Open-Loop Control of a Plant Described by a System with Nonsmooth Right-Hand Side

A Numerical Method for Finding the Optimal Solution of a Differential Inclusion

“…Reducing solving differential inclusions to a variational problem via corresponding support functions was carried out in papers [13], [14], [15]. Some other nonsmooth problems of optimal control and variational calculus were considered via similar methods in papers [16], [17]. The paper also uses some ideas of V. F. Demyanov scientific school on nondifferentiable minimization.…”

The Subdifferential Descent Method in a Nonsmooth Variational Problem

“…Problem (21) at each fixed t ∈ [0, T ] is a finite-dimensional problem of finding the distance from zero to a convex compact (the subdifferential). This problem can be effectively solved for a wide class of functions; the next paragraph describes its solution.…”

“…In works [17], [18] the methods of the subdifferential and the hypodifferential descents were applied to some classes of smooth variational problems with nonsmooth penalty summands which take into account the restriction on the right endpoint. These methods were also applied to constructing optimal control in problems with the subdifferentiable quality functional in paper [19] and also to the problem of transferring a system of differential equations from one point to another in works [20], [21]. The finite-dimensional quasidifferential descent method was applied to optimization of a control system with a nonsmooth objective functional in Mayer form in paper [22].…”

The codifferential descent method in the problem of finding the global minimum of a piecewise affine objective functional in linear control systems

“…Введение. Несмотря на большое количество теоретических исследований негладких задач теории оптимального управления в различных постановках (в том числе получение принципа максимума для таких задач) [1][2][3][4][5][6][7], практическая сторона до сих пор остается плохо развитой в силу затруднения применения, как правило, сложно устроенных условий оптимальности при построении численных методов для решения конкретных задач. В некоторых работах численные методы основаны на предварительном процессе сглаживания целевой функции.…”

“…С помощью формулы Коши легко непосредственно проверить, что функция x(T, σ p ) аффинна по своему аргументу σ p . Действительно, (1), нормированная в нуле. Отсюда и из замечания 4 следует: из сделанного предположения о том, что функция ψ(x) кусочно-аффинна, вытекает кусочная аффинность функции ϕ(σ p ).…”