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On a Necessary and Sufficient Condition for Convergence of the Iterative algorithms Used in solving Dynamics Complex Systems

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IFAC Proceedings Volumes 2001年第3期34卷 207-211页

作者： Valentin Garban Marin S. Bica Computer Science and Control Systems Department Military Technical Academy B-dul George Coşbuc Nr. 81-83 Bucharest Romania Fax: 0040-1.3355763

The analisys and design of dynamic systems suposses to solve the linear algebraic system Ax = b , where A ϵ M n ( R ) is inversable and bϵ R n . The iterative methods are preferred for big values of n and particular forms of the matrix A (tridiagonal, pentadiagonal, blocks modular) to solve the equivalent system X = BX + b , where B = I n -A . The central topic of this paper is to proof the necessary and enough conditions of convergence of the iterative, arbitrary process X m+1 = BX m + b 1 , cu x 0 ϵ R n , associated to the equation X = BX + b , but in terms of A matrix (Theorem 1).

关键词： Accretive operators convergence of iterative methods Lipschitzian application solving algorithms vector norm

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Time reduction of the Dynamic Programming computation in the case of hybrid vehicle

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INTERNATIONAL JOURNAL OF APPLIED ELECTROMAGNETICS AND MECHANICS 2017年第Sup2期53卷 S213-S227页

作者： Vinot, Emmanuel IFSTTAR 25 Ave Francois Mitterrand F-69500 Bron France

Deterministic Dynamic Programming is frequently used to solve the management problem of hybrid vehicles (choice of mode and power sharing between thermal and electric sources). However, it is time consuming and thus difficult to use in global sizing optimization or in parametric studies. This paper presents a comparison between three methods to compute the DDP problems. These methods are applied on the well known case of the Toyota PRIUS. It proves that a dense matrix method can reduce the computation time by up to 10 compared to more intuitive solving methods.

关键词： Deterministic Dynamic Programming solving algorithms hybrid vehicle

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Dynamic Temporal Logical Operations in Multi-Agent Logics

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ALGEBRA AND LOGIC 2023年第5期61卷 407-419页

作者： Rybakov, V. V. Siberian Fed Univ Inst Math & Informat Krasnoyarsk Russia Inst Informat Syst Novosibirsk Russia

We study temporal multi-agent logics using a new approach to defining time for individual agents. It is assumed that in any time state each agent (in a sense) generates its own future time, which will only be available for analysis in the future. That is, the defined time interval depends both on the agent and on the initial state where the agent starts to act. It is also assumed that the agent may have intervals of forgotten (lost) time. We investigate problems of unification and problems of computable recognizing admissible inference rules. An algorithm is found for solving these problems based on the construction of a finite computable set of formulas which is a complete set of unifiers. We use the technique of projective formulas developed by S. Ghilardi. It is proved that any unifiable formula is in fact projective and an algorithm is constructed which creates its projective unifier. Thereby we solve the unification problem, and based at this, find the solution to the open problem of computable recognizing admissible inference rules.

关键词： temporal logics multi-agent logics admissible inference rules unification problem solving algorithms

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Multi-Agent Logics with Multi-Valuations and Intensional Logical Operations

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LOBACHEVSKII JOURNAL OF MATHEMATICS 2020年第2期41卷 243-251页

作者： Rybakov, V. V. Siberian Fed Univ Inst Math & Informat Krasnoyarsk 660041 Russia Russian Acad Sci Inst Informat Syst Siberian Branch Novosibirsk Russia

We consider a multi-agent logic based on linear temporal logic. This logic uses as the semantics relational temporal models with multi-valuations-the models have separate valuations for all agents. We introduce in the logical language two new intensional logical operations-plausibleanddominates-to capture the feature of uncertainty. The main mathematical problem we are dealing with is the satisfiability problem. We solve it and find deciding algorithm. In the final part of paper we discuss interesting open problems for possible further investigations.

关键词： multi-agent logics information knowledge temporal logic multivaluations at relational models satisfiability problem solving algorithms

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A comprehensive survey of sparse regularization: Fundamental, state-of-the-art methodologies and applications on fault diagnosis

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EXPERT SYSTEMS WITH APPLICATIONS 2023年第PartA期229卷

作者： Li, Qing Anhui Agr Univ Dept Mech Engn Hefei 230036 Peoples R China

Sparse regularization has been attracting much attention in industrial applications over the past few decades. By exploiting the latent data structure in low-dimensional subspaces, a significant amount of research achievements have been realized in signal/image processing, pattern recognition and system identification, etc. However, very few systematic review or comprehensive survey are reported for sparse regularization including fundamentals, state-of-the-art methodologies, and applications on fault diagnosis. To fill this gap, this article conducts an in-depth review of the state-of-the-art technologies of sparse regularization, and the R & D of sparse regulariza-tion applied to fault diagnosis will also be summarized. Specifically, we discuss the rationales of cause formu-lation, algorithm idea, algorithm merits, algorithm demerits and computing techniques for each category. The availability and practicability of several representative models of sparse regularization are investigated with real-world experimental datasets. Finally, benefiting from theoretical developments of the sparse regularization, open/upcoming challenges, instructive perspectives, as well as possible future trends of the sparse regularization for prognostic and health management (PHM) are discussed.

关键词： Sparse regularization Convex sparse regularization Nonconvex sparse regularization solving algorithms Fault diagnosis

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