Space Decomposition Technique Research Articles

Output feedback quantized observer‐based synchronization of linear multi‐agent systems over jointly connected topologies

SummaryThe synchronization problem of linear over‐actuated multi‐agent systems with unmeasurable states is studied in this paper, under both limited communication data rate and switching topology flows. A class of adaptive quantized observer‐based encoding–decoding schemes and a class of certainty equivalence principle‐based control protocols are proposed. By developing the graph‐based space decomposition technique and analyzing the closed‐loop quantized dynamic equations, it is shown that if the network topology flow is jointly connected, the communication channels are periodic active, and the agent dynamics is observable, and with the orthogonal system matrix, the proposed communication and control protocols can ensure the closed‐loop system to achieve synchronization exponentially fast with finite bits of information exchange per step. Copyright © 2015 John Wiley & Sons, Ltd.

Left invertible completions of upper triangular operator matrices with unbounded entries

Given two closed, in general unbounded, operators A and C, we investigate the left invertible completion of the partial operator matrix $$\left( {\begin{array}{*{20}{c}} A&? \\ 0&C \end{array}} \right)$$ . Based on the space decomposition technique, the alternative sufficient and necessary conditions are given according to whether the dimension of $$\mathcal{R}(A)^ \bot$$ is finite or infinite. As a direct consequence, the perturbation of left spectra is further presented.

The Stationary Distribution and Extinction of Generalized Multispecies Stochastic Lotka-Volterra Predator-Prey System

This paper is concerned with the existence of stationary distribution and extinction for multispecies stochastic Lotka-Volterra predator-prey system. The contributions of this paper are as follows. (a) By using Lyapunov methods, the sufficient conditions on existence of stationary distribution and extinction are established. (b) By using the space decomposition technique and the continuity of probability, weaker conditions on extinction of the system are obtained. Finally, a numerical experiment is conducted to validate the theoretical findings.

Noise in oscillators: a review of state space decomposition approaches

We review the state space decomposition techniques for the assessment of the noise properties of autonomous oscillators, a topic of great practical and theoretical importance for many applications in many different fields, from electronics, to optics, to biology. After presenting a rigorous definition of phase, given in terms of the autonomous system isochrons, we provide a generalized projection technique that allows to decompose the oscillator fluctuations in terms of phase and amplitude noise, pointing out that the very definition of phase (and orbital) deviations depends of the base chosen to define the aforementioned projection. After reviewing the most advanced theories for phase noise, based on the use of the Floquet basis and of the reduction of the projected model by neglecting the orbital fluctuations, we discuss the intricacies of the phase reduction process pointing out the presence of possible variations of the noisy oscillator frequency due to amplitude-related effects.

Left invertibility of formal Hamiltonian operators

In this paper, we investigate the left invertible completion of the formal Hamiltonian operators with unbounded entries. In particular, the left invertible completion of Hamiltonian cases is also given. Based on the space decomposition technique, the sufficient and necessary conditions are given according to whether the dimension of is finite or infinite.

Meanshift Tracking with Kalman Filter and Rotation-Invariant Features

This paper presents an improve Meanshift tracking algorithm based on Kalman filter and Rotation-Invariant Features. Firstly, this paper forecasts the original alternate position using Kalman filter. Secondly, a kind of spatial histogram based on GRA (Gradient Radius Angle, GRA) is introduced, which is a rotation-invariant descriptor combined the information of gradient. At last, this paper searches the scale factor by the normal scale space decomposition technique. Experiments show that the method concerned in this paper has better performances than two improved algorithms.

The asymptotic behavior of the strong solutions for a non-autonomous non-local PDE model with delay

In this paper, we study the asymptotic behavior of the strong solutions of a non-autonomous non-local PDE model with time delay. We present the existence and structure of the uniform attractor by constructing the skew product flow of the family of processes generated by the strong solutions. In order to obtain the existence of the uniform attractor, we prove the family of processes satisfies uniform condition (C) by using some special technique of phase space decomposition. Additionally, it is shown that all the bounded complete trajectories are globally asymptotic stable under some assumptions. As the application of our result, we obtain a globally asymptotic stable nontrivial strong periodic solution of a non-local PDE model.

A solid model-based off-line adaptive controller for feed rate scheduling for milling process

Most CAM packages available today provide NC simulation systems that generally use inexact solid representation as they are computationally intensive. Popular inexact volumetric NC simulation packages use either a voxel based 2.5D approach (particularly Image-space modeling) or Polyhedral approximations of 3D objects. The former does not degenerate with time but has limited resolution whereas the latter has a selectable resolution but degenerates rapidly with time. As against these, the authors’ use octree solid representation in their volumetric NC simulation system. This hierarchical space decomposition (HSD) technique combines the benefits of both the earlier approaches, i.e., it has a selectable resolution and does not degenerate with time. The basic input to the octree-based NC simulation system is the NC cutter path either in cutter location (CL) format or G/ M-code format. After the CL data are interpreted, the swept volume of the cutter is intersected with the blank at every small sampling interval along the tool path and the intersection is considered as the undeformed chip. The chip parameters necessary for predicting the milling force are extracted and using the material removal rate (MRR) model and cutting force is predicted. According to the simulation result the feed rate is adjusted based on force calculation to generate optimized CL File. The improvement can be seen from the experimental results presented. Such a simulation system will be useful, in addition to the visual check, for automatic verification of safety of machining and conformance of the produced part to design specifications as well as for the optimization of the feed rate and spindle speed.

Lyapunov-Based Approach to Multiagent Systems With Switching Jointly Connected Interconnection

This note addresses a coordination problem of a multiagent system with jointly connected interconnection topologies. Neighbor-based rules are adopted to realize local control strategies for these continuous-time autonomous agents described by double integrators. Although the interagent connection structures vary over time and related graphs may not be connected, a sufficient condition to make all the agents converge to a common value is given for the problem by a proposed Lyapunov-based approach and related space decomposition technique

Influence of modeling structure in probabilistic sequential decision problems

Markov Decision Processes (MDPs) are a classical framework for stochastic sequential decision problems, based on an enumerated state space representation. More compact and structured representations have been proposed: factorization techniques use state variables representations, while decomposition techniques are based on a partition of the state space into sub-regions and take advantage of the resulting structure of the state transition graph. We use a family of probabilistic exploration-like planning problems in order to study the influence of the modeling structure on the MDP solution. We first discuss the advantages and drawbacks of a graph based representation of the state space, then present our comparisons of two decomposition techniques, and propose to use a global approach combining both state space factorization and decomposition techniques. On the exploration problem instance, it is proposed to take advantage of the natural topological structure of the navigation space, which is partitioned into regions. A number of local policies are optimized within each region, that become the macro-actions of the global abstract MDP resulting from the decomposition. The regions are the corresponding macro-states in the abstract MDP. The global abstract MDP is obtained in a factored form, combining all the initial MDP state variables and one macro-state “region” variable standing for the different possible macro-states corresponding to the regions. Further research is presently conducted on efficient solution algorithms implementing the same hybrid approach for tackling large size MDPs.

Dual three-phase induction motor drive with digital current control in the stationary reference frame

Among different multiphase motor drive solutions, one of the most widely discussed is the voltage source inverter (VSI) fed dual three-phase induction machine. Over the years, various topics pertinent to this specific motor drive system have been investigated in considerable depth and, more recently, various reports on real-world applications have emerged. In this paper, a drive system that has been developed specifically for electrical vehicles is described. For vector control purposes, the drive was modeled using an approach that is based on the vector space decomposition technique since it directly leads to the proposed current control method in the stationary reference frame.

A space decomposition method for parabolic equations

A convergence proof is given for an abstract parabolic equation using general space decomposition techniques. The space decomposition technique may be a domain decomposition method, a multilevel method, or a multigrid method. It is shown that if the Euler or Crank–Nicolson scheme is used for the parabolic equation, then by suitably choosing the space decomposition, only O(| log τ |) steps of iteration at each time level are needed, where τ is the time-step size. Applications to overlapping domain decomposition and to a two-level method are given for a second-order parabolic equation. The analysis shows that only a one-element overlap is needed. Discussions about iterative and noniterative methods for parabolic equations are presented. A method that combines the two approaches and utilizes some of the good properties of the two approaches is tested numerically. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 27–46, 1998

The improved compact QP method for resolving manipulator redundancy

The compact QP method is an effective and efficient algorithm for resolving the manipulator redundancy under inequality constraints. In this paper, a more computationally efficient scheme which will improve the efficiency of the compact QP method-the improved compact BP method-is developed. With the technique of work space decomposition, the redundant inverse kinematics problem can be decomposed into two subproblems. Thus, the size of the redundancy problem can be reduced. For an n degree-of-freedom spatial redundant manipulator, instead of a 6/spl times/n matrix, only a 3/spl times/(n-3) matrix is needed to be manipulated by Gaussian elimination with partial pivoting for selecting the free variables. The simulation results on the CESAR manipulator indicate that the speedup of the compact QP method as compared with the original QP method is about 3.3. Furthermore, the speedup of the improved compact QP method is about 5.6. Therefore, it is believed that the improved compact QP method is one of the most efficient and effective optimization algorithm for resolving the manipulator redundancy under inequality constraints.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A theory for memory-based learning

A memory-based learning system is an extended memory management system that decomposes the input space either statically or dynamically into subregions for the purpose of storing and retrieving functional information. The main generalization techniques employed by memory-based learning systems are the nearest-neighbor search, space decomposition techniques, and clustering. Research on memory-based learning is still in its early stage. In particular, there are very few rigorous theoretical results regarding memory requirement, sample size, expected performance, and computational complexity. In this paper, we propose a model for memory-based learning and use it to analyze several methods— ε-covering, hashing, clustering, tree-structured clustering, and receptive-fields—for learning smooth functions. The sample size and system complexity are derived for each method. Our model is built upon the generalized PAC learning model of Haussler (Haussler, 1989) and is closely related to the method of vector quantization in data compression. Our main result is that we can build memory-based learning systems using new clustering algorithms (Lin & Vitter, 1992a) to PAC-learn in polynomial time using only polynomial storage in typical situations.

Stability analysis for discrete event dynamic systems and the state space decomposition techniques

In this paper, stability and stable behavior of discrete event dynamic systems (DEDS) are further researched. In DEDS, stability is charaterized by periodicity. It has been proved that the state space of a stable DEDS can be divided into some different stable regions according to periodic characters (order and initial step) of states, and stable regions with same periodic order correspond to identical stable equilibrium region. In the paper, a method to decomposite state space and to determine equilibrium region is given. The results of the paper has a certain theoretic and applied worth, especially, for organizing reasonably production of flexible manufacturing systems (FMS). Finally, an example is taken to illustrate the conclusions given in the paper.

Issues on feature-based editing and interrogation of solid models

Operations that create additive or subtractive volume features, such as bosses or slots, simplify the computer aided design of mechanical parts. Surface features, whether extracted automatically or selected interactively, group functionally related boundary elements, and thus provide an expedient interface between CAD systems and analysis or manufacturing applications. Despite much progress in CAD, design remains an iterative process and involves error-prone modifications of previous solutions. Features should in principle offer a high level vocabulary for characterizing errors and for specifying how they should be corrected. This paper points out the semantic ambiguities of simplistic feature-based commands for editing models. It recommends procedural models for editing volume features, and corrective volumes for editing surface features. It shows how space decomposition techniques and CSG expressions based on active zones reduce the cost of executing an editing command. Error detection may be automated by supporting intentional features, which correspond to the desired characteristics of the model, and by endowing them with domain dependent validity criteria expressed in terms of associated geometric elements. The paper demonstrates that validity may be tested by simply interrogating a mixed-dimensional geometric structure which is used to represent not only the model, but also the interactions between the geometric elements associated with intentional features.