Generalizing results by Bryant and Griffiths [Duke Math. J., 1995, V.78, 531–676], we completely describe local conservation laws of second-order (1 + 1)-dimensional evolution equations up to contact equivalence. The possible dimensions of spaces of conservation laws prove to be 0, 1, 2 and infinity. The canonical forms of equations with respect to contact equivalence are found for all nonzero ...

We present in these lectures, in an informal manner, the very basic ideas and results of stochastic calculus, including its chain rule, the fundamental theorems on the representation of martingales as stochastic integrals and on the equivalent change of probability measure, as well as elements of stochastic differential equations. These results suffice for a rigorous treatment of important appl...

In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a stochastic control problem for an evolution system in a Hilbert space. The regularity of the solution of the adjoint equation, that is a backward stochastic equat...

Stockpiling and blending play a major role in maintaining the quantity and quality of the raw materials fed into processing plants, especially the cement, iron ore and steel making, and coal-fired power generation industries that usually require a much uniformed feed. Due to the variable nature of such materials, they even come from the same source and the produced ores or concentrates are seld...

Robust Parameter Design (RPD) has been used as the primary technique to reduce process and product variability. The offline choice of appropriate control factor settings allows RPD to ensure that noise factors have a minimum influence on responses. In this article, an alternative methodology of automatic process control is proposed, that is, controllable factors are adjusted online based on inp...

We formulate and solve a problem that combines the features of the so-called monotone follower of singular stochastic control theory with optimal stopping. In particular, we consider a stochastic system whose uncontrolled state dynamics are modelled by a general one-dimensional Itô diffusion. The aim of the problem that we solve is to maximise the utility derived from the system’s state at the ...

Abstract We consider a class of discrete-time stochastic control systems, with Borel state and action spaces, and possibly unbounded costs. The processes evolve according to the equation xt+1 = F (xt, at, ξt), t = 0, 1, . . . , where the ξt are i.i.d. random vectors whose common distribution is unknown. Assuming observability of {ξt}, we use the empirical estimator of its distribution to constr...

We study quadratic optimal stochastic control problems with control dependent noise state equation perturbed by an affine term and with stochastic coefficients. Both infinite horizon case and ergodic case are treated. To this purpose we introduce a Backward Stochastic Riccati Equation and a dual backward stochastic equation, both considered in the whole time line. Besides some stabilizability c...

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the...