Order Discrete-time Systems Research Articles

Couple-Group Consensus for First Order Discrete-Time Multiagent Systems With Competition-Cooperation and Input Saturation Constraints

Collaborative consensus control of multiagent systems has become an important research topic in the field of artificial intelligence in recent years. This paper deals with the couple-group consensus for the first order discrete-time systems with input saturation constraints. Compared to most previous studies, this article focuses on the control input constraints phenomenon in couple-group consensus problem. Based on the relationship between competition and cooperation, a new negotiation protocol is designed to achieve couple-group consensus. Furthermore, combining graph theory with Lyapunov theorem, the control gain condition is obtained. Finally, the results of numeric modeling show that the method is correctness and effectiveness.

The discrete fractional duffing system: Chaos, 0-1 test, C0 complexity, entropy, and control.

In this paper, we study the dynamics and control of a Caputo fractional difference form of the Duffing map. We use phase plots, bifurcation diagrams, and Lyapunov exponents to establish the existence of chaos over a wide range of fractional orders and examine the nature of the dynamics. Also, we present the 0-1 test to detect chaos and C0 complexity, which is an alternative nonlinear statistical measure that can quantify the regularity of a time series. In addition, we measure the approximate entropy to see the performance of our numerical results. Through phase plots and bifurcation diagrams, it is shown that the proposed fractional map exhibits a range of different dynamical behaviors including chaos and coexisting attractors. A one-dimensional feedback stabilization controller is proposed. The asymptotic convergence of the proposed controller is established by means of the stability theory of linear fractional order discrete-time systems. Simulation results have been carried out to illustrate the findings of the study.

Chaos and control of a three-dimensional fractional order discrete-time system with no equilibrium and its synchronization

Chaotic systems with no equilibrium are a very important topic in nonlinear dynamics. In this paper, a new fractional order discrete-time system with no equilibrium is proposed, and the complex dynamical behaviors of such a system are discussed numerically by means of a bifurcation diagram, the largest Lyapunov exponents, a phase portrait, and a 0–1 test. In addition, a one-dimensional controller is proposed. The asymptotic convergence of the proposed controller is established by means of the stability theory of linear fractional order discrete-time systems. Next, a synchronization control scheme for two different fractional order discrete-time systems with hidden attractors is reported, where the master system is a two-dimensional system that has been reported in the literature. Numerical results are presented to confirm the results.

Effect of initialization on optimal control problem of fractional order discrete-time system

Initialization effect on optimal control problem (OCP) of fractional order discrete-time system (FODS) is considered here. Formulation and numerical solution of OCP of initialized FODS is presented. Performance index (PI) considered is of general form and the system dynamics are given by fractional order differential equations (FDEs) in discrete-time domain. By using Hamiltonian approach, we obtain the necessary conditions. Optimal conditions are solved using a general numerical method. The effect of initialization is studied by changing length of the history period as well as nature of the history function. Numerical example is included to illustrate the initialization effect. It has been observed that initialization effect reduces with the increase in order of the fractional derivative.

Chaos synchronization of fractional–order discrete–time systems with different dimensions using two scaling matrices

Abstract In this paper, we study the synchronization of fractional–order discrete–time chaotic systems by means of two scaling matrices Θ and Φ. The considered synchronization scheme can be tailored to encompass several types of classical synchronization types. We proposed two nonlinear control strategies for the Θ–Φ synchronization of an m–dimensional drive system and an n–dimensional response system, whereby the synchronization dimension d = m and d = n, respectively. Numerical examples are presented to test the findings of the study.

Stability of Fractional Variable Order Difference Systems

Abstract The problem of stability of the Grünwald-Letnikov-type linear fractional variable order discrete-time systems is discussed. As a definition of the Grünwald-Letnikov difference is a convolution type, the 𝓩-transform is used as an effective tool for the stability analysis. The conditions for asymptotic stability and for instability are presented. In the case of a scalar system we state conditions that guarantee asymptotic stability in inequalities for a coefficient that appears on the right hand side of the equation defined the system}. We describe regions of the stability for systems accordingly to locus of eigenvalues of a matrix associated to the considered system. In the general case of the linear difference systems one can determine the regions of location of eigenvalues of matrices associated to the systems in order to guarantee the asymptotic stability of the considered systems. Some of the frames of these regions are illustrated in the examples.

Model-free adaptive command-filtered-backstepping sliding mode control for discrete-time high-order nonlinear systems

A new model-free adaptive sliding mode control method is proposed to solve some control issues in a class of discrete-time high-order nonlinear systems whose dynamics are unknown in this paper. In order to simplify the nonlinear system, a new concept called pseudo-partial derivative matrix (PPDM) is introduced to facilitate the nonlinear system by using a compact form dynamic linearization approach. Therefore, to estimate the PPDM, the identified adaptive observer is constructed using the input/output data from each subsystem of the higher order discrete time system. Taking into account the amplitude and rate constraints of real-world input signals, an anti-windup dynamic compensator is developed. Furthermore, the problems of complexity explosion and non-causality are solved by using discrete-time command filters while designing the controller. It has been shown that all the control variables in closed-loop systems are uniformly-ultimately bounded. An example of a linear induction motor taking into account the end effects is used to verify the effectiveness of the presented control strategy through simulations and experiments.

On fractional–order discrete–time systems: Chaos, stabilization and synchronization

In this paper, we propose three systems, namely the fractional Lozi map, the fractional Lorenz map, and the fractional flow map. We study some of the important dynamics of these maps including the bifurcation graphs. In addition, we propose control laws aimed at stabilizing and synchronizing a combination of these three maps. The convergence of the stabilized states and the synchronization errors is established by means of the linearization method. Numerical simulations are also presented to confirm the main findings of the study.

Systems with Fractional Variable-Order Difference Operator of Convolution Type and Its Stability

In the paper the Grunwald–Letnikov-type linear fractional variable order discrete-time systems are studied. The conditions for stability and instability are formulated. The regions of the systems stability are determined accordingly to locus of eigenvalues of a matrix associated to the considered system.DOI: http://dx.doi.org/10.5755/j01.eie.24.5.21846

On the Fractional Variable Order Cucker–Smale Type Model

In the paper the Cucker-Smale type models with a fractional variable order operator are considered. The asymptotic stability of a class of linear fractional variable order discrete-time systems is used to study a consensus in the nonlinear fractional variable order discrete-time systems. Basing on a linearization method of the considered multi-agent system we give the sufficient conditions that guarantee the consensus. Finally, an example illustrates our results.

Fractional variable order discrete-time systems, their solutions and properties

ABSTRACTIn this paper, fractional variable order discrete state-space systems based on different definitions of fractional variable order difference are investigated.The general solution of these systems is derived. Moreover, necessary and sufficient conditions for reachability and observability are given and proven. The sufficient conditions for controllability are proposed too.

Observability of linear discrete-time systems of algebraic and difference equations

ABSTRACTThe notion of observability for higher order discrete-time systems of algebraic and difference equations is studied. Such systems are also known as polynomial matrix descriptions . Attention is first given to a special form of descriptor systems with a state lead in the output. This system is transformed into its causal and noncausal subsystems and observability criteria are given in terms of the subsystem's matrices, and the fundamental matrix sequence of the matrix pencil (σE − A). Afterwards, the higher order system is studied. By transforming it into a first-order descriptor system of the above form, an observability criterion is provided for the higher order system in terms of the Laurent expansion at infinity of the system's polynomial matrix. In addition, observability is connected with the coprimeness of the polynomial matrices of the higher order system and the coprimeness of the matrix pencils of the descriptor system.

Positive fractional variable order discrete-time systems

This paper introduces and characterizes linear Positive Fractional Variable Order Discrete-Time Systems described in pseudo state-space form for different types of fractional variable order differences. The verifiable necessary and sufficient conditions of positivity are also given.

Multiparameter Fractional Difference Linear Control Systems

The Riemann-Liouville-, Caputo-, and Grünwald-Letnikov-type fractional order difference operators are discussed and used to state and solve the controllability and observability problems of linear fractional order discrete-time control systems with multiorder and multistep. It is shown that the obtained results do not depend on the type of fractional operators and steps. The comparison of systems is made under the number of steps needed, firstly to achieve a final point, and secondly to distinguish initial conditions for particular operator.

Local controllability of nonlinear discrete-time fractional order systems

Abstract The Riemann-Liouville, Caputo and Gr¨unwald-Letnikov fractional order difference operators are discussed and used to state and solve the controllability problem of a nonlinear fractional order discrete-time system. It is shown that independently of the type of fractional order difference, such a system is locally controllable in q steps if its linear approximation is globally controllable in q steps

PFC Design via FRIT Approach and Adaptive PID Control System Design for Discrete-time Systems

This paper deals with a design problem of an adaptive PID control for discrete-time systems with a parallel feedforward compensator (PFC) which is designed for making the augmented controlled system ASPR. A PFC design scheme by a FRIT approach with only using an input/output experimental data set will be proposed for discrete-time systems in order to design an adaptive PID control system. Furthermore, the effectiveness of the proposed PFC design and an adaptive PID control method will be confirmed through numerical simulations for an uncertain discrete-time system.

PFC design via FRIT Approach for Adaptive Output Feedback Control of Discrete-time Systems

SUMMARY This paper deals with a design problem of an adaptive output feedback control for discrete-time systems with a parallel feedforward compensator (PFC), which is designed for making the augmented controlled system “Almost Strictly Positive Real” (ASPR). A PFC design scheme by a fictitious reference iterative tuning (FRIT) approach with only using an input/output experimental data set will be proposed for discrete-time systems in order to design an adaptive output feedback control system. Furthermore, the effectiveness of the proposed PFC design method will be confirmed through numerical simulations by designing an adaptive control system with adaptive NN (neural network) for an uncertain discrete-time system. © 2014 Wiley Periodicals, Inc. Electr Eng Jpn, 187(1): 24–32, 2014; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/eej.22456

Design of Output Feedback Compensator for Discrete Time System via Reduced Order Model

A method to design an output feedback compensator for a higher order discrete time system with distinct complex eigenvalues via its reduced order model is presented. Its application is shown for vibration control of a smart cantilever beam. As the states are not needed for feedback, the method is simple and can be easily implemented.

DESIGN OF REDUCED ORDER H∞ FILTERS FOR DISCRETE TIME SYSTEMS

In this contribution the design of reduced order H∞ filters of order n-κ is investigated for nth order discrete time systems with m measurements of which κ are undisturbed. Assuming a reduced order observer structure for the H∞ filter, the filter gains achieving H∞ optimal a priori estimates z(k) and a posteriori estimates z+ (k) are derived using the Bounded Real Lemma. A simple example demonstrates the proposed design procedure.

Iterative learning control based on the gradient method for linear discrete-time systems

Methods of iterative learning control for discrete-time systems have already been proposed. However, the applicability of these schemes depends essentially on the structure of the system. There are systems to which these schemes cannot be applied, even if the system models are completely known. In this paper we present a scheme, based on the gradient method, of iterative learning control for linear discrete-time systems in order to overcome these difficulties. The applicability of this scheme depends only on the amount of uncertainty in the system parameters. Some convergence conditions expressed as ranges of parameters are also presented for practical application to systems with uncertainty.