LINEAR TIME QUADRATIC OPTIMAL CONTROL SYSTEMS

Abstract

In this project, we discussed both linear time invariance and time varying optimal control problems with quadratic performance index, and approximated control variable, state variable and performance index using Legendre scaling function and Chebyshev scaling function methods with unknown coefficients. The linear time invariant and time varying problems were parameterized based on control-state parameterization technique such that the objective function and the constraints are casted in terms of state variable and control variable. These two methods were converting the linear time quadratic optimal control problems into quadratic programming problems and the converted problems were solved using MATLAB. Finally, some different illustrative examples were solved to show the applicability and effectiveness of the presented methods. Then these two methods were examined on the same examples and when we increase the order of polynomial (M), then the computational results of the proposed methods gave better results but when we compare these two methods, Legendre scaling function was better than Chebyshev scaling function with regard to optimal value. Hence, the Legendre scaling function method is more suitable for solving the linear time quadratic optimal control systems. This project can be extending to solve nonlinear time quadratic optimal control problems with inequality constraints using these two methods.