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.
