A classification of generalised state space reduction methods for linear multivariable systems
A hierarchical decomposition of decision process Petri nets for modeling complex systems
We provide a framework for hierarchical specification called Hierarchical Decision Process Petri Nets (HDPPNs). It is an extension of Decision Process Petri Nets (DPPNs) including a hierarchical decomposition process that generates less complex nets with equivalent behavior. As a result, the complexity of the analysis for a sophisticated system is drastically reduced. In the HDPPN, we represent the mark-dynamic and trajectory-dynamic properties of a DPPN. Within the framework of the mark-dynamic...
A mathematical model for file fragment diffusion and a neural predictor to manage priority queues over BitTorrent
BitTorrent splits the files that are shared on a P2P network into fragments and then spreads these by giving the highest priority to the rarest fragment. We propose a mathematical model that takes into account several factors such as the peer distance, communication delays, and file fragment availability in a future period also by using a neural network module designed to model the behaviour of the peers. The ensemble comprising the proposed mathematical model and a neural network provides a solution...
Aggregation of a class of large-scale, interconnected, nonlinear dynamical systems.
An algorithm for reducing the dimension and size of a sample for data exploration procedures
The paper deals with the issue of reducing the dimension and size of a data set (random sample) for exploratory data analysis procedures. The concept of the algorithm investigated here is based on linear transformation to a space of a smaller dimension, while retaining as much as possible the same distances between particular elements. Elements of the transformation matrix are computed using the metaheuristics of parallel fast simulated annealing. Moreover, elimination of or a decrease in importance...
Approximation of large-scale dynamical systems: an overview
In this paper we review the state of affairs in the area of approximation of large-scale systems. We distinguish three basic categories, namely the SVD-based, the Krylov-based and the SVD-Krylov-based approximation methods. The first two were developed independently of each other and have distinct sets of attributes and drawbacks. The third approach seeks to combine the best attributes of the first two.
Closed-loop structure of decouplable linear multivariable systems
Considering a controllable, square, linear multivariable system, which is decouplable by static state feedback, we completely characterize in this paper the structure of the decoupled closed-loop system. The family of all attainable transfer function matrices for the decoupled closed-loop system is characterized, which also completely establishes all possible combinations of attainable finite pole and zero structures. The set of assignable poles as well as the set of fixed decoupling poles are determined,...
Cross-Gramian based model reduction for data-sparse systems.
Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs
Necessary and sufficiently conditions are derived for the decomposition of a second order linear time- varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation...
Decomposition of the symptom observation matrix and grey forecasting in vibration condition monitoring of machines
With the tools of modern metrology we can measure almost all variables in the phenomenon field of a working machine, and many of the measured quantities can be symptoms of machine conditions. On this basis, we can form a symptom observation matrix (SOM) intended for condition monitoring and wear trend (fault) identification. On the other hand, we know that contemporary complex machines may have many modes of failure, called faults. The paper presents a method of the extraction of the information...
Decoupling in singular systems: a polynomial equation approach
Disturbance decoupling of nonlinear MISO systems by static measurement feedback
This paper highlights the role of the rank of a differential one-form in the solution of such nonlinear control problems via measurement feedback as disturbance decoupling problem of multi-input single output (MISO) systems. For the later problem, some necessary conditions and sufficient conditions are given.
Efficient numerical algorithms for balanced stochastic truncation
We propose an efficient numerical algorithm for relative error model reduction based on balanced stochastic truncation. The method uses full-rank factors of the Gramians to be balanced versus each other and exploits the fact that for large-scale systems these Gramians are often of low numerical rank. We use the easy-to-parallelize sign function method as the major computational tool in determining these full-rank factors and demonstrate the numerical performance of the suggested implementation of...
Euler-Poincaré reduction of externally forced rigid body motion
Extracting second-order structures from single-input state-space models: Application to model order reduction
This paper focuses on the model order reduction problem of second-order form models. The aim is to provide a reduction procedure which guarantees the preservation of the physical structural conditions of second-order form models. To solve this problem, a new approach has been developed to transform a second-order form model from a state-space realization which ensures the preservation of the structural conditions. This new approach is designed for controllable single-input state-space realizations...
Free algebras and noncommutative power series in the analysis of nonlinear control systems: an application to approximation problems [Book]
Further results on sliding manifold design and observation for a heat equation
This article presents new extensions regarding a nonlinear control design framework that is suitable for a class of distributed parameter systems with uncertainties (DPS). The control objective is first formulated as a function of the distributed system state. Then, a control is sought such that the set in the state space where this relation is true forms an integral manifold reachable in finite time. The manifold is called a Sliding Manifold. The Sliding Mode controller implements a theoretically...
Global phase synchronization for a class of dynamical complex networks with time-varying coupling delays.
control design for an adaptive optics system
In this paper we first present a full order controller for a multi- input, multi-output (MIMO) adaptive optics system. We apply model reduction techniques to the full order controller and demonstrate that the closed-loop (CL) system with the reduced order controller achieves the same high level of performance. Upon closer examination of the structure of the reduced order controller it is found that the dynamical behavior of the reduced order controller can be accurately approximated by...
Interconnect synthesis in high speed digital VLSI routing.