Since the beginning of the 21st century, artificial intelligence (AI) has been reshaping almost
all areas of human society, which has high potential to spark the fourth industrial revolution …

Suppose ze Z is the state at time zero of a dynamical system defined on a Banach space Z,
and the state at time t is z (t). If we assume that the dynamics which govern the evolution …

In many areas of applied mathematics, decentralization of information is a ubiquitous
attribute affecting how to approach a stochastic optimization, decision and estimation, or …

The purpose of this paper is to compare the results which have been recently obtained in
optimal stochastic control. Various maximum principles are shown to derive from a general …

The classical theory of controllability for deterministic systems is extended to linear
stochastic systems defined on infinite-dimensional Hilbert spaces. Three types of stochastic …

The commonly adopted route to control a dynamic system and make it follow the desired
behavior consists of two steps. First, a model of the system is learned from input–output data …

We discuss several concepts of controllability for partially observable stochastic systems:
complete controllability, approximate controllability, and stochastic controllability. We show …

We consider optimal control problems for systems described by stochastic differential
equations with delay (SDDE). We prove a version of Bellman's principle of optimality (the …

In this paper we will give a general formulation of the certainty equivalence principle for
stochastic optimal control problems. Special attention is paid to the question:" What do we …

We attempt to give a historical account of the main ideas leading to the development of
nonlinear filtering and stochastic control as we know it today. We present a development of …