Class Of Discrete-time Linear Systems Research Articles

Iterative Learning Control Based on Nesterov Accelerated Gradient Method

Based on Nesterov accelerated gradient method, the problem of iterative learning control for a class of linear discrete-time systems is considered in this paper. Firstly, the iterative learning control problem of linear discrete-time systems is transformed into an iterative least-squares problem. Then, the Nesterov accelerated gradient method is introduced into the iterative learning control framework. Note that the Nesterov accelerated gradient learning algorithm has the capability of fast convergence. It is shown that the algorithm presented in this paper can guarantee the output tracking error converges to zero with rate O(1/k) , where k is the iteration counter. Moreover, the monotonic convergence of the Nesterov accelerated gradient learning algorithm is analyzed and discussed. Finally, the effectiveness of the proposed method is verified by two simulation examples.

Anisotropy-Based Controller Design for Linear Discrete-Time Systems with Multiplicative Noise

This paper extends anisotropy-based control theory methods to the class of linear discrete-time systems with multiplicative noise, which involves an informational criterion to describe the stochastic uncertainty of an external disturbance. An approximate calculation method for the anisotropic norm of such systems using decomposition into linear subsystems without multiplicative noise is suggested. The cases of perfect and imperfect state measurements are considered. The existence criterion for anisotropy-based controllers in form of special matrix inequalities is established.

PID output-feedback control under event-triggered protocol

This paper is concerned with the proportional-integral-derivative (PID) output-feedback control problem for a class of linear discrete-time systems under event-triggered protocols. The controller and the actuators are connected through a communication network of limited bandwidth, and an event-triggered communication mechanism is adopted to decide when a certain control signal should be transmitted to the respective actuator. Furthermore, a novel PID output-feedback controller is designed where the accumulative sum-loop (the counterpart to the integral-loop in the continues-time setting) operates on a limited time-window with hope to mitigate the effect from the past measurement data. The main objective of the problem under consideration is to design a desired PID controller such that the closed-loop system is exponentially stable and the prescribed disturbance rejection attenuation level is guaranteed under event-triggered protocols. By means of the Lyapunov stability theory combined with the orthogonal decomposition, sufficient conditions are established under which the addressed PID controller design problem is recast into a linear convex optimization one that can be easily solved via available software packages. Finally, a simulation example is exploited to illustrate the usefulness and effectiveness of the established control scheme.

Improved Tobit Kalman filtering for systems with random parameters via conditional expectation

This paper is concerned with the Tobit Kalman filtering problem for a class of linear discrete-time system with random parameters. The elements of both the system matrix and the measurement matrix are allowed to be random variables in order to reflect the reality. The information matrix is employed to 1) derive the covariance between any two random variables; and 2) establish a novel weighting covariance formula to address the quadratic terms associated with the random matrices. A set of Bernoulli random variables is introduced to govern the censoring phenomenon on the measurement output. The conditional expectation, as a basic tool, is utilized to deal with the dependence among the random variables. Within the framework of the traditional Kalman filtering, the proposed filtering algorithm includes the information from both the random parameters and the censored measurements. A simulation example is presented to illustrate the effectiveness and applicability of the designed algorithm.

Optimal linear filtering design for discrete‐time systems with cross‐correlated stochastic parameter matrices and noises

This study investigates the design of an optimal linear estimator for a class of discrete-time linear systems with correlated stochastic parameter matrices and noises. The considered systems are endowed with the following two main features: (i) cross-correlated stochastic matrices involved in the state and observation equations are assumed and (ii) the process and observation noises have cross-correlation at the same time instant. A decorrelation framework is established to reconstruct such systems. With the equivalent transformation of original dynamic systems resulting from decorrelating operations, the optimal linear recursive filter in the minimum mean square error sense is developed by employing the results of Kalman filtering. The discrete-time linear systems with multiple packet dropouts are modelled as a particular case, and then the proposed filter is applied directly to estimate the system state, while a comparative analysis between the new method and the existing approaches is provided. Simulations demonstrate the effectiveness of the presented algorithm.

The Robust Output Tracking Problem for a Class of Discrete-time Linear Systems

The Robust Output Tracking Problem for a Class of Discrete-time Linear Systems

Event-triggered fault detection for a class of discrete-time linear systems using interval observers

This paper provides a novel event-triggered fault detection (FD) scheme for discrete-time linear systems. First, an event-triggered interval observer is proposed to generate the upper and lower residuals by taking into account the influence of the disturbances and the event error. Second, the robustness of the residual interval against the disturbances and the fault sensitivity are improved by introducing l1 and H∞ performances. Third, dilated linear matrix inequalities are used to decouple the Lyapunov matrices from the system matrices. The nonnegative conditions for the estimation error variables are presented with the aid of the slack matrix variables. This technique allows considering a more general Lyapunov function. Furthermore, the FD decision scheme is proposed by monitoring whether the zero value belongs to the residual interval. It is shown that the information communication burden is reduced by designing the event-triggering mechanism, while the FD performance can still be guaranteed. Finally, simulation results demonstrate the effectiveness of the proposed method.

Detection of Intermittent Fault for Discrete-Time Systems with Output Dead-Zone: A Variant Tobit Kalman Filtering Approach

This paper is concerned with the intermittent fault detection problem for a class of discrete-time linear systems with output dead-zone. Dead-zone phenomenon exists in many real practical systems due to the employment of low-cost commercial off-the-shelf sensors. Two Bernoulli random variables are utilized to model the dead-zone effect and a variant formation of Tobit Kalman filter is brought forward to generate a residual that can indicate the occurrence of an intermittent fault. A numerical example is presented to demonstrate the effectiveness and applicability of the proposed technique. The statistical performance of the technique is illustrated as well.

Finite-time stability for a linear discrete-time delay systems by using discrete convolution: An LMI approach

The problem of finite-time stability for a class of linear discrete-time systems with state delay is studied. The Lyapunov-Krasovskii-like functional which is based on discrete convolutions of delayed state vector and time-dependent discrete vector functions is used. In order to obtain much less conservative results, new sufficient condition is derived in form of linear matrix inequalities. Numerical example is given to demonstrate the effectiveness of the proposed stability criterion. It was shown that the obtained results are less conservative than some existing ones in the literature. A computer simulation was performed for the analysis of the dynamical behaviour of this system.

On some class of periodic-discrete homogeneous difference equations via Fibonacci sequences

The intent of this paper is to solve the homogeneous linear difference equations with periodic coefficients. For this purpose, we turn our study in solving a class of discrete-time linear systems, in the algebra of square matrices. The tools used repose predominately on the combinatorial properties of the generalized Fibonacci sequences in the algebra of square matrices. Some explicit solutions are established and special cases are discussed. Illustrative examples are given.

Unknown input and state estimation for linear discrete-time systems with missing measurements and correlated noises

This paper is concerned with the problem of simultaneous input and state estimation for a class of linear discrete-time systems with missing measurements and correlated noises. The missing measurements occur in a random way and are governed by a series of mutually independent random variables obeying a certain Bernoulli distribution. The process and measurement noises under consideration are correlated at the same time instant. Our attention is focused on the design of recursive estimators for both input and state such that, for all missing measurements and correlated noises, the estimators are unbiased and the estimation error covariances are minimized. This objective is achieved using direct algebraic operation and the design algorithm for the desired estimators is given. Finally, an illustrative example is presented to demonstrate the effectiveness of the proposed design scheme.

ADP based optimal tracking control for a class of linear discrete-time system with multiple delays

In this paper, a new optimal tracking control scheme for a class of linear discrete-time systems with multiple delays is proposed using an iterative adaptive dynamic programming algorithm. First, the minimum delays equivalent system of the original system with multiple delays is derived based on the coordinate transformation technique, and then the corresponding Bellman equation and Q-function are presented, respectively. Then, a model-free optimal tracking controller is designed to minimize the augmented quadratic performance index based on the adaptive dynamic programming algorithm, which without requiring any knowledge of the system dynamics. Simulation results show the effectiveness of the proposed control scheme.

Unbiased information filtering for systems with missing measurement based on disturbance estimation

This paper designs the information filters for a class of linear discrete-time systems with unknown disturbance. A recursive three-step information filter (RTSIF) is presented at first, which is used to estimate the unknown disturbance and state separately. In the presence of measurement dropout, a recursive three-step information filter with missing measurement (RTSIFMM) is also developed, in which the missing measurement is modelled as Bernoulli process with a binary variable. Two types of stochastic stability are introduced to give the boundedness of proposed filter. It is shown that the estimation error will be bounded, if some assumptions are satisfied. The relationships between the designed filter in this paper and some existing results are given. Finally, a simulation example is applied to demonstrate the effectiveness of the proposed filter.

Iterative learning control design method for linear discrete‐time uncertain systems with iteratively periodic factors

In this study, a two-dimensional (2D) H ∞-based method is presented for the iterative learning control (ILC) design problem of a class of linear discrete-time systems with iteratively periodic factors, including initial states, parametric uncertainties, disturbances, measurement noises, and reference trajectories. First, the ILC design problem of the linear systems is described as a controller design problem of 2D uncertain Roesser models. Second, the H ∞ performance of 2D Roesser models is studied under a general boundary condition. Third, an ILC design criterion is presented to achieve the perfect tracking and specified H ∞ performance by using linear matrix inequality approaches. Finally, a numerical example is given to illustrate the efficiency of the proposed ILC design method.

Two-Stage Feedback Control Design for a Class of Linear Discrete-Time Systems With Slow and Fast Modes

In this paper, we first review the new algorithm for the two-stage feedback controller design of linear discrete-time systems, and then provide conditions for its applicability. The design algorithm is specialized and simplified for a class of linear systems with slow and fast modes (multitime scale systems or singularly perturbed systems). The proposed design significantly reduces computational full-state feedback design requirements and provides independent and accurate feedback controller design techniques in slow and fast time scales. We present also conditions needed for applicability of the proposed two-stage design in two time scales. The power of the two-stage design lies in the fact that different types of controllers can be designed for different subsystems using the corresponding feedback gains obtained by performing calculations only with the subsystem (reduced-order) matrices.

Decentralized Navigational State Estimation for Networked Multiple Vehicles Subject to Limited Data Rate

In this paper, a decentralized receding horizon fusion strategy (DRHF), mainly based on cooperative packets and relative observations, is proposed for navigational state estimation problems of networked vehicles: a class of linear discrete-time systems with limited data rate. The resulting min-max problem is solved by recursive scheme, which is suitable for recursive computation in online applications. The convergence properties of the optimal estimator are also studied. Finally, an illustrative example of networked UAVs is given to demonstrate the main features of the proposed estimator design approach.

Model-free optimal control design for a class of linear discrete-time systems with multiple delays using adaptive dynamic programming

In this paper, a model-free optimal control scheme for a class of linear discrete-time systems with multiple delays in state, control and output vectors is proposed. The optimal control can be obtained using only measured input/output data from systems, by adaptive dynamic programming (ADP) technology. First, we give a class of systems what we want to address. Then, a model-free optimal control is designed to minimize the given cost functional by ADP technology, which combines a similar Q-learning method with a value iteration (VI) algorithm, using only the measured input/output data. Finally, several numerical examples are given to illustrate the effectiveness of our approach.

Non-Fragile Mixed H<sub>2</sub>/H<sub>∞</sub> Full-Order Filter for a Class of Linear Discrete-Time Systems with Filter Parameters Uncertainty

The problem of how to design a non-fragile mixedH2/Hfull-order filter for a class of linear discrete-time system is discussed in this paper. The designed mixedH2/Hfull-order filter parameters are assumed to be of additive norm-bounded variations. Sufficient conditions for the existence of the non-fragile mixedH2/Hfull-order filter are given in linear matrix inequality (LMI) forms. A numerical example is then proposed to illustrate the necessity of considering the parameter variations of the full-order filter through the analysis of the poles of the filter error dynamic system. The results show that when the parameters of the designed non-fragile mixedH2/Hfull-order filter are of variations, the poles of the filter error dynamic system are inside the unit circle, the filter error dynamic system is still stable. On the other hand, if the parameter variations of the full-order filter are not considered when the mixedH2/Hfull-order filter is designed, the poles of the filter error dynamic system are outside the unit circle, the filter error dynamic system is unstable when the parameters of the designed mixedH2/Hfull-order filter are of variations.

Reduced order disturbance observer for discrete-time linear systems

In the paper, an output-based disturbance observer of reduced order is presented for a class of discrete-time linear systems. First, a general form of a disturbance observer is proposed when full states are available. Then, by combining a state function estimator of minimal order, an output-based disturbance observer is derived. The existence condition will be formulated in the form of a static output feedback. Through examples, the effectiveness and advantages of the proposed approach will be demonstrated. A servo control problem in practice is addressed to show the validity of the approach. Furthermore, it will be shown that the proposed approach does provide a smaller order of disturbance observer than that of conventional approaches, while maintaining satisfactory performances.

Low-sensitivity H ∞ filter design for linear delta operator systems with sampling time jitter

This article is concerned with the problem of designing H ∞ filters for a class of linear discrete-time systems with low-sensitivity to sampling time jitter via delta operator approach. Delta-domain model is used to avoid the inherent numerical ill-condition resulting from the use of the standard shift-domain model at high sampling rates. Based on projection lemma in combination with the descriptor system approach often used to solve problems related to delay, a novel bounded real lemma with three slack variables for delta operator systems is presented. A sensitivity approach based on this novel lemma is proposed to mitigate the effects of sampling time jitter on system performance. Then, the problem of designing a low-sensitivity filter can be reduced to a convex optimisation problem. An important consideration in the design of correlation filters is the optimal trade-off between the standard H ∞ criterion and the sensitivity of the transfer function with respect to sampling time jitter. Finally, a numerical example demonstrating the validity of the proposed design method is given.