Discrete-time Algorithm Research Articles

Statistical Analysis of a Third-Order Cumulants Based Algorithm for Discrete-Time Errors-in-Variables Identification

This paper deals with identification of dynamic discrete-time errors-in-variables systems. The statistical accuracy of a least squares estimator based on third-order cumulants is analyzed. In particular, the asymptotic covariance matrix of the estimated parameters is derived. The results are supported by numerical simulation studies.

Optimum grouping in a modified genetic algorithm for discrete-time, non-linear system identification

The genetic algorithm approach is widely recognized as an effective and flexible optimization method for system identification. The flexibility of a genetic algorithm allows various strategies to be applied to it. One of the strategies applied is the modified genetic algorithm which relies on, among other things, the separation of the population into groups where each group undergoes mutual recombination operations. The strategy has been shown to be better than the simple genetic algorithm and conventional statistical method, but it contains inadequate justification of how the separation is made. The usage of objective function values for separation of groups does not carry much flexibility and is not suitable since different time-dependent data have different levels of equilibrium and thus different ranges of objective function values. This paper investigates the optimum grouping of chromosomes by fixed group ratios, enabling more efficient identification of dynamic systems using a NARX (Non-linear AutoRegressive with eXogenous input) model. Several simulated systems and real-world timedependent data are used in the investigation. Comparisons based on widely used optimization performance indicators along with outcomes from other research are used. The issue of model parsimony is also addressed, and the model is validated using correlation tests. The study reveals that, when recombination and mutation are used for different groups, equal composition of both groups produces a better result in terms of accuracy, parsimony, speed, and consistency.

A ROBUST AND GLOBALLY CONVERGENT PCA LEARNING ALGORITHM

Principal component analysis (PCA) using neural networks is an active research field with many applications to signal processing and data analysis. This paper presents a PCA neural network endowed with a novel learning algorithm, and an analysis of its features. As the basic discrete-time Oja's PCA neural network does not converge globally, it is important to derive a robust and globally convergent PCA learning algorithm. Based on previous works on the globally convergent PCA learning algorithm, a robust and globally convergent PCA learning algorithm is proposed in this paper. The behavior of this discrete-time learning algorithm is directly studied in this paper. We show that the algorithm is robust and globally convergent. The selection of the parameters of this algorithm will also be discussed in details. Finally, simulation results are provided to verify the theoretical results presented. Compared to other PCA learning algorithms, the proposed algorithm performs favorably in terms of robust stability, global convergence, speed and accuracy.

Global Optimization Using Diffusion Perturbations with Large Noise Intensity

This work develops an algorithm for global optimization. The algorithm is of gradient ascent type and uses random perturbations. In contrast to the annealing type procedures, the perturbation noise intensity is large. We demonstrate that by properly varying the noise intensity, approximations to the global maximum can be achieved. We also show that the expected time to reach the domain of attraction of the global maximum, which can be approximated by the solution of a boundary value problem, is finite. Discrete-time algorithms are proposed; recursive algorithms with occasional perturbations involving large noise intensity are developed. Numerical examples are provided for illustration.

The Evolution and Emergence of Integrated Social and Financial Networks with Electronic Transactions: A Dynamic Supernetwork Theory for the Modeling, Analysis, and Computation of Financial Flows and Relationship Levels

In this paper, we propose a rigorous dynamic supernetwork theory for the integration of social networks with financial networks with intermediation in the presence of electronic transactions. We consider decision-makers with sources of funds, financial intermediaries, as well as demand markets for the various financial products. Through a multilevel supernetwork framework consisting of the financial network and the social network we model the multicriteria decision-making behavior of the various decision-makers, which includes the maximization of net return, the maximization of relationship values, and the minimization of risk. Increasing relationship levels in our framework are assumed to reduce transaction costs as well as risk and to have some additional value for the decision-makers. We explore the dynamic evolution of the financial flows, the associated product prices, as well as the relationship levels on the supernetwork until an equilibrium pattern is achieved. We provide some qualitative properties of the dynamic trajectories, under suitable assumptions, and propose a discrete-time algorithm which is then applied to track the evolution of the relationship levels over time as well as the financial flows and prices. The equilibrium pattern yields, as a byproduct, the emergent structure of the social and financial networks since it identifies not only which pairs of nodes will have flows but also the size of the flows, i.e., the relationship levels and the financial transactions.

Global Convergence Analysis of a Discrete Time Nonnegative ICA Algorithm

When the independent sources are known to be nonnegative and well-grounded, which means that they have a nonzero pdf in the region of zero, Oja and Plumbley have proposed a "Nonnegative principal component analysis (PCA)" algorithm to separate these positive sources. Generally, it is very difficult to prove the convergence of a discrete-time independent component analysis (ICA) learning algorithm. However, by using the skew-symmetry property of this discrete-time "Nonnegative PCA" algorithm, if the learning rate satisfies suitable condition, the global convergence of this discrete-time algorithm can be proven. Simulation results are employed to further illustrate the advantages of this theory.

Reference management using state observers

The reference management algorithm is an auxiliary system which modifies the reference signal to fulfil the state and control constraints. In the previous works, most of such algorithms require the assumption that the state vector of the closed-loop system including the plant state is directly measurable, which may be unrealistic for some applications. In this paper, we develop a new reference management algorithm for discrete-time constrained systems with unmeasurable plant states. The present algorithm assures the constraints fulfilment when an ellipsoidal set of possible plant state vectors is available instead of the plant state itself. It is shown that the set of possible plant states can be obtained from the measured outputs by using the Luenberger-type observer or the set-valued observer. The effectiveness of the present method is demonstrated by a numerical example.

ROBUST NEURAL IDENTIFICATION OF ROBOTIC MANIPULATORS USING DISCRETE TIME ADAPTIVE SLIDING MODE LEARNING

The problem of identification of uncertain nonlinear systems using feedforward neural networks is investigated. The weights of the neural identifier are updated on-line by a discrete-time learning algorithm based on the sliding mode control technique, which is well known with its robustness to uncertainties. The learning parameters are adjusted to force the error between the actual and desired neural network outputs to satisfy a stable difference error equation and a quasi-sliding mode on the zero learning error is established. The behaviour of the proposed discrete-time algorithm is illustrated by using it for the neural identification of an experimental robotic manipulator. The results show that the neural model inherits some of the advantages of the sliding mode control approach, such as high speed of learning and robustness, and is able to follow the actual robot joint trajectories with a high accuracy.

Improved algorithms and methods for room sound-field prediction by acoustical radiosity in arbitrary polyhedral rooms.

This paper explores acoustical (or time-dependent) radiosity--a geometrical-acoustics sound-field prediction method that assumes diffuse surface reflection. The literature of acoustical radiosity is briefly reviewed and the advantages and disadvantages of the method are discussed. A discrete form of the integral equation that results from meshing the enclosure boundaries into patches is presented and used in a discrete-time algorithm. Furthermore, an averaging technique is used to reduce computational requirements. To generalize to nonrectangular rooms, a spherical-triangle method is proposed as a means of evaluating the integrals over solid angles that appear in the discrete form of the integral equation. The evaluation of form factors, which also appear in the numerical solution, is discussed for rectangular and nonrectangular rooms. This algorithm and associated methods are validated by comparison of the steady-state predictions for a spherical enclosure to analytical solutions.

The Evolution and Emergence of Integrated Social and Financial Networks with Electronic Transactions: A Dynamic Supernetwork Theory for the Modeling, Analysis, and Computation of Financial Flows and Relationship Levels

In this paper, we propose a rigorous dynamic supernetwork theory for the integration of social networks with financial networks with intermediation in the presence of electronic transactions. We consider decision-makers with sources of funds, financial intermediaries, as well as demand markets for the various financial products. Through a multilevel supernetwork framework consisting of the financial network and the social network we model the multicriteria decision-making behavior of the various decision-makers, which includes the maximization of net return, the maximization of relationship values, and the minimization of risk. Increasing relationship levels in our framework are assumed to reduce transaction costs as well as risk and to have some additional value for the decision-makers. We explore the dynamic evolution of the financial flows, the associated product prices, as well as the relationship levels on the supernetwork until an equilibrium pattern is achieved. We provide some qualitative properties of the dynamic trajectories, under suitable assumptions, and propose a discrete-time algorithm which is then applied to track the evolution of the relationship levels over time as well as the financial flows and prices. The equilibrium pattern yields, as a byproduct, the emergent structure of the social and financial networks since it identifies not only which pairs of nodes will have flows but also the size of the flows, i.e., the relationship levels and the financial transactions.

Dynamics of international financial networks with risk management

In this paper, we develop an international financialnetwork model in which the sources of funds and the intermediaries are multicriteria decision-makers and are concerned with both net revenue maximization and risk minimization. The model allows for both physical as well as electronic transactions and considers three tiers of decision-makers who may be located in distinct countries and may conduct their transactions in different currencies. We describe the behaviour of the various decision-makers, along with their optimality conditions, and derive the variational inequality formulation of the governing equilibrium conditions. We then propose a dynamic adjustment process which yields the evolution of the financial flows and prices and demonstrate that it can be formulated as a projected dynamical system. We also provide qualitative properties including stability analysis results. Finally, we discuss a discrete-time algorithm which can be applied to track the dynamic trajectories and yields the equilibrium financial flows and prices. We illustrate both the modelling framework as well as the computational procedure with several numerical international financial network examples.

Dynamical free boundary problem for an incompressible potential fluid flow in a time-varying domain

Modeling of large lakes or oceans for environmental studies or deformable blood vessels for mini-invasive surgery involve dynamical free boundaries governed by their interaction with their immediate environment. The object of this paper is to further Shape Analysis techniques in the formulation and analysis of dynamical free boundary problems defined over a time-varying domain ( noncylindrical problems ). The generic example of a potential incompressible fluid flow with a pressure condition (Bernouilli type) on the dynamical free boundary is presented along with a discrete time algorithm to follow the evolution of the time-varying free boundary. The dynamical free boundary condition yields a new time-space differential equation for the normal component of the velocity field on the time-varying free boundary. These ideas and constructions can be extended to more complex and realistic models.

Statics and Dynamics of Global Supply Chain Networks with Environmental Decision-Making

In this paper, we develop static and dynamic models of global supply chains as networks with three tiers of decision-makers: manufacturers, retailers, and consumers associated with the demand markets, who compete within a tier but cooperate between tiers. The decision-makers may be based in the same or in different countries, may transact in different currencies, and are faced with different degrees of environmental concern. Moreover, we allow for electronic transactions in the form of electronic commerce between the decisionmakers. The proposed supernetwork framework formalizes the modeling and theoretical analysis of such global supply chains, and also enables the dynamic tracking of the evolution of the associated prices and product transactions (as well as the emissions) to the equilibrium state. Moreover, it measures the impacts on the environment associated with the behaviors of the decision-makers. Finally, we propose a discrete-time algorithm which allows for the discretization of the continuous time trajectories and which results in closed form expressions at each iteration.

Dynamics of International Financial Networks with Risk Management

In this paper, we develop an international financial network model in which the sources of funds and the intermediaries are multicriteria decision-makers and are concerned with both net revenue maximization and risk minimization. The model allows for both physical as well as electronic transactions and considers three tiers of decision-makers who may be located in distinct countries and may conduct their transactions in different currencies. We describe the behavior of the various decision-makers, along with their optimality conditions, and derive the variational inequality formulation of the governing equilibrium conditions. We then propose a dynamic adjustment process which yields the evolution of the financial flows and prices and demonstrate that it can be formulated as a projected dynamical system. We also provide qualitative properties including stability analysis results. Finally, we discuss a discrete-time algorithm which can be applied to track the dynamic trajectories and yields the equilibrium financial flows and prices. We illustrate both the modeling framework as well as the computational procedure with several numerical international financial network examples.

Dynamics of global supply chain supernetworks

In this paper, we develop a framework for the modelling, analysis, and computation of solutions to global supply chains. We consider three tiers of decision-makers: manufacturers, who may be located in the same or in different countries; intermediaries, in the form of retailers, who may be either physical or virtual, as in the case of electronic commerce; and consumers at the demand markets who may purchase the product in different currencies in the countries. We model the behavior of the decision-makers, derive the equilibrium conditions, and establish the variational inequality formulation. We then utilize the variational inequality formulation to obtain qualitative properties of the equilibrium product shipment and price pattern. In addition, we propose a dynamic adjustment process for the continuous time adjustment of the product flows and prices and formulate it as a projected dynamical system whose set of solutions coincides with the set of solutions to the variational inequality problem. A discrete-time algorithm is then applied to several numerical supply chain examples. This research extends the recent results surrounding the modelling of supply chains in a network equilibrium setting to the global arena.

A discrete-time compensation algorithm for hysteresis in piezoceramic actuators

A discrete-time Preisach model that captures hysteresis in a piezoceramic actuator is developed. The model is implemented using a numerical technique that is based on first-order reversal functions and is presented in a recursive form that is amenable for real-time implementation. The first-order reversal functions are experimentally obtained using a piezoceramic actuator in a stacked form. The developed model shows good agreement with actual measured data. Two hysteresis compensation schemes based on the developed discrete-time Preisach model are also developed and used in order to obtain any desired linear voltage-to-displacement relationship. The ability of the first hysteresis compensator to lead to an arbitrary linear voltage-to-displacement relationship is shown through experimental tests under the condition that no-load is applied to the actuator and then a load typical of many piezoactuator applications is applied to the actuator. The second hysteresis compensation scheme is used as part of an open-loop tracking controller and is shown experimentally to lead to high tracking accuracy.

Very high-speed true random noise generator

In this work an original CMOS implementation of a discrete-time deterministic-chaos algorithm for random number generation is presented. The proposed circuit topology prevents the degradation of the generated-sequence statistical properties that can be caused by several factors, including the parameter spreading of the technological processes. Experimental results show that the circuit can issue delta-correlated 1-bit digital sequences with a generation maximum frequency above 12 MHz.

A combinatorial approach for pricing Parisian options

This paper provides a discrete time algorithm, in the framework of the Cox–Ross–Rubinstein analysis (1979), to evaluate both Parisian options with a flat barrier and Parisian options with an exponential boundary. The algorithm is based on a combinatorial tool for counting the number of paths of a particle performing a random walk, that remains beyond a barrier constantly for a period strictly smaller than a pre-specified time interval. As a result, a binomial evaluation model is derived that is very easy to implement and that produces highly accurate prices.

Efficient arbitrary sampling rate conversion with recursive calculation of coefficients

In this paper, we present a novel algorithm for sampling rate conversion by an arbitrary factor. Theoretically, sampling rate conversion of a discrete-time (DT) sequence can be performed by converting the sequence to a series of continuous-time (CT) impulses. This series of impulses is filtered with a CT lowpass filter, and the output is then sampled at the desired rate. If the CT filter is chosen to have a rational transfer function, then this system can be simulated using a DT algorithm for which both computation and memory requirements are low. The DT implementation is comprised of a parallel structure, where each branch consists of a time-varying filter with one or two taps, followed by a fixed recursive filter operating at the output sampling rate. The coefficients of the time-varying filters are calculated recursively. This eliminates the need to store a large table of coefficients, as is commonly done.

Extension of discrete simple adaptive control with asymptotically perfect tracking

AbstractA discrete‐time algorithm for simple adaptive control, proposed by one of authors, circumvents some drawbacks of the algorithm derived directly from continuous‐time one. However, it leaves steady‐state output error between a controlled plant and a reference model. This paper proposes a modified algorithm, which removes the steady‐state output error. The stability of the algorithm is proved based on asymptotic output tracker theory, instead of command generator tracker theory. Finally, simulation results illustrate satisfactory control performance, that verifies the usefulness of the proposed algorithm. Copyright © 2002 John Wiley & Sons, Ltd.