In this paper, we present connections between recent developments on the linearly-solvable stochastic optimal control framework with early work in control theory based on the fundamental dualities between free energy and relative entropy. We extend these connections to nonlinear stochastic systems with non-affine controls by using the generalized version of the Feynman–Kac lemma. We present alt...

The purpose of this paper is to elucidate a dichotomy between past and future in prediction of multivariate time-series. More specifically, vector-valued gaussian stochastic processes may be deterministic in one time-direction and not the other. This fact, which is absent in scalar-valued processes, is deeply rooted in the geometry of the shift-operator. The exposition and the examples we discu...

The Pontrjagin maximum principle solves the problem of optimal control of a continuous deterministic system. The discrete maximum principle solves the problem of optimal control of a discrete-time deterministic system. The maximum principle changes the problem of optimal control to a two point boundary value problem which can be completely solved only in special tasks. It was probably the reaso...

An optimal indirect stochastic adaptive control is obtained explicitly for linear time-varying discrete-time systems with general delay and white noise perturbation, while minimizing the variance of the output around a desired value one step ahead. The resulting controller incorporates parameter uncertainties. The solution unifies and generalizes previously known results, which become special c...

In this paper, we investigate pollutant reduction policies under uncertainty. We assume that when an agent reduces quantity of a pollutant, it incurs costs. We consider two kinds of policies distinguished by their costs. One policy incurs proportional reduction cost (Case 1) and the other incurs fixed and proportional reduction costs (Case 2). To solve these problems, we formulate the agent’s p...

We investigate how stochastic reaction processes are affected by external perturbations. We describe an extension of the deterministic metabolic control analysis (MCA) to the stochastic regime. We introduce stochastic sensitivities for mean and covariance values of reactant concentrations and reaction fluxes and show that there exist MCA-like summation theorems among these sensitivities. The su...

In the paper a stochastic control model is studied, that admits a diffusion approximation. In the prelimit model the disturbances are given by noise processes of various types: additive stationary noise, rapidly oscillating processes, and discontinuous processes with large intensity for jumps of small size. We show that a feedback control, that satisfies a Lipschitz condition and is δ−optimal f...

Controlled discrete-time stochastic processes are studied using the convex-analytic approach. Some new properties of strategic measures spaces are established, particular Markov models are considered. The meaningful example is presented.