Necessary optimality conditions in a nonsmooth control problem with variable structure

An optimal control problem with nonsmooth performance criterion described by a system of ordinary differential equations is considered. Necessary first-order optimality conditions are obtained.     

二次盐水及离子膜电解工序常见问题简析

介绍了二次盐水及离子膜电解工序的主要设备和流程,对二次盐水及离子膜电解工序运行中出现的问题进行了分析,并提出了解决措施。     

A stochastic maximum principle for systems with jumps, with applications to finance

We consider a stochastic control problem with linear dynamics with jumps, convex cost criterion, and convex state constraint, in which the control enters the drift, the diffusion, and the jump coefficients. We allow these coefficients to be random, and do not impose any L^p-bounds on the control.

We obtain a stochastic maximum principle for this model that provides both necessary and sufficient conditions of optimality. This is the first version of the stochastic maximum principle that covers the consumption–investment problem in which there are jumps in the price system.     

Synthesizing plans that contain actions with context-dependent effects1

This paper presents a method of solving planning problems that involve actions whose effects change according to the situations in which they are performed. The approach is an extension of the conventional planning methodology in which plans are constructed through an iterative process of scanning for goals that are not yet satisfied, inserting actions to achieve them, and introducing subgoals to these actions. This methodology was originally developed under the assumption that one would be dealing exclusively with actions that produce the same effects in every situation. The extension involves introducing additional subgoals to actions above and beyond the preconditions of execution normally introduced. These additional subgoals, called secondary preconditions, ensure that the actions are performed in contexts conducive to producing the effects we desire. This paper defines and analyzes secondary preconditions from a mathematically rigorous standpoint and demonstrates how they can be derived from regression operators.     

Casual reasoning in planning1

Reasoning about actions necessarily involves tracking the truth of assertions about the world over time. The SIPE planning system retains the efficiency of the STRIPS assumption for this while enhancing expressive power by allowing the specification of a causl theory. Separation of knowledge about causality from knowledge about actions relieves operators of much of their representational burden and allows them to be applicable in a wide range of contexts. The implementation of causal theories is described, together with examples and evaluations of the system's expressive power and efficiency.     

On the design of multiple key hashing files for concurrent orthogonal range retrieval between two disks

This paper concerns the following problem: given a set of multi-attribute records, a fixed number of buckets and a two-disk system, arrange the records into the buckets and then store the buckets between the disks in such a way that, over all possible orthogonal range queries (ORQs), the disk access concurrency is maximized. We shall adopt the multiple key hashing (MKH) method for arranging records into buckets and use the disk modulo (DM) allocation method for storing buckets onto disks. Since the DM allocation method has been shown to be superior to any other allocation methods for allocating an MKH file onto a two-disk system for answering ORQs, the real issue is knowing how to determine an optimal way for organizing the records into buckets based upon the MKH concept.

A performance formula that can be used to evaluate the average response time, over all possible ORQs, of an MKH file in a two-disk system using the DM allocation method is first presented. Based upon this formula, it is shown that our design problem is related to a notoriously difficult problem, namely the Prime Number Problem. Then a performance lower bound and an efficient algorithm for designing optimal MKH files in certain cases are presented. It is pointed out that in some cases the optimal MKH file for ORQs in a two-disk system using the DM allocation method is identical to the optimal MKH file for ORQs in a single-disk system and the optimal average response time in a two-disk system is slightly greater than one half of that in a single-disk system.     

Application of boundary element method to 3-D problems of coupled thermoelasticity

This paper deals with a new boundary element method for analysis of the quasistatic problems in coupled thermoelasticity. Through some mathematical manipulation of the Navier equation in elasticity, the heat conduction equation is transformed into a simpler form, similar to the uncoupled-type equation with the modified thermal conductivity which shows the coupling effects. This procedure enables us to treat the coupled thermoelastic problems as an uncoupled one, A few examples are computed by the proposed BEM, and the results obtained are compared with the analytical ones available in the literature, whereby the accuracy and versatility of the proposed method are demonstrated.     

Ergodicity of filtering process by vanishing discount approach

A new approach to study ergodicity of filtering processes is presented. It is based on the vanishing discount approach to discounted functional of filtering process. We show that limit superior of the Cesaro averages of the functionals is the same for all initial conditions from which the uniqueness of invariant measures of filtering processes follows. The approach is based on certain assumption for which we provide a sufficient condition using concavity arguments. In addition we show the existence of solutions to the Poisson equation corresponding to filtering process with concave functional. The assumptions are then extended to the controlled case and using similar concave arguments we obtain the existence of solutions to the Bellman equation corresponding to partially observed average cost per unit time problem.     

A note on the first-passage problem and VanMarcke’s approximation — short communication

Given a scalar, stationary, Markov process, this short communication presents a closed-form solution for the first-passage problem for a fixed threshold b. The derivation is based on binary processes and the general formula of Siegert [Siegert AJF. On the first-passage time probability problem. Physical Review 1951; 81:617–23]. The relation for the probability density function of the first-passage time is identical to the commonly used formula that was derived by VanMarcke [VanMarcke E. On the distribution of the first-passage time for normal stationary random processes. Journal of Applied Mechanics ASME 1975; 42:215–20] for Gaussian processes. The present derivation is based on more general conditions and reveals the criteria for the validity of the approximation. Properties of binary processes are also used to derive a hierarchy of upper bounds for any scalar process.