Abstract
An algorithm is proposed to solve the linear quadratic optimal control problem subject to terminal state constraints, state and control constraints and interior point constraints. The algorithm is based on parameterizing the system state variables using a finite length Chebyshev series of unknown parameters, and the control variables are obtained as a function of the approximated state variables such that the system differential equations are satisfied. After reformulating the problem using the proposed algorithm, the constrained optimal control problem is converted into a quadratic programming problem which can be solved easily. Moreover, by using the proposed algorithm there is no need to integrate the system or costate differential equations.
