A distributed block approach to solving near-block-diagonal systems with an application to a large macroeconometric model

This paper illustrates some benefits of small-scale distributed processing in solving near-block-diagonal systems. We review the theoretical advantages of distributed block algorithms and apply such an algorithm to solve a large nonlinear macroeconometric model. For our application, on a four-processor UNIX server, the algorithm achieves a speedup factor of more than 6 over the standard algorithm on a single processor. A speedup factor of about 2 is due to the added efficiency of the block algorithm on a single processor, and the remaining factor of 3 results from distributing the work over four processors.The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or other members of its staff. We would like to thank Ray Board, Neil Ericsson, Mico Loretan, and an anonymous referee for helpful comments.     

Toward a theory and method for cooperative systems, with application to auditing

Cooperative distributed knowledge-base systems—sometime termed distributed artificial Intelligence (DAI)—offer computer methods for coordinating group expertise in the solving of problems. Much of the research to the present has been empirical testing of informal methods. There is a need for more formal methods to guide the design and development of DAI. At the same time, object-oriented programming methods provide a natural means or representing real-world objects in a way that facilitates communication among those objects. In this paper we propose a methodology for integrating formal methods of knowledge theory with object-oriented methods in a way that may facilitate the development of more robust DAI systems. Our exposition takes the reader from conceptual development to fundamentals of an application in auditing.     

Analysis of the precision of generalized chain codes for the representation of planar curves

This paper examines a set of line-segment approximation codes for the representation of planar curves (the so-called generalized chain codes) and shows that the average quantization error (measure of code's precision) is directly proportional to the grid size and is independent of the form of the code. Thus, to achieve a desired level of precision for the representation of a line drawing, only the size of the grid need be determined; the form of the code can be chosen on the basis of other criteria, such as compactness, smoothness, or relative ease of encoding and processing.     

On the application of matrix generalized inverses to the construction of inverse systems

A discrete-time fast regulator with fast observer is considered in this paper. The system is assumed as a linear time-invariant nth order r-input, m-output system. Complete controllability and complete observability are assumed. No assumptions are made on the non-singularity of the system matrix and integrality of n/r and n/m. It is shown that the fast regulator with fast observer transfers any initial state to the origin within the number of steps equal to the sum of observability and controllability indices. Simple design methods for fast regulator and fast observer are presented. Also, it is illustrated geometrically how the state point is transferred to a subspace with successively decreased dimension for each step until it arrives at the origin.     

On the application of matrix generalized inverses to the design of observers for time-varying and time-invariant linear systems

A method for the design of Luenberger observers is developed utilizing the simplest generalized inverse of matrices. The method can be applied to time-invariant and to time-varying systems.     

A systematic method for the hybrid dynamic modeling of open kinematic chains confined in a closed environment

This work presents a systematic method for the dynamic modeling of multi-rigid links confined within a closed environment. The behavior of the system can be completely characterized by two different mathematical models: a set of highly coupled differential equations for modeling the confined multi-link system when it has no impact with surrounding walls; and a set of algebraic equations for expressing the collision of this open kinematic chain system with the confining surfaces. In order to avoid the Lagrangian formulation (which uses an excessive number of total and partial derivatives in deriving the governing equations of multi-rigid links), the motion equations of such a complex system are obtained according to the recursive Gibbs–Appell formulation. The main feature of this paper is the recursive approach, which is used to automatically derive the governing equations of motion. Moreover, in deriving the motion equations, the manipulators are not limited to planar motions only. In fact, for systematic modeling of the motion of a multi-rigid-link system in 3D space, two imaginary links are added to the \(n\)-real links of a manipulator in order to model the spatial rotations of the system. Finally, a 2D and a 3D case studies are simulated to demonstrate the effectiveness of the proposed approach.     

Expressions for the generalized Drazin inverse of a block matrix in a Banach algebra

The aim of this paper is to establish explicit representations of the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra, which covers the case when the generalized Schur complement is equal to zero.     

Elaboration of a generalized approach to control and to synchronize the fractional-order chaotic systems

In this paper, a new general optimal structure and parameters of the fractional-order feedback control law (OSP-FoF) is developed for controlling and synchronizing a large class of fractional-order chaotic systems (FoCS). The design of the OSP-FoF model is based on bounded-input bounded-output stabilization arguments, small gain theorem (SGT), and the matrix norms. The proposed model is theoretically rigorous and represents a powerful and simple approach which provides a reasonable trade-off between computational overhead, storage space, numerical accuracy and stability analysis for control and synchronization purposes of FoCS. Simulation results for the stabilization and synchronization of fractional-order hyperchaotic systems demonstrate the effectiveness of this newly proposed approach.     

Adaptive stabilization of generalized Hamiltonian systems with dissipation and its applications to power systems

The adaptive stabilization of the generalized Hamiltonian control systems with dissipation, which has a linearly parameterized Hamiltonian function with respect to unknown constants, is considered here. The theoretic result is then applied to power system that cannot be treated by backstepping introduced by Kokotovic et al. Simulations show that the designed adaptive control law is very effective.     

Robust control for nonlinear time-varying systems with application to a robotic manipulator

Sliding mode control methods have been used widely because they provide robustness against parameter variations and disturbances. This paper focuses on the problem of a robust output-sliding control design for a class of nonlinear time-varying systems. Output signals are used for the switching function definition. The control law formulation is emphasized. Input and output linearization is used. Output tracking can be achieved against a class of time-varying parameter variations and external disturbances. An application to a two-degree-of-freedom manipulator indicates that the proposed switching control law drives the system state trajectories onto the chosen sliding mode in finite time and the output tracking is guaranteed.     

Alternating two-stage methods for consistent linear systems with applications to the parallel solution of Markov chains

Two-stage methods in which the inner iterations are accomplished by an alternating method are developed. Convergence of these methods is shown in the context of solving singular and nonsingular linear systems. These methods are suitable for parallel computation. Experiments related to finding stationary probability distribution of Markov chains are performed. These experiments demonstrate that the parallel implementation of these methods can solve singular systems of linear equations in substantially less time than the sequential counterparts.     

区块链技术在票据业务应用中的优势及影响

票据为实体经济发展服务,是金融市场的重要金融工具之一。区块链的快速发展为票据业务带来新的技术途径,结合电子票据业务流程,进一步分析了数字票据在票据业务中应用的优势,区块链数字票据可简化金融机构票据业务,降低交易风险。文章结合互联网金融企业业务特点,进一步探索了数字票据在互联网金融公司中的应用。随着数字票据的技术进步和应用落地,将会对金融服务创新带来生机,对进一步推动数字普惠金融有重要意义。     

Comments on "On the application of matrix generalized inverses to the design of observer for time-varying and time-invariant linear systems"

It is shown by counterexample that the correction paper [1] of the paper is incorrect. Following a definition and a theorem, we present a corrected version of the authors' theorem to make the results of the paper precise.     

Comments on "On the application of matrix generalized inverses to the design of observers for time-varying and time-invariant linear systems"

In this discussion, several comments on the eigenvalue assignment algorithm in the above paper are made for the purpose of better illustration and clarity.     

Continuous output‐feedback control for a class of switched high‐order planar systems and its application

This paper deals with the problem of continuous output‐feedback stabilization for a class of switched high‐order planar systems under arbitrary switchings. Based on the common Lyapunov function design method, by using the adding a power integrator technique and designing an implementable observer, a continuous output‐feedback controller is constructed such that the closed‐loop system is global stabilization and the output can be regulated to the origin. As an application, the developed strategy is utilized to the control design for the continuous stirred tank reactor with two modes feed stream. The simulation results verify the efficiency of the proposed design scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

Analysis of linear asynchronous hybrid stochastic systems and its application to multi-agent systems with Markovian switching topologies

This paper studies the stability and stabilisation of a class of asynchronous hybrid stochastic systems described by linear Markov jump systems with asynchronous parameters induced by hysteretic mode and input delay. By exploring the essential properties of the Markov chain and developing novel Lyapunov function/functional based approaches, we derive sufficient conditions in terms of sizes of the delays ensuring the mean square asymptotical stability of the systems. Interestingly, the Lyapunov functional based approach further leads to the mean square stability criteria that depend only on the drift part and allow an arbitrary large delay for the diffusion part, which is different from the Lyapunov-Razumikhin based results. The theoretical results are applied to solve the consensus problems of multi-agent systems with Markovian switching topologies and input delay. Numerical examples demonstrate the established results.     

Stabilization of a class of cascade nonlinear switched systems with application to chaotic systems

In this study, the problem of finite‐time practical control of a class of nonlinear switched systems in the presence of input nonlinearities is investigated. The subsystems of the switched system are considered as complex nonlinear systems with a cascade structure. Each subsystem is fluctuated by lumped uncertainties. Moreover, some parts of the system's dynamics are considered to be unknown in advance. This paper sets no restrictive assumption on the switching logic of the system. Therefore, the aim is to propose a controller to work under any arbitrary switching signals. After providing a smooth sliding manifold, a simple adaptive control input is developed such that the system trajectories approach the prescribed sliding mode dynamics in finite‐time sense. The adopted control signal does not use the upper bounds of the lumped uncertainties, and it is robust against unknown nonlinear parts of the subsystems. It is proved that the origin is the (practical) finite‐time stable equilibrium point of the overall closed‐loop system. Subsequently, the proposed control rule is modified to handle the same switched system with no input nonlinearities. Computer simulations via 2 chaotic electric direct current machines demonstrate the robust performance of the derived variable structure control algorithm against system fluctuations and nonlinear inputs.