Computational Method for Optimal Guidance and Control Using Adaptive Gaussian Quadrature Collocation

Costate approximation in optimal control using integral Gaussian quadrature orthogonal collocation methods

Two methods are presented for approximating the costate of optimal control problems in integral form using orthogonal collocation at Legendre–Gauss (LG) and Legendre–Gauss–Radau (LGR) points. It is shown that the derivative of the costate of the continuous-time optimal control problem is equal to the negative of the costate of the integral form of the continuous-time optimal control problem. Us...

A Computational Method for Solving Optimal Control Problems and Their Applications

In order to obtain a solution to an optimal control problem‎, ‎a numerical technique based on state-control parameterization method is presented‎. ‎This method can be facilitated by the computation of performance index and state equation via approximating the control and state variable as a function of time‎. ‎Several numerical examples are presented to confirm the analytical findings and illus...

The Gaussian Quadrature Method

A Method for Solving Optimal Control Problems Using Genetic Programming

This paper deals with a novel method for solving optimal control problems based on genetic programming. This approach produces some trial solutions and seeks the best of them. If the solution cannot be expressed in a closed analytical form then our method produces an approximation with a controlled level of accuracy. Using numerical examples, we will demonstrate how to use the results.

A Gauss–Lobatto quadrature method for solving optimal control problems

This paper proposes a direct approach for solving optimal control problems. The time domain is divided into multiple subdomains, and a Lagrange interpolating polynomial using the Legendre–Gauss– Lobatto points is used to approximate the states and controls. The state equations are enforced at the Legendre–Gauss–Lobatto nodes in a nonlinear programming implementation by partial Gauss–Lobatto qua...