چكيده به لاتين
The objective of this thesis is to design an optimal control law for a class of multivariable linear systems with lumped uncertainty, taking into account the operational constraints of the system and based on output feedback. For this purpose, first by using the dynamic model and system's output information, the cost function and constraints of the constrained optimization problem are appropriately defined. Then, a Projection Recurrent Neural Network is employed to solve the problem online and find the optimal control signal. High computational speed, stability and giving an explicit form of the control law are among the features of the projection recurrent network. The methods of the thesis are presented in two approaches in terms of control configuration and the type of optimization problem. In the first approach, a direct output feedback configuration is taken, in which first, an augmented minimum-phase system is composed using a parallel feed-forward compensator; Then, the constrained optimization problem is written to stabilize the external dynamics of the augmented system with input constraints. In this case, along with the constrained stabilization of the external subsystem, due to the use of the feedforward compensator, the stability of the internal states is also guaranteed without the need to measure or estimate them. In this way, advantages such as satisfying the input constraints and the possibility of using the method for non-minimum-phase systems are obtained. Nevertheless, there are shortcomings such as not generalizing to time-varying tracking problems and not considering output constraints. In the second approach, with the aim of dealing with these cases, an integral-type primary performance index is selected. Therefore, output errors are considered up to a finite horizon in order to achieve proper tracking performance in the problem. This index is converted into a finite-dimensional cost function using the Taylor approximation method. In the following, with the aid of the concept of Control Barrier Function, the output constraints are transformed into inequalities that can be integrated with the cost function in a constrained optimization problem in such a way that observing the transformed inequalities provides a sufficient condition for satisfying the output constraints. In this method, due to the appearance of states and uncertainties in the optimization problem, the output feedback configuration is realized through estimating the states and uncertainties using high-order derivative-based Extended State Observers. The stability of this method is shown in an integrated analysis of the closed-loop dynamics and recurrent neural network. In each of the mentioned approaches, by providing simulated examples, the capability of the methods to achieve the desired goals is illustrated along with mentioning the advantages and disadvantages of each. Furthermore, the high effectiveness of the proposed methods is demonstrated by making comparisons with related advanced methods.
