methods are illustrated using different well-known control benchmarks.
