Legendre Approximations for Solving Optimal Control Problems Governed by Ordinary Differential Equations

Abstract

In this paper Legendre integral method is proposed to solve optimal control problems governed by higher order ordinary differential equations. Legendre approximat ion method reduced the problem to a constrained optimizat ion problem. Penalty partial quadratic interpolation method is presented to solve the resulting constrained optimization problem. Error estimates for the Legendre appro ximations are derived and a technique that gives an optimal appro ximat ion of the problems is introduced. Numerical results are included to confirm the efficiency and accuracy of the method.

Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method

“…Interestingly, Chebyshev-Gauss-Lobatto points have also been used as collocation and interpolation points in the solutions of optimal control problems governed by Volterra integrodifferential equations [9,10]. Using either of the two collocation points to collocate (7) together with the initial conditions given in (3b) will result in a system of + 1 linear algebraic equations in + 1 unknowns.…”

Optimal control of system governed by nonlinear volterra integral and fractional derivative equations

“…In Peyghami et al (2012, the authors proposed some hybrid approaches leveraging steepest descent and two-step Newton methods for achieving optimal control together with the associated optimal state. Some other methods have been described in El-Kady and Moussa (2013); Li (2010); Maleknejad et al (2012).…”

Existence of optimal control for an integro‐differential Bolza problem

“…Most of the existing results concern the existence of a solution to (), its uniqueness and continuous dependence on parameters, as well as numerical methods of finding it. Numerical solutions to optimal control problems governed by integro‐differential equations of Volterra type were studied, for example, in Reference 2 (case of nonlinear control system and nonlinear integral cost functional), and in References 3 and 4 (case of linear system and quadratic cost functional). Optimal control of feedback type involving also the past history of the solution has been obtained in Reference 5 for a scalar linear system (with f 2 = u ) and quadratic cost functional.…”