Class Of Linear Discrete Systems Research Articles

A Distributionally Robust Optimization Based Method for Stochastic Model Predictive Control

Two stochastic model predictive control algorithms, which are referred to as distributionally robust model predictive control algorithms, are proposed in this article for a class of discrete linear systems with unbounded noise. Participially, chance constraints are imposed on both of the state and the control, which makes the problem more challenging. Inspired by the ideas from distributionally robust optimization (DRO), two deterministic convex reformulations are proposed for tackling the chance constraints. Rigorous computational complexity analysis is carried out to compare the two proposed algorithms with the existing methods. Recursive feasibility and convergence are proven. Simulation results are provided to show the effectiveness of the proposed algorithms.

Correlation Analysis of Japanese Literature and Psychotherapy Effects Based on an Equation Diagnosis Algorithm.

Objective On the basis of inheriting the classical aesthetic orientation of Japanese literature, contemporary Japanese literature changes the creative methods of traditional Japanese writers, strives to transcend the national limitations of Japanese literature, and strives to capture literary materials with a “modern feel.” Combined with modern western literary techniques to express the “modern self,” and integrating popular literature with pure literature, Japanese writers created a “healing” literature that is popular all over the world. There is some value in exploring the correlation between Japanese literature and the influence of psychotherapy. Method In this paper, an equation diagnosis algorithm based on iterative learning for a class of linear discrete systems is studied, and the existing discrete iterative learning diagnostics are improved. We exchange the order of time domain and iterative domain to achieve the purpose of point-by-point equation diagnosis. On this basis, a virtual influence initial value estimation algorithm with a sliding window is proposed. The impact that has not been diagnosed is estimated and used as the initial value of the impact, so as to reduce the number of iterations and improve the efficiency of equation diagnosis. This paper takes the public and readers as different perspectives, based on the use and satisfaction theory and prospect theory, and uses interviews and questionnaires to study the communication effect of Japanese literature from the three dimensions of cognition, emotion, and behavior. The cognitive part includes the public's understanding and readers' understanding and reading; the emotional part includes the public's and readers' impressions and emotional attitudes; the behavioral part includes the public's reading situation and readers' behavior changes. Results/Discussion. In the survey of loyal readers, although readers' understanding of Japanese literature has improved compared with the general public, it is not high, and their liking and influence on behavior are slightly lower than the preset level. This paper believes that the existing problems of Japanese literature dissemination are mainly concentrated in three aspects: the market is somewhat biased, which narrows the cognitive scope of users; as a cross-cultural literary work, Japanese literature still makes readers feel that it exists; there is some sense of estrangement, which will affect their enjoyment in reading; as a niche interest, readers lack timely communication and sharing objects after reading, so it is difficult to enhance their sense of identity.

Robust feedback feed-forward PD-type iterative learning control for uncertain discrete systems over finite frequency ranges

This paper proposes a robust feedback feed-forward proportional-derivative type (PD-type) iterative learning control (ILC) scheme for a class of linear discrete systems with polytopic uncertainty over finite frequency ranges. First, the ILC process is transformed into an equivalent discrete linear repetitive process. Then, with the help of the generalized Kalman–Yakubovich–Popov lemma, the issue of a robust control law design algorithm in the process model is converted into the problem of solutions to the corresponding linear matrix inequality conditions. This procedure not only meets the robust performance specifications along the trial, but also guarantees the monotonic converge of the trial-to-trial error dynamics over finite frequency ranges. Finally, the simulations for a direct current servo motor system are adopted to show the effectiveness and superiority of the proposed method. Compared with previously established works, the new algorithm is more effective in delivering higher performance and achieving better tracking effect.

Recursive State and Random Fault Estimation for Linear Discrete Systems under Dynamic Event-Based Mechanism and Missing Measurements

This paper is concerned with the event-based state and fault estimation problem for a class of linear discrete systems with randomly occurring faults (ROFs) and missing measurements. Different from the static event-based transmission mechanism (SETM) with a constant threshold, a dynamic event-based mechanism (DETM) is exploited here to regulate the threshold parameter, thus further reducing the amount of data transmission. Some mutually independent Bernoulli random variables are used to characterize the phenomena of ROFs and missing measurements. In order to simultaneously estimate the system state and the fault signals, the main attention of this paper is paid to the design of recursive filter; for example, for all DETM, ROFs, and missing measurements, an upper bound for the estimation error covariance is ensured and the relevant filter gain matrix is designed by minimizing the obtained upper bound. Moreover, the rigorous mathematical analysis is carried out for the exponential boundedness of the estimation error. It is clear that the developed algorithms are dependent on the threshold parameters and the upper bound together with the probabilities of missing measurements and ROFs. Finally, a numerical example is provided to indicate the effectiveness of the presented estimation schemes.

The use of the localization method for calculation of the robust PID regulator parameters for unmanned aircraft servo motor

The problem of controlling a typical nonlinear servo motor of an unmanned aercraft with non-stationary parameters using a robust PID controller is considered. The procedure for calculating the parameters of a robust PID controller based on the localization method (further - LM PID controller) for continuous and discrete control systems is studied. The influence of disturbing factors (internal and external) acting on the servo motor is considered. It is established that the main perturbations acting on the servo drive include internal perturbations, which are changes in the time constant and its gain from the temperature of the environment and the quality of the supply voltage. The simulation in the class of linear and nonlinear continuous systems showed that a servo drive with a ML PID controller has the property of robustness in the working range of changes in both the input signal and the parameters of the servo drive and controller. Simulation results showing the research are presented. When describing a servo motor with an LM PID controller in the class of linear discrete systems, its robustness is limited by a narrow range of variation of both its parameters and the quantization period of the input signal. As the degree of uncertainty in the parameters of the servo motor increases (approaching the working range of their change), the discrete system loses stability. For the synthesis of robust control circuits of an unmanned aercraft with given characteristics, mathematical dependences of the settling time and static error of a typical servo motor with LM PID controller from the quantization period of the input signal and the degree of uncertainty in its parameters are presented.

Optimal Linear Estimators for Time-Delay Systems with Fading Measurements and Correlated Noises

The optimal linear estimation problems are investigated in this paper for a class of discrete linear systems with fading measurements and correlated noises. Firstly, the fading measurements occur in a random way where the fading probabilities are regulated by probability mass functions in a given interval. Furthermore, time-delay exists in the system state and observation simultaneously. Additionally, the multiplicative noises are considered to describe the uncertainty of the state. Based on the projection theory, the linear minimum variance optimal linear estimators, including filter, predictor, and smoother are presented in the paper. Compared with conventional state augmentation, the new algorithm is finite-dimensionally computable and does not increase computational and storage load when the delay is large. A numerical example is provided to illustrate the effectiveness of the proposed algorithms.

Fault Diagnosis for Linear Discrete Systems Based on an Adaptive Observer

This paper presents a fault diagnosis algorithm to estimate the fault for a class of linear discrete systems based on an adaptive fault estimation observer. And observer gain matrix and adaptive adjusting rule of the fault estimator are designed. Furthermore, the adaptive regulating algorithm can guarantee the first-order difference of a Lyapunov discrete function to be negative, so that the observer is ensured to be stable and fault estimation errors are convergent. Finally, simulation results of an aircraft F-16 illustrate the advantages of the theoretic results that are obtained in this paper.

Design of Iterative Learning Controllers for Linear Discrete Systems with Multiple Time Delays

The problem of iterative learning control is considered for a class of linear discrete systems with multiple time delays. In this paper, it is assumed that the initial condition for discrete time-delay systems is unknown at each iteration. For such a class of discrete time-delay systems, a method is presented whereby a class of discrete iterative learning control schemes can be constructed. It is shown that under some given conditions, the constructed iterative learning controllers can guarantee the asymptotic convergence of the output error between the given desired output and the actual output through the iterative learning process. Finally, a numerical example is given to demonstrate the validity of the results.

Asymptotic Stability of a Class of Linear Discrete Systems with Multiple Independent Variables

This paper investigates the problem of asymptotic stability for a class of linear shift-invariant discrete systems with multiple independent variables. We establish the equivalence of this problem and that of robust stability for a class of ordinary linear shiftvarying discrete systems with the matrix uncertainty set defined by the coefficient matrices of the original system. On the basis of this equivalence, by using the variational method and Lyapunov’s second method, necessary and sufficient conditions for asymptotic stability are obtained in different forms for the class of systems considered. The parametric classes of Lyapunov functions which define the necessary and sufficient conditions of asymptotic stability are determined. We use the piecewise linear polyhedral Lyapunov functions of the infinity vector norm type to derive an algebraic criterion for asymptotic stability of the given class of discrete systems in the form of solvability conditions of a set of matrix equations. A simple sufficient condition of asymptotic stability is also obtained which becomes necessary and sufficient for several special cases of the discrete systems under consideration.

Introduction to fractional linear systems. Part 2: Discrete-time case

In the paper, the class of discrete linear systems is enlarged with the inclusion of discrete-time fractional linear systems. These are systems described by fractional difference equations and fractional frequency responses. It is shown how io compute the impulse response and transfer function. Fractal signals are introduced as output of special linear systems: fractional differaccumulators, systems that can be considered as having fractional poles or zeros. The concept of fractional differaccumulation is discussed, gencralising the notions of fractal and lif noise, and introducing two kinds of fractional differaccumulated stochastic proccss: hyperbolic, resulting from fractional accumulation (similar to the continuous-time casc), and parabolic noise, resulting from fractional differencing.

A Control Algorithm for a Class of Discrete Time-delay Systems Based on Staged Transformation and Its Application

In this paper, a stabilizing control algorithm for a class of discrete linear systems with delayed control is presentedbased on staged design idea. A timedelay transformation with past control information is introduced to transform a time-delay system into a linear delay-free system. The stabilizing controller to the primitive time-delay system is derived via a staged design method. The simulation study shows the effectiveness of the presented design method for an industrial electric heater example.

Comments on "Asymptotic stability for a class of linear discrete systems with bounded uncertainties" [with reply

In the above-named work, M.S. Mahmoud and A.A. Bahnasawi (see ibid., vol.33, p.572-5, June 1988) present a class of feedback controllers and claims that these controllers yield a closed-loop system which is asymptotically stable for all allowable uncertainties. The commenter claims that the results they present are incorrect and indicates why he thinks so. The authors reply point by point to the commenter's remarks.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Asymptotic stability for a class of linear discrete systems with bounded uncertainties

The problem of stabilizing linear discrete systems with additive-type bounded uncertainties is considered. It is established that when matching conditions hold, a two-part feedback control can be designed: a linear part to assign the eigenvalues within the unit cycle and a nonlinear part to ensure the uniform asymptotic stability for arbitrary initial conditions and bounded admissible uncertainties. >

Structural stability via the density of a class of linear discrete systems

In this paper we prove that the set of multiplicatively separated linear discrete systems is dense in the set of linear systems and we find a relationship between the set of structurally stable systems and the set of the systems which have an exponential dichotomy.

On the application of Liapunov's direct method to discrete dynamic systems with stochastic parameters

A Liapunov function specially suitable for the study of the almost sure asymptotic stability of a class of linear discrete systems, described by a set of second order differential equations with stochastic parameters, is presented. A theorem and related corollaries, applicable to systems involving general types of forces, are obtained. The proposed technique is shown to be useful in minimizing the computational efforts associated with relatively large dynamic systems. Several examples, including systems involving follower forces, are included to demonstrate the effectiveness of the method.

Sensitivity and parameter identifiability in linear systems

In this paper a class of discrete linear systems affected by a time varying parameter are considered. By means of a sensitivity analysis effective parameter identifiability conditions are obtained. An application to the identification of a cross-flow heat exchanger is finally discussed.

Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria †

The optimal control for a discrete-time linear system with quadratic criterion functional is derived for the case where the system parameters are subject to a discrete-time, discrete-state Markov process. Utilization of the results is demonstrated in a numerical example using Samuelson's multiplier-accelerator macroeconomic model.

On computer requirement reductions in linear-discrete system state estimation

A procedure is presented for reducing the on-line computing time and storage requirements when estimating the state of a class of linear-discrete systems.

Parameter identification for a class of linear discrete systems

Parameter identification for a class of linear discrete systems