Contribution to robust fault-tolerant predictive control with constraints for hybrid systems.

Abstract

In this dissertation, the main objective is to focus on proposing a new reliable control scheme to handle the undesirable associated inputs (faults/time –delay) of HS. In this regard, we raised two aspects to be studied in this dissertation: the hybrid control (HC) and the control of hybrid systems in the presence of faults and time-delay with constraints (HFTPC). The hybrid control design (HFTPC) is based on the interaction of two components: a robust model predictive control (RMPC) to cope with time delay as continuous dynamic and robust fault tolerant predictive control as discrete dynamic. The aim of this work is designing a robust optimal fault-tolerant predictive control (HFTPC) for a trajectory tracking, applied to a class of non-linear hybrid actuator systems subject to faults and time-delay. In fact, the introduction of time-delay and actuator faults into a hybrid system model results in a dynamic system converted to a strict feedback model. To improve the dynamic performances and decrease the conservatism, a dynamic mechanism of estimation is employed to estimate the actuators faults, in order to compute the optimal solution, while the performance of the hybrid system is preserved. The optimal solution of the HFTPC approach is computed online, by minimizing an upper bound of a specific cost function on infinite horizon, using min-max optimization method to derive necessary conditions in terms of LMIs; subject to the imposed constraints, faults and time-delays. However, an inspiring analysis is provided to improve the dynamics of a hybrid manipulator arm, which can be extended for some classes of hybrid systems, to decrease the computation burden. The state-space model has been reformulated by introducing the output tracking errors, in order to increase the hybrid controller degrees of freedom. Then, an optimal control strategy is designed to operate in the industrial robot arm with the desired position, with a compensation of the loss of efficiency or failure of the actuator in the presence of time-delays. To achieve this optimality, we have used the Lyapunov-Krasovskii function combined with an optimized cost function and observer error, to establish necessary paradigm to obtain a stable and less conservative conditions that is dependent delay-range in terms of LMIs, in order to enhance the feasibility and the stability of the closed loop system. The obtained results are improved and outperformed those obtained using the QP method. In addition, they have been compared with several existing works mentioned in this dissertation