This paper addresses the robust stability for a class of linear discrete-time stochastic systems with convex polytopic uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established...

We solve optimal transportation problem using stochastic optimal control theory. Indeed, for a super linear cost at most quadratic at infinity, we prove Kantorovich duality theorem by a zero noise limit (or vanishing viscosity) argument.. We also obtain a characterization of the support of an optimal measure in Monge-Kantorovich minimization problem (MKP) as a graph. Our key tool is a duality r...

The paper provides a review of the basics of financial engineering, with a few examples. We emphasize connections with control theory in a broad sense rather than with stochastic control theory in particular, and the reader is not assumed to be versed in stochastic processes. After a discussion of the main methods of financial risk management, a state-space framework for modeling financial mark...

We consider a class of stochastic control problems where uncertainty is due to driving noises of general nature as well as to rapidly fluctuating processes affecting the drift. We show that, when the noise ”intensity” is small and the fluctuations become fast, the stochastic problems can be approximated by a deterministic one. We also show that the optimal control of the deterministic problem i...

Optimal trajectories of deterministic systems satisfy Pontryagin’s maximum principle and can be computed efficiently. Related results for stochastic systems exist but they lack the simplicity and computational efficiency of the deterministic case. Here we show that a certain class of both discrete-time and continuous-time nonlinear stochastic control problems obey a classic maximum principle, i...

Decentralized stochastic control refers to themulti-stage optimization of a dynamical system bymultiple controllers that have access to different information. Decentralization of information gives rise to new conceptual challenges that require new solution approaches. In this expository paper, we use the notion of an information-state to explain the two commonly used solution approaches to dece...

We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form of stochastic maximum principle. AMS Subject Classification. 93Exx

This paper presents a “Fingerprint Method” for modeling and subsequently characterizing stochastically controlled actuator arrays. The actuator arrays are built from small actuator cells with structural elasticity. These cells are controlled using a bistable stochastic process wherein all cells are given a common input probability (control) value which they use to determine whether to actuate o...

Based on frequency-domain transformation technique, this paper proposes an attack detection scheme for stochastic control systems under stochastic cyber-attacks and disturbances. The focus is on designing an anomaly detector for the stochastic control systems. First, we construct a model of stochastic control system with stochastic cyber-attacks which satisfy the Markovian stochastic process. A...

In this paper we study a class of pathwise stochastic control problems in which the optimality is allowed to depend on the paths of exogenous noise (or information). Such a phenomenon can be illustrated by considering a particular investor who wants to take advantage of certain extra information but in a completely legal manner. We show that such a control problem may not even have a “minimizin...