Continuous-time Ones Research Articles

Turing-like patterns induced by the competition between two stable states in a discrete-time predator–prey model

Patterns, typical spatiotemporal ordered structures, are widely present in a variety of systems, which are the results of the emergence of complex systems. The theory of Turing, occupying a long-range inhibitor and a short-range activator, provides an explanation for the diversity of Turing patterns. Turing-like patterns, caused by various non-Turing mechanisms, have also been investigated in various models. Patterns resulting from Turing or non-Turing mechanisms have predominantly focused on continuous-time models, however, for populations with non-overlapping generations, discrete-time models are more realistic than continuous-time ones. Here, we investigated a type of Turing-like patterns in a discrete-time model. The results show that the competition between two stable states can lead to the formation of Turing-like patterns. Specifically, we obtained a type of Turing-like patterns in a discrete-time model, which exist outside the parameter regions of Turing instability. Only by applying strong impulse noise to the homogeneous stable state can the patterns be excited. And the excitation threshold is related to the control parameter. Analysis shows that the Turing-like patterns are the results of competition between two stable states corresponding to adjacent orbits, and the excitation threshold is determined by the relative position between orbits. This findings exemplify the multitude of mechanisms observed in nature that give rise to the emergence of Turing or Turing-like patterns, and shed light on the pattern formation for Turing/Turing-like patterns.

Exponential Stability of Impulsive Timescale-Type Nonautonomous Neural Networks With Discrete Time-Varying and Infinite Distributed Delays.

Global exponential stability (GES) for impulsive timescale-type nonautonomous neural networks (ITNNNs) with mixed delays is investigated in this article. Discrete time-varying and infinite distributed delays (DTVIDDs) are taken into consideration. First, an improved timescale-type Halanay inequality is proven by timescale theory. Second, several algebraic inequality criteria are demonstrated by constructing impulse-dependent functions and utilizing timescale analytical techniques. Different from the published works, the theoretical results can be applied to GES for ITNNNs and impulsive stabilization design of timescale-type nonautonomous neural networks (TNNNs) with mixed delays. The improved timescale-type Halanay inequality considers time-varying coefficients and DTVIDDs, which improves and extends some existing ones. GES criteria for ITNNNs cover the stability conditions of discrete-time nonautonomous neural networks (NNs) and continuous-time ones, and these theoretical results hold for NNs with discrete-continuous dynamics. The effectiveness of our new theoretical results is verified by two numerical examples in the end.

Nonextensive Footprints in Dissipative and Conservative Dynamical Systems

Despite its centennial successes in describing physical systems at thermal equilibrium, Boltzmann–Gibbs (BG) statistical mechanics have exhibited, in the last several decades, several flaws in addressing out-of-equilibrium dynamics of many nonlinear complex systems. In such circumstances, it has been shown that an appropriate generalization of the BG theory, known as nonextensive statistical mechanics and based on nonadditive entropies, is able to satisfactorily handle wide classes of anomalous emerging features and violations of standard equilibrium prescriptions, such as ergodicity, mixing, breakdown of the symmetry of homogeneous occupancy of phase space, and related features. In the present study, we review various important results of nonextensive statistical mechanics for dissipative and conservative dynamical systems. In particular, we discuss applications to both discrete-time systems with a few degrees of freedom and continuous-time ones with many degrees of freedom, as well as to asymptotically scale-free networks and systems with diverse dimensionalities and ranges of interactions, of either classical or quantum nature.

Discrete-Time-Distributed Adaptive ILC With Nonrepetitive Uncertainties and Applications to Building HVAC Systems

Aiming to addressing the nonrepetitive uncertainties of multiagent systems, this work proposes a discrete-time-distributed adaptive iterative learning control (DDAILC) scheme for an output consensus problem, where two fundamental requirements in the traditional distributed iterative learning control (ILC) methods, i.e., the identical initial states and the repetitive desired trajectories, are removed. Furthermore, the algorithm design and analysis are directly aimed at discrete-time nonlinear multiagent systems, rather than continuous-time ones, to meet the needs of practical implementations. The iteration-varying trajectory of the virtual leader is included in the learning control protocol for a compensation. The adaptive parameter-updating law works along the iteration dimension by using a general consensus error that contains the output data of adjacent agents. To ensure the estimation of the control gain to be nonzero, a semisaturator is utilized in the parameter-updating law. The convergence of the output consensus is shown rigorously. Both numerical and practical examples are used to test the theoretical results. Moreover, the DDAILC efficiently improves performance of the building heating, ventilation, and air conditioning (HVAC) system by utilizing both the distributed topology and the repetitive dynamic characteristic.

Bipartite synchronization of signed networks via aperiodically intermittent control based on discrete-time state observations

In this paper, bipartite synchronization of signed networks with stochastic disturbances via aperiodically intermittent control is investigated. The aperiodically intermittent control presented is based on discrete-time state observations rather than continuous-time ones. To formulate signed networks and exhibit the competitive relation, a structurally balanced signed network is built and all the units are divided into two subcommunities. By employing Lyapunov method and graph theory, some sufficient conditions on bipartite synchronization are given. Meanwhile, when aperiodically intermittent control degenerates into periodically intermittent control and feedback control respectively, two corollaries are also provided to ensure the bipartite synchronization of the signed networks. Ultimately, two applications to coupled single-link robot arms and coupled oscillators are presented and corresponding numerical examples are respectively provided to verify the feasibility and effectiveness of the theoretical results.

From Continuous-Time Chaotic Systems to Pseudo Random Number Generators: Analysis and Generalized Methodology.

The use of chaotic systems in electronics, such as Pseudo-Random Number Generators (PRNGs), is very appealing. Among them, continuous-time ones are used less because, in addition to having strong temporal correlations, they require further computations to obtain the discrete solutions. Here, the time step and discretization method selection are first studied by conducting a detailed analysis of their effect on the systems’ statistical and chaotic behavior. We employ an approach based on interpreting the time step as a parameter of the new “maps”. From our analysis, it follows that to use them as PRNGs, two actions should be achieved (i) to keep the chaotic oscillation and (ii) to destroy the inner and temporal correlations. We then propose a simple methodology to achieve chaos-based PRNGs with good statistical characteristics and high throughput, which can be applied to any continuous-time chaotic system. We analyze the generated sequences by means of quantifiers based on information theory (permutation entropy, permutation complexity, and causal entropy × complexity plane). We show that the proposed PRNG generates sequences that successfully pass Marsaglia Diehard and NIST (National Institute of Standards and Technology) tests. Finally, we show that its hardware implementation requires very few resources.

Compositional abstraction-based synthesis for continuous-time stochastic hybrid systems

In this paper, we propose a compositional framework for the construction of discrete-time finite abstractions, also known as finite Markov decision processes, from continuous-time stochastic hybrid systems by quantifying the distance between their outputs in a probabilistic setting. The proposed scheme is based on the notion of stochastic simulation functions, which is used to relate continuous-time stochastic systems with their discrete-time counterparts. Accordingly, one can employ discrete-time abstract systems as substitutions of the continuous-time ones in the controller design process with guaranteed error bounds on their output trajectories. To this end, we first derive sufficient small-gain type conditions for the compositional quantification of the probabilistic distance between the interconnection of original continuous-time stochastic hybrid systems and their discrete-time (finite or infinite) abstractions. We then construct finite abstractions together with their corresponding stochastic simulation functions for a particular class of nonlinear stochastic hybrid systems having some stability property. We illustrate the effectiveness of the proposed results by applying our approaches to the temperature regulation in a circular building and constructing compositionally a discrete-time abstraction from its original continuous-time dynamics in a network containing 1000 rooms. We employ the constructed discrete-time abstractions as substitutes to compositionally synthesize policies regulating the temperature of each room for a bounded time horizon.

Hybrid Output Regulation of DC-DC Converter for Dynamic Wireless Charging System

This paper illustrates a control strategy for voltage regulation problem of DC-DC converter in dynamic wireless charging applications. The control goal is to compensate for the disturbances on the input voltage of the DC-DC converter that changes periodically due to the motion of the electric vehicle assumed to have a constant speed. The paper aims at comparing two different control solutions based on continuous and hybrid internal model-based regulators. According to the relative distance of the transmitter coils the fluctuation of the input voltage is approximated as a continuous-time or a spline-based periodic signal and internal model-based solutions, which are continuous time or hybrid according to the fluctuation modelling, are proposed to compensate for such a disturbance. The control performance of the proposed control schemes are tested through simulation by showing how, as long as the relative distance between the coils increases, the more involved hybrid solutions improve the performances when compared with the more simple continuous-time ones.

A new frequency weighted Fourier-based method for model order reduction

This paper presents a new, analytically driven frequency weighted model order reduction method. The method is grounded on the Fourier-based decomposition of a high-order state space model. The method is designed for discrete-time systems, but it can be easily applied to continuous-time ones. The main advantage of the proposed algorithm is a class of quadratic time complexity as compared to the cubic one for the classical frequency weighted method, the major feature resulting from the application of analytical methods for calculation of factorizations for controllability and observability Gramians. The simulation experiment confirms the effectiveness of the proposed method both in terms of high modeling accuracy and low computational cost.

Digital redesign of analogue dynamic output-feedback controllers for polytopic systems

ABSTRACTThis paper is devoted to the problem known as digital redesign, i.e. given a previously designed stabilising continuous-time controller for a continuous-time plant, synthesise a digital controller that provides the hybrid closed-loop system with output trajectories as similar as possible to the continuous-time ones. To accomplish this goal, two distinct optimisation criteria are investigated: (i) the Euclidean norm of the difference between the dynamic matrix of the discretised closed-loop continuous-time system and the dynamic matrix that represents the discretised open-loop system fed back by the designed digital controller; (ii) the norm of the transfer function from the noise input to the error between the outputs of the two systems. As main novelties with respect to the existing results on digital redesign, the proposed conditions can deal with polytopic systems, and can synthesise reduced-order dynamic output-feedback digital controllers as well.

Fuzzy Approaches to Option Price Modeling

The aim of this paper is to review the literature that has addressed direct and inverse problems in option pricing in a fuzzy setting. In a direct problem, the stochastic process for the underlying asset is assumed and the option prices are derived by no-arbitrage or equilibrium conditions. In an inverse problem, the option prices are taken as given and used to infer the underlying asset process. Models are divided into discrete-time and continuous-time ones. Special attention is paid to real options, a particular class of nonfinancial options that are used to evaluate real investments. Directions for future research are outlined. In particular in inverse problems, there is still room for promising research, both in discrete time and in continuous time. Moreover, given that many proposed methods remain difficult to use in practice, there is mainly the need to apply the fuzzy models obtained on real market data and to compare the results with nonfuzzy techniques in order to assess the usefulness and the improvements in the modeling of imprecise data with fuzzy sets and fuzzy random variables.

Dual estimation: Constructing building energy models from data sampled at low rate

Estimation of energy models from data is an important part of advanced fault detection and diagnosis tools for smart energy purposes. Estimated energy models can be used for a large variety of management and control tasks, spanning from model predictive building control to estimation of energy consumption and user behavior. In practical implementation, problems to be considered are the fact that some measurements of relevance are missing and must be estimated, and the fact that other measurements, collected at low sampling rate to save memory, make discretization of physics-based models critical. These problems make classical estimation tools inadequate and call for appropriate dual estimation schemes where states and parameters of a system are estimated simultaneously. In this work we develop dual estimation schemes based on Extended Kalman Filtering (EKF) and Unscented Kalman Filtering (UKF) for constructing building energy models from data: in order to cope with the low sampling rate of data (with sampling time 15min), an implicit discretization (Euler backward method) is adopted to discretize the continuous-time heat transfer dynamics. It is shown that explicit discretization methods like the Euler forward method, combined with 15min sampling time, are ineffective for building reliable energy models (the discrete-time dynamics do not match the continuous-time ones): even explicit methods of higher order like the Runge–Kutta method fail to provide a good approximation of the continuous-time dynamics which such large sampling time. Either smaller time steps or alternative discretization methods are required. We verify that the implicit Euler backward method provides good approximation of the continuous-time dynamics and can be easily implemented for our dual estimation purposes. The applicability of the proposed method in terms of estimation of both states and parameters is demonstrated via simulations and using historical data from a real-life building.

Generic and parsimonious stochastic modelling for hydrology and beyond

ABSTRACTThe old principle of parsimonious modelling of natural processes has regained its importance in the last few years. The inevitability of uncertainty and risk, and the value of stochastic modelling in dealing with them, are also again appreciated, after a period of growing hopes for radical reduction of uncertainty. Yet, in stochastic modelling of natural processes several families of models are used that are often non-parsimonious, unnatural or artificial, theoretically unjustified and, eventually, unnecessary. Here we develop a general methodology for more theoretically justified stochastic processes, which evolve in continuous time and stem from maximum entropy production considerations. The discrete-time properties thereof are theoretically derived from the continuous-time ones and a general simulation methodology in discrete time is built, which explicitly handles the effects of discretization and truncation. Some additional modelling issues are discussed with a focus on model identification and fitting, which are often made using inappropriate methods.EDITOR Z.W. Kundzewicz ASSOCIATE EDITOR S. Grimaldi

Efficient zero location tests for delta-operator-based polynomials

Two different kinds of stability tests, or more generally zero location tests, are proposed when a real polynomial formulated in the delta-operator is given. The method used is a simple linear transformation based on some known discrete-time tests, including the Schur-Cohn test (SCT), and the proposed algorithms are computationally efficient. Furthermore, it is shown that as the sampling interval vanishes, all new algorithms converge to their continuous-time limits, therefore providing smooth transitions from the shift-operator-based discrete-time tests to the continuous-time ones. One of these limits is the classic Routh test (RT), and the other is a new test, closely related to the RT. Examples are given to demonstrate the tests which show clear numerical advantages over the traditional shift-operator-based ones such as the SCT in case of fast sampling. The significance of these new tests lies beyond the fact that they have provided efficient and reliable zero location tests directly in the delta-domain. These tests provide the missing links between the discrete-time shift-operator-based tests and the continuous-time ones. As a consequence, two separate and yet related families of zero location tests are established, which include the well-known RT and the SCT.

Quadratic forms and approximate feed back linearization in discrete time

Quadratic feedback linearization is discussed for discrete-time systems, i.e. approximate feedback linearization up to the second order with respect to input and state variables. After introducing in discrete time two equivalence classes, invariant under quadratic static state feedback and diffeomorphism, two canonical quadratic representations are proposed. Then it is shown that any nonlinear discrete-time dynamics, which are controllable in their first approximations, can be linearized up to the second order under dynamic feedback. The results stated here can be considered as the general discrete-time analogues of the continuous-time ones (Kang and Krener 1992).

High Performance Servo-System by Rotational Machines. Digital Speed Control of 2-mass Systems with a Tortional Torque Observer.

Recently, many researches for vibration suppression control of 2-mass systems have been reported because the effects of non-stiff coupling cannot be ignored when a faster speed response is required for motor driving systems. An observer based approach is one of the representative methods to suppress the vibration which assumes that the disturbance torque changes very slowly, or even is constant during the sampling period, and uses a disturbance observer to estimate the tortional torque. And the systems are almost analyzed as continuous time ones. But in case that the system is composed of small equipment, the resonance frequency becomes high enough to be close to the sampling frequency of the speed detector, so we have to use high gains for the observer with the result that the noise and parameter error have strong effects on the calculation of the observer.In this paper, treating the system as a discrete time one, we propose a novel vibration suppression control method. Assuming that the torsional torque is composed of a periodic component and dc component, we use PI type controller for the speed control system and feed the estimation torque forward to the current reference to suppress the vibration. Experimental results show the validity of the proposal method.

Metastable operation in RS flip-flops

A new model for representing the different types of behaviour exhibited by an RS flip-flop under metastable operation is presented. Although it reflects flip-flop transient operation, the new model handles logical variables instead of continuous time ones. The model is applied to flip-flops for both simultaneous input changes and runt pulses.