Approximations of Relaxed Optimal Control Problems

Optimal Control of Mechanical Systems

“…A great amount of work is devoted to numerical methods for optimal control problems (see [5,[7][8][9] and references therein). One can find a fairly complete review of the main results in [6,8].…”

“…Using a discretization of (4.8), we can obtain a finite-dimensional approximating problem. Note that discrete approximation techniques have been recognized as a powerful tool for solving optimal control problems [6,8]. Let N be a sufficiently large positive integer number and let Ᏻ N := {t 0 = 0, t 1 ,...,t N = 1} be a (possible nonequidistant) partition of [0,1] with…”

“…There is a number of results scattered in the literature on numerical methods for optimal control problems that are very often closely related, although apparently independent. One can find a fairly complete review in [5][6][7][8][9].…”

“…There are many variants of gradient algorithms depending on whether the problem is a priori discretized in time, and on the optimization solver used. A gradient-based method evaluates gradients of the objective functional [5,6]. The calculation of second-order derivatives of the objective functional can be avoided by applying a sequential-quadratic-programming-(SQP-)type optimization algorithm in which these derivatives are approximated by quasi-Newton formulas.…”

A computational approach to optimization of controlled mechanical systems

“…There is a number of results scattered in the literature on numerical methods for optimal control problems that are very often closely related, although apparently independent. One can find a fairly complete review in [33], [29], [30], [5], [6].…”