This paper proposes a novel interpretation of the hybrid Deep Learning (DL) models in the form of an auxiliary semiclassical Optimal Control Problem (OCP) with a switched structure. The proposed equivalent reformulation of the problem of training a hybrid deep neural network allows to apply a widely developed solution methodology for OCPs to the trainable design of the network under consideration. In particular, we consider the reduced gradient method for a concrete numerical solution of the obtained OCP. We also establish the non-effectiveness of the generic necessary optimality conditions for a possible numerical treatment of the auxiliary OCP in the hybrid DL framework.

This paper is devoted to a novel approximation technique for optimal feedback control. We study a constrained Optimal Control Problem (OCP) in the context of a closed-loop dynamic system described by Ordinary Differential Equations (ODEs). The approximate optimal feedback control design we develop involves a specific$\beta$-relaxation technique (see [1]). We present here an initial research related to explicit approximations of the optimal control processes governed by the closed-loop dynamic systems. The obtained mathematical result has a potential to be extended to some concrete numerical solution algorithms for optimal feedback control problems.

This contribution deals with a new computational approach to optimal control design for a class of switched systems. The control strategy we develop is based on the proximal point method applied to a specific optimal control problem (OCP) with switched dynamics. The class of OCPs under consideration is widely applicable in optimization of electronic systems. We create constructive approximations for the initial sophisticated OCP, establish numerical stability of the resulting computational algorithm and develop an optimal control strategy. We finally discuss some numerical issues, study an illustrative example and also point possible generalizations of the elaborated control design in the context of hybrid dynamic systems.