Optimal Control of Evolution Differential Inclusions with Polynomial Linear Differential Operators

Abstract

In this chapter, we studied a new class of problems in the theory of optimal control defined by polynomial linear differential operators. As a result, an interesting Mayer problem arises with higher order differential inclusions. Thus, in terms of the Euler-Lagrange and Hamiltonian type inclusions, sufficient optimality conditions are formulated. In addition, the construction of transversality conditions at the endpoints of the considered time interval plays an important role in future studies. To this end, the apparatus of locally adjoint mappings is used, which plays a key role in the main results of this chapter. The presented method is demonstrated by the example of the linear optimal control problem, for which the Weierstrass-Pontryagin maximum principle is derived.

Optimal control of hyperbolic type discrete and differential inclusions described by the Laplace operator

“…It is well known [34] that in the problem with ordinary polynomial linear differential operators Ax = s k=1 p k (t)D k x of the s-th order with variable coefficients p k : [0, T ] → R 1 and with the operator of derivatives D k (k = 1, . .…”

“…Over the past decades, great progress has been made in various areas of optimal control problems described by ordinary [1,2,4,7,9,10,14,19,21,23,25,30,31,33,34,37,40] and partial differential equations/inclusions [3, 5, 11-13, 16, 18, 20, 22, 29, 32, 36, 39, 41]. The work [6] investigates boundary value problems for systems of Hamilton-Jacobi-Bellman first-order partial differential equations and variational inequalities, the solutions of which obey the viability constraints.…”

Optimization of boundary value problems for higher order differential inclusions and duality

“…Over the past decades, great progress has been made in various areas of optimal control problems described by ordinary [1,6,8,10,11,13,14,16,19,20,24,[28][29][30][31][36][37][38][39] and partial differential equations/inclusions [4,5,15,[21][22][23]26]. In the paper [12] the averaging method is used to study singularly perturbed differential inclusions in an evolutionary triplet.…”