Controlled Wild Algebras

The controlled wild algebra is introduced, a covering criterionfor a finite-dimensional algebra to be controlled wild is given,and this criterion is applied to the algebras with radical squarezero, algebras with zero relations, local algebras and finitep-group algebras. 2000 Mathematical Subject Classification:16G20, 16G60.     

Controlled jump processes

Finite and infinite planning horizon Markov decision problems are formulated for a class of jump processes with general state and action spaces and controls which are measurable functions on the time axis taking values in an appropriate metrizable vector space. For the finite horizon problem, the maximum expected reward is the unique solution, which exists, of a certain differential equation and is a strongly continuous function in the space of upper semi-continuous functions. A necessary and sufficient condition is provided for an admissible control to be optimal, and a sufficient condition is provided for the existence of a measurable optimal policy. For the infinite horizon problem, the maximum expected total reward is the fixed point of a certain operator on the space of upper semi-continuous functions. A stationary policy is optimal over all measurable policies in the transient and discounted cases as well as, with certain added conditions, in the positive and negative cases.     

Controlled Geometry via Smoothing

We prove that Riemannian metrics with a uniform weak norm can be smoothed to having arbitrarily high regularity. This generalizes all previous smoothing results. As a consequence we obtain a generalization of Gromov's almost flat manifold theorem. A uniform Betti number estimate is also obtained. Received: August 31, 1995.     

Controlled Deformation of Solids

A model of the control of elastic deformation of solids with a gradual variation in the position of the load is described. The search for a constrained extremum of the objective function is reduced to an unconstrained extremum problem. Possible engineering applications are suggested.     

Liapunov asymptotic stability and Zhukovskij asymptotic stability

In this paper the Liapunov stability and Zhukovkij stability of motion in continuous dynamical systems are discussed. It is shown that each type of asymptotic stability is typically characterized by omega limit set of an orbit of this type of stability.     

Controlled diffusions with boundary-crossing costs

This paper considers control of nondegenerate diffusions in a bounded domain with a cost associated with the boundary-crossings of a subdomain. Existence of optimal Markov controls and a verification theorem are established.Research supported by ARO Contract No. DAAG29-84-K-0005 and AFOSR 85-0227.     

Controlled networks and their applications

A new kind of networks is considered in which the flow is controlled by reconfiguring the network. Flow control models in the network are considered, and optimal flow control problems in the network are stated.     

On integral stability and Lipschitz stability of motion

We establish new conditions of integral stability and uniform Lipschitz stability based on the use of the comparison principle and a matrix-valued Lyapunov function. Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal Vol. 49, No. 1, pp. 77–83, January, 1997.     

Controlled diffusions in a random medium

Using homogenization theory we treat the problem of controlled diffusions in a random medium with rapidly varying composition. This involves homogenization of a nonlinear Bellman dynamic programming equation wtih rapidly varying random coefficients. The appropriate "averaged form" of this equation is derived to define the limiting contrl problem; and a precise convergence result is given     

Finitary Treatment of Operator Controlled Derivations

By combining the methods of two former papers of ours ([6] and [7]) we develop a finitary ordinal analysis of the axiom system KPi of Kripke‐P atek set theory with an inaccessible universe. As a main result we obtain an upper bound (in the fast‐growing hierarchy) for the provably recursive functions of KPi.     

C*-Algebras and Controlled Topology

We describe some aspects of the relationship between the controlled topology and C*-algebra approaches to the Novikov conjecture.     

Controlled rounding for tables with subtotals

The problem of rounding in statistical tables to protect confidentiality is an important problem in the area of data publication, especially for official statistics. Controlled rounding involves rounding the table data to a prespecified base while ensuring additivity to totals. Previous research provided a formulation of the controlled rounding problem of a simple two-way table as a transportation problem. This paper extends that work to tables with subtotals by using a capacitated transshipment formulation. It is shown that some forms of tables with subtotals always have a controlled rounding solution. Other table structures cannot be guaranteed such a solution under zero-restrictedness. Initial computational experience suggests that the method is viable for use in practical situations.     

Controlled Ornstein-Uhlenbeck process with chance constraints

In Ref. 1, existence and optimality conditions were given for control systems whose dynamics are determined by a linear stochastic differential equation with linear feedback controls; moreover, the state variables satisfy probability constraints. Here, for the simplest case of such a model, the Ornstein-Uhlenbeck velocity process, we evaluate the necessary conditions derived in Ref. 1 and compute a time-optimal control such that a given threshold value > 0 is crossed with probability of at least 1 – .This work was supported by the Sonderforschungsbereiche 21 and 72, University of Bonn, Bonn, West Germany.     

Controlled Markov set-chains under average criteria

In this paper, applying an interval arithmetic analysis, we consider the average case of controlled Markov set-chains, whose process allows for fluctuating transition matrices at each step in time. We introduce a v-step contractive property for the average case, under which a Pareto optimal periodic policy is characterized as a maximal solution of optimality equation. Also, in the class of stationary policies, the behavior of the expected reward over T-horizon as T approaches ∞ is investigated and the left- and right-hand side optimality equations are given, by which a Pareto optimal stationary policy is found. As a numerical example, the Taxicab problem is considered.     

Controlled markov processes and viscosity solutions

Controlled markov processes and viscosity solutions by W. H. Fleming and H. M. Soner. Springer-Verlag, New York (1993), 428 pp., $ 49.95. ISBN 0-387-97927-1.     

Arrow-Mangasarian Sufficient Conditions for Controlled Semimartingales

Abstract

This article shows a version of Arrow's generalization of Manga-sarian's sufficient conditions valid for controlled stochastic differential equations driven by semimartingales. The infinite horizon case is covered. An example is given.     

Controlled topology invariants of translation actions

We develop invariants Ωn of a translation action of a group on Rm analogous to the Bieri-Neumann-Strebel-Renz invariants Σn. The invariants Σn were defined to be the set of “directions” e∈_∂∞Rm such that a suitable universal G-space is (n−1)-connected over the half-spaces defined by e. We replace half-spaces by topologically more natural neighborhoods of e to obtain the new invariants Ωn. The invariants Σn and Ωn are related as follows: e∈Ωn if and only if every e^′ in an open -neighborhood of e lies in Σn.     

On short wave stability and sufficient conditions for stability in the extended Rayleigh problem of hydrodynamic stability

We consider the extended Rayleigh problem of hydrodynamic stability dealing with the stability of inviscid homogeneous shear flows in sea straits of arbitrary cross section. We prove a short wave stability result, namely, if k > 0 is the wave number of a normal mode then k > k _c (for some critical wave number k _c) implies the stability of the mode for a class of basic flows. Furthermore, if $ K(z) = \frac{{ - (U'_0 - T_0 U'_0 )}} {{U_0 - U_{0s} }} $ K(z) = \frac{{ - (U'_0 - T_0 U'_0 )}} {{U_0 - U_{0s} }} , where U ₀ is the basic velocity, T ₀ (a constant) the topography and prime denotes differentiation with respect to vertical coordinate z then we prove that a sufficient condition for the stability of basic flow is $ 0 < K(z) \leqslant \left( {\frac{{\pi ^2 }} {{D^2 }} + \frac{{T_0^2 }} {4}} \right) $ 0 < K(z) \leqslant \left( {\frac{{\pi ^2 }} {{D^2 }} + \frac{{T_0^2 }} {4}} \right) , where the flow domain is 0 ≤ z ≤ D.