TURK 2025

In controlling many real processes, the implementation of frequent changes in the values of control actions is either associated with great difficulties in implementation or is completely impossible. Therefore, from a practical point of view, there is a need to study optimal control problems on given classes, for example, on classes of piecewise constant, piecewise linear and other control actions. Various other aspects of optimal control on the class of piecewise linear functions have been studied by many authors [1–3].
In the article, the minimization problem is investigated of piecewise linear functional in non-linear optimization of oscillation processes described by Fredholm integro-differential equations. An algorithm has been developed for constructing a generalized solution to boundary value problem that describes the oscillation processes. Using the maximum principle for systems with distributed parameters, optimality conditions are determined in the form of equality and inequality.