Provider: Czech digital library/Česká digitální knihovna - Institution: Academy of Sciences Library/Knihovna Akademie věd ČR - Data provided by Europeana Collections- The paper presents an iterative ...algorithm for computing the maximum cycle mean (or eigenvalue) of n×n triangular Toeplitz matrix in max-plus algebra. The problem is solved by an iterative algorithm which is applied to special cycles. These cycles of triangular Toeplitz matrices are characterized by sub-partitions of n−1.- All metadata published by Europeana are available free of restriction under the Creative Commons CC0 1.0 Universal Public Domain Dedication. However, Europeana requests that you actively acknowledge and give attribution to all metadata sources including Europeana
In recent years, Large Deviations theory has found important applications in many areas of engineering and science including communication and control systems. The objective of this note is to ...introduce and explore connections between certain fundamental concepts of Large Deviations theory and Information Theory, by introducing deterministic measures of information. The connections are established through the so-called rate functional associated with the Large Deviations principle, which lead to a natural definition of (max, plus) deterministic measure of information.
The solution of some forms of nonlinear H∞/L2-gain problems can be obtained via solution of the corresponding Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs). Alternatively, the ...solution of some classes of HJB PDEs have representations as solutions of L2-gain problems. Both can be obtained through solution of corresponding fixed-point problems - where the operators are the semigroups associated with the PDEs. In the linear/quadratic case, the solutions of these problems can be obtained simply by solution of associated Riccati equations. Here, an exploration of a way in which the operators for linear/quadratic problems can be combined (in the semiconvex dual space) to obtain operators, and hence solutions, for more general problems is begun.
This paper defines a max-plus algebra of signals for the evaluation of timing behavior of discrete event systems modeled by timed event graphs. The scope of this work is limited to infinite. periodic ...sequences for whhich finite representations called signals can be Computed. The implementation of this Inax-plus algebra allows a user to Compute supremal controllers for real-time. discrete event systems
We extend the hierarchical control method in (Li et al., 2004) to a more generic setting which involves cyclically repeated processes. A hierarchical architecture is presented to facilitate control ...synthesis. Specifically, a conservative max-plus model for cyclically repeated processes is introduced on the upper level which provides an optimal online plan list. An enhanced min-plus algebra based scheme on the lower level not only handles unexpected events but, more importantly, addresses cooperation issues between sub-plants and different cycles. A rail traffic example is given to demonstrate the effectiveness of the proposed approach.
Max-plus methods have been explored for solution of first-order, nonlinear Hamilton-Jacobi-Bellan partial differential equations (HJB PDEs) and corresponding nonlinear control problems. Specific ...applications to date have been to H/sub /spl infin// control and estimation. These methods exploit the max-plus linearity of the associated semigroups. In particular, although the problems are nonlinear, the semigroups are linear in the max-plus sense. These methods have been used successfully to compute solutions. Although they may be faster than more traditional methods, they still generally suffer from the curse of dimensionality - only the coefficient in the exponential rate of computational growth is reduced. There are natural spaces over the max-plus algebra in which to express solutions of HJB PDEs. The natural analog to the Laplace transform in ordinary spaces is the Legendre/Fenchel transform over max-plus spaces, the range space being referred to as the dual space. One can transform the semigroup operators into operators on the dual space. There are natural operations on the transformed operators which may be used to construct solutions of nonlinear control problems. In this paper, a method for exploiting operations in the Legendre/Fenchel transform space is used to develop a method for certain problems where the computational growth in the most time-consuming portion of the computations can be hugely reduced. One has computational growth which is linear in a certain measure of problem complexity for which linear/quadratic problems have the minimal complexity. Although the curse of dimensionality is unavoidable, the computational cost reductions are very high for some classes of problems.
The functional spaces that are an analog of Sobolev spaces, but on the basis of another algebraic operations (min -plus), are constructed from a convex Hamiltonian. The non-stationary ...Hamilton-Jacoby-Bellman equations are considered in these spaces following the standard extension of corresponding differential operator. The Cauchy problem has a unique solution which belongs to the spaces constructed. The corresponding semigroup of transformations coincides with that one which discribes the evolutinary process in the Lagrange problem.
Les espaces fonctionnelles qui sont des analogues des espaces de Sobolev mais sur une autre structure algébrique (celle de min-plus algébre) sont construits pour une Hamiltonien convexe. L'équation non-stationnaire de Hamilton-Jacoby-Bellmann est examinée dans ces espaces d'après la prolongation standard de l'opérateur différentiel correspondent. Le problème de Cauchy posséde une unique solution appartenant aux espaces construites. Le semi-groupe correspondent des transformations coïncide avec celui qui détermine l'évolution dans le problème de Lagrange.
Model predictive control (MPC) is a very popular controller design method in the process industry. One of the main advantages of MPC is that it can handle constraints on the inputs and outputs. ...Usually MPC uses linear discrete-time models. Recently we have extended this framework to max-plus-linear discrete event systems. In this paper we further explore this topic. More specifically, we focus on the closed-loop behavior and on the tuning aspects of MPC for max-plus-linear discrete event systems.
Bipartite systems form a subclass of min-max-plus systems, the latter are characterized by the operations maximization, minimization and addition. Such systems are nonlinear in both the linear ...classes of max-plus systems and min-plus systems. Structural and nonstructural fixed-points will be defined and properties pertaining to them will be derived. Bipartite systems can be thought of to be built up from more elementary subsystems (`molecules'). The decomposition into such elementary subsystems will be studied and also how properties of the `total' system depend on properties of these subsystems. Some counterexamples to some conjectures in an earlier paper on bipartite systems will be given as well.
The max-plus algebra has maximization and addition as basic operations, and can be used to model a certain class of discrete event systems. In contrast to linear algebra and linear system theory many ...fundamental problems in the max-plus algebra and in max-plus-algebraic system theory-still need to be solved. In this paper we discuss max-plus-algebraic analogues of some basic matrix decompositions from linear algebra that play an important role in linear system theory. We use algorithms from linear algebra to prove the existence of max-plus-algebraic analogues of the QR decomposition and the singular value decomposition.
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