Abstract:
In this dissertation, an approach for finding the cost function to the time-invariant linear quadratic regulator (LQR) problem is proposed. The proposed approach is based on the solution to the inverse LQR problem. First, we introduce LQR method for designing the controller gain matrix which will make it better to understand the inverse LQR problem. Also, LQR is applied to time-delayed system. Next, an efficient method, to determine a solution to the general case of inverse LQR, linear matrix inequality (LMI) is described. This report includes linear matrix inequality method applied to multi input multi output system as well as to single-input single-output system. The first formulation technique, LMI, provides unique solution if the solution is feasible. If the solution is not feasible, in that case, we have introduced gradient descent method. The gradient descent is a least square minimisation technique which is applied to approximate the solution. When LMI produces infeasible solution resulting from the perturbed estimated controller gain matrix K which is obtained from noisy experimental data, by the estimation error then the gradient descent method is very useful. A proposed gradient descent algorithm is also proposed to find a good initial point for LMI minimization problem. Further, we provide some examples to illustrate how to apply our approach to different systems. Next, the mathematical model of DC servo motor is explained followed by application of the proposed approach to DC servo motor. The results show that we find weight matrices Q and R for the given controller gain matrix to be optimal
