design constraints is indeed difficult, if not impossible [9, 10]. Although being apparently ad- vantageous, the aforementioned design issues along with implementation complexity inhibits its translation to practice, especially in systems, where safety is an overriding concern. Moreover, the design is far more difficult for general nonlinear dynamical systems. Most of the research on FTC conducted till date, is on model based FDI without an FTC function or on fault tolerant control (FTC) design without the requirement of FDI module for computational simplicity.
As an alternative, an integrated fault estimator (FE) based active FTC architecture can be re- sorted to. Such a design can be realized in either ways by adopting a direct or an indirect adaptive control philosophy. However, FE/FTC design based on the philosophy of direct adaptive control is believed to exhibit high and aggressive control effort since its learning is directly dependent on the output [91]. To economize the control requirement, FE/FTC synthesis on the basis of indirect adaptive control methodology seems to be a suitable choice. Nevertheless, to the best of our knowledge, an FE/FTC design for nonlinear systems guaranteeing global/semiglobal output stability is not trivial. The bidirectional robustness interaction between the controller and the estimator in nonlinear systems results in the breakdown of theseparation principle. With the loss of design modularity, the stability margins of the closed loop system are substantially decreased and the trajectories will experience a finite escape time. The active FTC algorithms proposed so far in this context largely assume systems with Lipschitz nonlinearities. Moreover, inte- grated FE/FTC design has been proposed for general nonlinear dynamics using neural networks and NDOB based control approaches [80–88] only guarantee semi global uniformly ultimately bounded (UUB) closed loop trajectories. The assumptions are neither rigorously analyzed nor are well justified from a theoretical design perspective. Estimation accuracy is unguaranteed.
Herein, disturbance observers are used to estimate time dependent unknown signals and neural networks/fuzzy observers with a composite weight learning law are used to estimate unknown system nonlinearities and failure induced uncertainties. Owing to the usage of both disturbance observers and neural network/fuzzy estimators, these control methodologies are computationally intensive and also exhibit high control usage. Bidirectional uncertainty interactions now exist between the neural network estimator, disturbance observer and the controller which adversely effect estimation performance thereby affecting the output. However, such robustness interaction issues have not at all been investigated in the above works and other pertinent literature. On the same lines, rigorous mathematical analysis proving the modularity of the triple along with insights on estimation correctness of the coexisting neural network estimator and the disturbance observer, is challenging and remains open. On the other front, development of globally stable FE/FTC for nonlinear systems using only disturbance observers which can successfully com- pensate state dependent nonlinearities, actuator faults/failures(not necessarily parameterized) and external disturbances, will be an interesting and impactful contribution. In this direction, when an ADRC strategy using an NDOB [92, 93], is adopted into the FE/FTC framework, a bidirectional robustness interaction between the control system and the estimator creeps in. To remove these interactions, the existing ADRC methods based on NDOB, presume that the time derivative of the unknown lumped disturbance is zero which is restrictive. Therefore, apart from
tems guarantees of global output asymptotic stability and relaxation of the foregoing assumption will definitely attract applicability to a wide range of systems.
As an addition to the preceding problem, the following issue is certainly generic to any inte- grated FE based FTC intended for nonlinear uncertain systems. Within such an active FTC architecture, the time available for fault estimation and subsequent recovery plays a crucial role in deciding the existence of stable adaptive solutions. Considering practical situations such as in mission critical systems, where the time window in which the faulty system is stabilizable is very short [8,94]. As a matter of fact, if the actuator fault/failure is not accommodated within a specific finite time, the inputs and outputs will encroach their safety limits and eventually lead to mission failures, which is undesirable. Therefore, finite time system performance recovery from the effects of actuator failure is necessary for complex safety systems, where time is a crucial parameter. To the best of our knowledge, the simultaneous treatment of all these factors within an FE/FTC scheme for nonlinear systems has not yet been explicitly considered.
• Most of the existing results on adaptive compensation of actuator failures assume the occurrence of a finite number of faults and failures, meaning that a single actuator fails only once and does not recover thereafter. In other words, this implies that there exists a finite time after which the failure topology never changes and the system is not subjected to any further faults/failures.
These existing results are derived from the closed-loop stability analysis using Lyapunov functions involving unknown fault/failure parameter estimation errors. Hence, the Lyapunov functions will experience jumps at the time instances when failures occur. Moreover, boundedness of the Lyapunov function or rather that of the output tracking error, at all instances of failures can only be guaranteed if and only if the jumps are limited to be finite. This validates the presumption on the applicability of direct adaptive control strategies to the problem of FTC which states the existence of an upper bound on the total number of actuator failures and restricts any change in the failure pattern after a finite span of time. However, in practice, the actuator failure topology may change intermittently without violating the relative degree condition. More generally, this implies that an actuator can infinitely switch between its faulty and healthy states provided that there is a finite time lapse between its two states of operation. In contrast to finite number of actuator failures, an adaptive compensation of possibly infinite number of unknown actuator failures using direct adaptive control methodologies [5,32,54,66,67,95] fail to ensure boundedness of the overall closed loop system dynamics. Very few results on adaptive compensation of infinite actuator failures in nonlinear systems have been reported in literature [6], [75]. The method proposed in [6] assures convergence of the tracking error in the mean square sense. However, no explicit calculation of L2 or L∞ on the tracking errors is derived which could hint on the tuning of parameters to achieve better performance. Different from [6], the bound estimation based approach in [75] suffers from a very high control requirement. No rigorous analysis is reported and the upper bound on the tracking error is not time invariant. Further, no insights on transient and input performance improvements are provided and the work only focuses on achieving boundedness of closed loop trajectories. Improvement of output transient performance
and its consequent quantification have always been an exciting problem in adaptive control of nonlinear systems irrespective of the parametrization of uncertainties. Efforts are needed towards proposal of new indirect adaptive control strategies for FTC applications in nonlinear systems which yield an improvement in output transient and steady state performance without substantially increasing the input usage. Besides, the problems of finite time estimation based adaptive compensation of infinite actuator failures in nonlinear systems characterizing linearly parametrizable/unparametrizable uncertainties and actuator failures, are not yet addressed in FTC literature and still remain open.
Compared to direct adaptive FTC strategies, one of the major advantages of the estimator/identifier based fault compensation design is that it uses only as much control effort as needed [96]. Hence, following development of a direct ARFTC to improve the transient performance without increasing the control usage, we adopt an indirect adaptive framework for FTC is adopted all throughout to have a judicious usage of control. Thereafter, one can come up with various ideas to improve the output transient performance without significantly effecting the control input requirement. An example of such an advancement are the ABSC strategies proposed in this thesis, as they restrain from increasing the virtual control gains to render improved transients and resort to the thought for alternatives which contribute to the input performance as well.
Motivated by the above-mentioned open research issues, the contributions of this thesis are enu- merated and briefly discussed in the following section.