Abstract We review recent progress in optimal control stochastic thermodynamics. Theoretical advances provide in-depth insight into minimum-dissipation with either full or limited (parametric) control, and spanning the limits from slow to fast driving weak strong driving. Known exact solutions give a window properties of which are reproduced by approximate methods relevant limits. Connections b...

``When in a difficult situation, it is sometimes better to give up and start all over again.'' While this empirical truth has been regularly observed wide range of circumstances, quantifying the effectiveness such heuristic strategy remains an open challenge. In paper, we combine notions optimal control stochastic resetting address problem. The emerging analytical framework allows one not only ...

‎In the present paper‎, ‎optimal heating of temperature field which is modelled as a boundary optimal control problem‎, ‎is investigated in the uncertain environments and then it is solved numerically‎. ‎In physical modelling‎, ‎a partial differential equation with stochastic input and stochastic parameter are applied as the constraint of the optimal control problem‎. ‎Controls are implemented ...

We consider an existence theorem for controi systems whose state variables for every t are in C, the set of continuous functions varying over a given set L The dependence of the state variables upon a ~ / i s induced by their dependence upon the initial state and the state equation governing the system. In contrast, the control u ---u(t) is taken as a measurable function of t alone. The usual s...

In this paper, we study a class of optimal stochastic control problems involving two different time scales. The fast mode of the system is represented by deterministic state equations whereas the slow mode of the system corresponds to a jump disturbance process. Under a fundamental “ergodicity” property for a class of “infinitesimal control systems” associated with the fast mode, we show that t...

This paper examines the numerical implementation of a linear programming (LP) formulation of stochastic control problems involving singular stochastic processes. The decision maker has the ability to influence a diffusion process through the selection of its drift rate (a control that acts absolutely continuously in time) and may also decide to instantaneously move the process to some other lev...

Modelling of the motion of a helicopter with a suspended load is described. The mathematical model takes into account stochastic disturbances acting on the load suspension point. The proposed approach allows solution of the problem of optimal control with minimization of oscillation and control power expenditure. The evolution of the system solution with time is investigated for various disturb...

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 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...