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Abstract
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Time-delay, uncertainty, input constraint, and fragility of the controller are the factors that are encountered in a vast majority of practical systems. These issues cause degradation in the performance of the controller or even make systems unstable. Controlling systems in the presence of such issues arisen in practice with classic controllers is not efficient and, in some cases, not straightforward.
This thesis aims to address the consideration of time-delay, uncertainties, input constraint, and fragility of the controller, simultaneously in designing an optimal controller using robust model predictive control (RMPC). The uncertainties are considered to be in a general additive form, and the control signal is perturbed with additive perturbation. The design of non-fragile RMPC is then interpreted as an optimization problem with respect to some conditions in terms of linear matrix inequalities. By employing the Lyapunov stability theory and linear matrix inequality technique, sufficient conditions are derived to determine the non-fragile robust model predictive control for all admissible additive uncertainties and perturbed control signals by minimizing the upper bound of the cost function.
The proposed controller is designed in two versions; delay-independent and delay–dependent. Within the first approach, the information of delay is not considered in the design of the controller. To have a less conservative controller when the range of time- delay is available, especially for small delays, a delay-dependent version is developed in the next step through considering a suitable form of a quadratic function including some integral terms to contain the information of time-delay. In this respect, the proposed controller provides a suitable linear feedback control law depending on time-delay such that a robust performance being achieved to the possible existence of uncertainties. The efficiency of the proposed methodology in controlling time-delay systems with uncertain
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