چكيده به لاتين
In this thesis, the problem of integrated fault-tolerant control design for affine nonlinear systems subject to component and actuator faults is investigated. The proposed integrated method covers the both detection and compensation of the faults in the presence and absence of the input and state constraints and guarantees the tracking of the reference states while minimizing the cost function desired by the designer. In this regard, to eliminate the need for knowledge of system dynamics and estimation of fault magnitudes, the proposed optimal method is developed based on reinforcement learning with a dual neural network (NN) approximation structure of identifier-critic. The structure of the identifier is considered as a single-layer adaptive NN, which is based on estimating the system in terms of filtered basis functions. Using the Lyapunov stability theory, it is shown that in addition to the convergence of the identifier outputs to the system states, the weights of the identifier NN also converge to their true values, which is a necessary condition for the convergence of training process to the optimal control policy in this structure. the identifier NN weight update law, the experience replay method is used, and the forgetting factor is considered variable in it, leading to increased convergence rate and robustness to measurement noise, as well as reducing estimation error. In this method, solving the optimal fault-tolerant tracking control problem for the main system in both constrained and unconstrained cases is equivalent to solving the optimal unconstrained stabilization problems for an augmented system that consists of the dynamics of the tracking errors and the reference path. The cost function in stabilization problems is considered in a discounted form, where the boundedness of control input and the safety of system states are guaranteed, respectively, by selecting an appropriate cost function on the input signal and suitable control barrier functions on the states. The critic NN is responsible for approximating the cost function and is trained simultaneously with the identifier NN. On the other hand, when a fault occurs in the system, it operates under inappropriate control until the fault occurrence is detected, which does not necessarily guarantee stability. Therefore, to enable training initiation from the controller before the fault occurrence, a stabilizing term is included in the critic NN update law. In this structure, fault detection is performed solely based on the instantaneous value of the residual error of the Hamilton-Jacobi-Bellman (HJB) equation, without the need for any model. The Uniformly Ultimately Boundedness (UUB) of identifier and critic NN weight errors and, as a result, the convergence of the control input to the neighborhood of the optimal solution are all proved by Lyapunov theory. The simulation results are given to validate the effectiveness of the developed methods.
