This paper presents a version of the Certainty Equivalence Principle, usable for nonlinear, variable end-time, partial observation Zero-Sum Differential Games, which states that under the unicity of the solution to the auxiliary problem, optimal controllers can be derived from the solution of the related perfect observation game. An example is provided where in one region, the new extended resu...

We consider a single-echelon, single-item inventory system where both demand and lead-time are stochastic. Continuous review policy is used to control the inventory system. The objective is to calculate the reorder point level under stochastic parameters. A case study is presented in Neonatal Intensive Care Unit. Keywords—Inventory control system, reorder point level, stochastic demand, stochas...

We consider linear control systems in a Hilbert space over an unbounded time interval of the form y′ α(t) = (A− αI)yα(t) +Bu(t), t ∈ (−∞, T ], with bounded control operator B, under appropriate stability assumptions on the operator A. We study how the space of states reachable at time T depends on the parameter α ≥ 0. We apply the results to study the dependence on α of the Cameron–Martin space...

We consider stochastic control systems affected by a fast mean reverting volatility Y (t) driven by a pure jump Lévy process. Motivated by a large literature on financial models, we assume that Y (t) evolves at a faster time scale t/ than the assets, and we study the asymptotics as → 0. This is a singular perturbation problem that we study mostly by PDE methods within the theory of viscosity so...

Decision-making under uncertainty is a natural part of everyday life of every human being. In societal science, various aspects of decision-making were studied, mostly in the area of psychology. In technical science, the process was formalized using probability theory yielding so called Bayesian theory of decision making (Berger, 1985). However, one of the key assumptions of this theory is that...

We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of optimality for two models. The first concerns the strict (classical) controls. The second is an extension of the first to relaxed controls, who are a measure va...

The heating, ventilation, and air-conditioning (HVAC) system account for substantial energy use in buildings, whereas a large group of occupants is still not actually feeling comfortable staying inside. This poses the issue developing energy-efficient HVAC control, i.e., reduce (cost) while simultaneously enhancing human comfort. brief pursues objective studies stochastic optimal control subjec...

This paper considers robust reduced order H∞ observer-based control for stochastic systems. The approach is divided into two steps. First, we search for a linear control law to ensure H∞ specification. Then, the obtained linear combination of the state is used to solve an “unbiasedness” (decoupling) condition on the drift part of the closed-loop system. Finally, deterministic functional filteri...

In this paper we solve a finite-horizon partially observed risk-sensitive stochastic optimal control problem for discrete-time nonlinear systems and obtain small noise and small risk limits. The small noise limit is interpreted as a deterministic partially observed dynamic game, and new insights into the optimal solution of such game problems are obtained. Both the risk-sensitive stochastic con...