We analyze interconnections of finitely many (exponentially) stable positive systems which interact via uncertain couplings of arbitrarily prescribed structure. We view the couplings as structured perturbations of the...
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ISBN:
(纸本)9783642028939
We analyze interconnections of finitely many (exponentially) stable positive systems which interact via uncertain couplings of arbitrarily prescribed structure. We view the couplings as structured perturbations of the direct sum of the subsystems and derive computable formulas for the corresponding stability radius with respect to some costumary perturbation norms.
This paper provides necessary and sufficient conditions for the asymptotic stability of linear positive systems subject to tithe-varying delays. It introduces and initiates an original method l or solving directly the...
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ISBN:
(纸本)9783642028939
This paper provides necessary and sufficient conditions for the asymptotic stability of linear positive systems subject to tithe-varying delays. It introduces and initiates an original method l or solving directly the proposed stability and stabilization problems without using the well-known Lyapunov theory that is commonly used in the field of stability analysis. In that way and for readers convenience, the paper avoids possible long and tedious superfluous calculus.
In this paper, we make clearly appear links in Max-Plus algebra between four apparently different concepts encountered in various domains, such as Positive invariance, Monotonicity, Strong lumpability and Coherency. T...
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ISBN:
(纸本)9783642028939
In this paper, we make clearly appear links in Max-Plus algebra between four apparently different concepts encountered in various domains, such as Positive invariance, Monotonicity, Strong lumpability and Coherency. The first concept concerns Positive invariance of a particular set by a (linear) map. The second concept concerns Monotonicity of a given matrix. The third concept concerns Strong lumpability and the last concept concerns Coherency. To achieve these objectives, we begin first by recalling the idempotent version of Haar's lemma, which gives necessary and sufficient conditions for the inclusion of "one sided" idempotent polyhedra. Then, we generalize this result to the case of the inclusion of "two sided" idempotent polyhedra. Finally, these results allow to formulate conditions for each concept and to give links between there. Recalling that Strong lumpability and Coherency are used for the aggregation (reduction) of systems. All the proofs are based on residuation theory, which play a central role in duality theory.
An explicit criterion for positive linear Volterra-Stieltjes differential systems is given. Then new explicit criteria for uniform asymptotic stability and exponential asymptotic stability of positive linear Volterra-...
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ISBN:
(纸本)9783642028939
An explicit criterion for positive linear Volterra-Stieltjes differential systems is given. Then new explicit criteria for uniform asymptotic stability and exponential asymptotic stability of positive linear Volterra-Stieltjes differential systems are presented. Finally, a crucial difference between the uniform asymptotic stability and the exponential asymptotic stability of linear Volterra-Stieltjes differential systems is shown.
Many of simulation based learning algorithms have been developed to obtain near optimal policies for Markov decision processes (MDPs) with large state space. However, most of them are for unichain problems. In view th...
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ISBN:
(纸本)9783642028939
Many of simulation based learning algorithms have been developed to obtain near optimal policies for Markov decision processes (MDPs) with large state space. However, most of them are for unichain problems. In view that some applications involve multichain processes and it is NP-hard to determine whether a MDP is unichain or not, it is desirable to obtain an algorithm that is applicable to multichain problems as well. This paper presents a rollout algorithm for multichain MDPs with average cost. Preliminary analysis of the estimation error and parameter settings are provided based on the problem structures, i.e., mixing time of transition matrix. Ordinal optimization and Optimal Computing Budget Allocation are also suggested to improve the efficiency of the algorithm.
In this short paper we show how the convergence of the iterative aggregation-disaggregation methods for computing the Perron eigenvector of a large sparse irreducible stochastic matrix can be improved by an appropriat...
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ISBN:
(纸本)9783642028939
In this short paper we show how the convergence of the iterative aggregation-disaggregation methods for computing the Perron eigenvector of a large sparse irreducible stochastic matrix can be improved by an appropriate ordering of the data and by the choice of a basic iteration matrix. Some theoretical estimates are introduced and a fast algorithm is proposed for obtaining the desired ordering. Numerical examples arc presented.
Structured singular system, depending on a parametric vector are considered. The identification of the parameters is analyzed in terms of the input-output behavior of the system. The role of the reachability and obser...
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ISBN:
(纸本)9783642028939
Structured singular system, depending on a parametric vector are considered. The identification of the parameters is analyzed in terms of the input-output behavior of the system. The role of the reachability and observability properties in this analysis is studied and a characterization of the structural identifiability property is given. Finally, the structural identifiability of a positive reachable system is Studied.
Water Supply Systems (WSS) are clearly dynamical systems. Processes associated with WSS include design, planning, maintenance, control, management, rehabilitation, enlargement, etc. Modeling and simulation of these pr...
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ISBN:
(纸本)9783642028939
Water Supply Systems (WSS) are clearly dynamical systems. Processes associated with WSS include design, planning, maintenance, control, management, rehabilitation, enlargement, etc. Modeling and simulation of these processes can be performed by using a number of variables and constraints that are non-negative in nature. Demands, diameters of pipes, flowrates, minimum pressure at demand nodes, volume of reservoirs, are only a few examples, taken from the purely technical context. In this paper we will focus on the design of WSS. This a mixed discrete-continuous constrained optimization problem that is addressed here by the use of an evolutionary technique based on swarm intelligence. Robustness is enforced by adding reliability to the system both to cope with abnormal conditions and by considering the likelihood of different state and load conditions. Application to a real-world problem is also provided.
We use orders of magnitudes of variables and parameters of a chemical system described by an ordinary differential equation, to obtain a partition of the state space in boxes (hyper-rectangles). From the fast system i...
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ISBN:
(纸本)9783642028939
We use orders of magnitudes of variables and parameters of a chemical system described by an ordinary differential equation, to obtain a partition of the state space in boxes (hyper-rectangles). From the fast system in each box, we derive rules of transition, and obtain a transition graph. This graph can be used for a qualitative simulation and validation of the system.
This contribution is a natural continuation of a series of papers devoted to analysis of models utilized by specialists in Cell Biology around E. Bob] and W. Boos. Our novelty may he seen in enriching the models in di...
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ISBN:
(纸本)9783642028939
This contribution is a natural continuation of a series of papers devoted to analysis of models utilized by specialists in Cell Biology around E. Bob] and W. Boos. Our novelty may he seen in enriching the models in direction of controllability in the spirit of biology engineering. Besides the standard properties of the models such as existence of appropriate solutions and their uniqueness the following issues are of interest: Asymptotic behavior (e.g. steady states and pseudo-steady states), controllability and also special features such as various types of symmetries, periodicity etc. Our aim is focused on periodicity of solutions of models whose state objects share the properties of concentrations, i.e. probabilities.
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