optimal controller design for a group of linear systems with the approach of simultaneous determination of model and controller parameters

This paper designs an optimal controller for the simultaneous determination of physical model parameters and LQR controller parameters. In some systems, it is possible to determine some of the model parameters by the designer. In conventional methods of optimal controller design for this group of systems, first, the model parameters are determined by the designer, and then in a separate step, the controller is designed for the definite model. In this paper, a method for the simultaneous determination of these two sets of parameters is presented for continuous-time linear systems. Simultaneous parameter determination is a nonlinear and non-convex optimization problem that in this paper a new method is considered to solve this problem. The non-convex optimization problem is transformed into a convex optimization problem by performing simplifications and then solved by the CVX toolbox of MATLAB software. The result is a controller with less control cost in comparison to conventional methods for this group of systems. By providing a simulation example, the performance improvement of the proposed method is shown.