Discrete Time-varying Systems Research Articles

Iterative learning control approach for linear discrete time-varying systems with different initial time points

Different from the existing iterative learning control (ILC) works for dynamical systems with iteration-varying trial lengths, in which the terminal time points are not identical, this paper presents an ILC approach for linear discrete time-varying (LDTV) systems with different initial time points. A piecewise ILC law is designed by using the segment compensation techniques in time axis. Through a rigorous mathematical analysis, it is theoretically proved that as the mathematical expectation of the iterative initial state equals to the desired initial state, the ILC tracking error at the maximum universal time interval can be driven into a bounded region in mathematical expectation sense. Particularly, the mathematical expectation of the ILC tracking error at the maximum universal time interval can even be driven to zero under a certain initial state condition. Numerical simulations are provided to verify the effectiveness of the proposed ILC scheme.

Design of Functional Interval Observer for Discrete Time-Varying Nonlinear Interconnected Systems Based on Coding-Decoding Scheme

In this paper, we design a distributed functional interval observer for discrete time-varying nonlinear interconnected systems. The communication between subsystems adapts the coding-decoding scheme (CDS) to save bandwidth and avoid data conflicts. The state set is described by the ellipsoid which can improve estimation accuracy and reduce conservatism. Besides, we give the conditions for the establishment of the observer and the stability of the error dynamic system. The observer gain matrices are obtained by solving a set of linear matrix inequalities (LMI) and some given conditions. The shape matrix of the ellipsoid is determined by selecting the optimal solution. Finally, we give two simulation examples to prove the designed functional interval observer is effective.

Covariance intersection based event-triggered distributed state estimation under channel independent DoS attacks

This paper investigates the event-triggered distributed state estimation problem for a class of discrete time-varying systems in the presence of denial-of-service (DoS) attacks, where each sensor node selectively shares its local information with neighbors. In contrast to the previous studies where the DoS attacks are considered on sensor-to-filter channels, we deal with the situation that DoS attacks jam each filter-to-filter communication channel independently. To reduce the communication rate and save network resources, a novel event-triggered communication strategy is presented that takes into account the impact of DoS attacks and is specialized for each communication channel. Based on the covariance intersection fusion rule and weight rearrangement method, a distributed state estimation algorithm is proposed. Further, the consistency of estimates and mean-square boundedness of estimation errors are proved under system collective observability and some other mild assumptions. Lastly, a numerical simulation is conducted to demonstrate the developed results and the effectiveness of the proposed algorithm.

Finite-Horizon $H_{\infty }$ Consensus Control of Discrete Time-Varying Multiagent Systems: A Dynamic Event-Based Learning Approach

This paper addresses the finite-horizon <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus problem for general discrete time-varying multi-agent systems with energy-bounded external disturbances and limited network bandwidth resource. A dynamic event-based learning approach is proposed to produce a dynamic discrete-time event-triggered scheme and a dynamic distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus protocol. Based on the local state information, the dynamic distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus protocol is developed to guarantee the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus of the general discrete time-varying multi-agent systems with external disturbances. Besides, a novel criterion is established by employing the Lyapunov theory and considering the special dynamic triggering constraint, and the corresponding recursive learning algorithm is developed. In contrast with the previous works, the proposed dynamic event-based approach results in less network bandwidth utilization, and the novel recursive algorithm brings less conservatism of the designed controller. Finally, the effectiveness of the corresponding algorithm and the advantages of the proposed dynamic event-based approach are testified by a numerical simulation.

Event-Triggered Distributed State Estimation: A Conditional Expectation Method

This paper mainly focuses on distributed filtering for a discrete time-varying system observed by a sensor network, where each sensor can measure some partial state information of the system and communicate with its neighbours. A novel distributed event-triggered communication mechanism is designed to reduce the communication rate among the sensors and guarantee the performance of the filter. With a data scheduler, the sensor is able to decide whether to transmit data to its neighbours. By applying Gaussian approximation, an evaluation of the effect caused by the non-transmission event is derived, which characterizes the tradeoff between communication rate and state estimation performance. Subsequently, a corresponding sub-optimal filtering gain design protocol is proposed. Compared with the literature, the filtering algorithm proposed in this paper is less conservative. Finally, numerical simulation is provided to illustrate the improvement of performance and the robustness of the approximation.

Quadratic filtering for discrete time-varying non-Gaussian systems under binary encoding schemes

This paper is concerned with the recursive quadratic filtering problem for a class of linear discrete-time systems subject to non-Gaussian noises. Considering its robustness against channel noises, the binary encoding scheme is utilized in the process of data transmission from sensors to the filter. Under such a scheme, the original signal is first encoded into a bit string, and then transmitted via memoryless binary symmetric channels (with certain crossover probabilities). Subsequently, the received bit string is recovered by a decoder at the receiver end. The primary purpose of this paper is to design a recursive quadratic filter for the underlying non-Gaussian systems with a minimized upper bound on the filtering error covariance. For this purpose, an augmented system is first constructed by aggregating the original vectors and their second-order Kronecker powers. Accordingly, an upper bound on the filtering error covariance is obtained in the form of solutions to certain Riccati-like difference equations, and the obtained bound is then minimized by properly choosing the filter parameter. Moreover, sufficient conditions are established to guarantee the boundedness of filtering error covariance. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed quadratic filtering algorithm.

Unbiased minimum-variance estimation and dynamic event-driven disturbance rejection control for discrete time-varying systems

This paper studies a dynamic event-driven disturbance rejection control problem for a class of linear discrete time-varying systems with unknown external disturbances, random process and measurement noises. To obtain the accurate estimates of both the system states and external disturbances, simultaneously, an unbiased minimum-variance time-varying extended state observer is designed, and the stability of the estimation error system is analyzed. Then, a dynamic event-driven disturbance rejection controller is designed by minimizing the upper bound of the cost function of the closed-loop system over a finite horizon. It can be shown that, by applying the proposed control approach, not only the transmission frequency of the control signal is reduced, but also the external disturbances are compensated actively. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed control approaches.

Confidence set-membership FIR filter for discrete time-variant systems

In this paper, a confidence set-membership filter based on the finite impulse response (FIR) structure is proposed for time-variant systems that are simultaneously subject to both the unknown but bounded noises and the Gaussian noises. At each step, the filter provides a confidence state set that includes the true state with an adjustable confidence level. The FIR structure improves the robustness and brings more degrees of freedom to the filter design. Multiple recent measurements within a moving horizon are fully utilized to construct and optimize each confidence state set. Under two different size criteria, an analytical solution and an LMI-based numerical solution for the filter gain are derived by minimizing the size of the confidence state set, respectively. Finally, an example is given to illustrate the effectiveness and superiority of the algorithms.

A formula for the lower Bohl exponent of discrete time-varying systems

A formula for the lower Bohl exponent of discrete time-varying systems

Distributed $H_{\infty }$-Consensus Estimation for Random Parameter Systems Over Binary Sensor Networks: A Local Performance Analysis Method

This paper deals with the distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> -consensus estimation problem for a class of discrete time-varying random parameter systems over binary sensor networks, where the statistical information of the random parameter matrix is characterized by a generalized covariance matrix known a priori. As a binary sensor can only provide one bit of information according to a given threshold, an indicator variable is introduced so as to extract functional information (from the sensor output) that can be employed to estimate the system state. With the introduced indicator variable, a distributed estimator is constructed for each binary sensor with guaranteed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> -consensus performance constraint on the estimation error dynamics over a finite horizon. By means of a local performance analysis method, indicator-variable-dependent conditions are established for the existence of the desired distributed estimators whose gains are calculated by solving a set of recursive linear matrix inequalities. Finally, the applicability and effectiveness of the developed distributed estimation scheme are demonstrated through a numerical example.

Quadratic filtering for non-Gaussian stochastic parameter systems with buffer-aided strategy

This paper is concerned with the quadratic filtering problem for a class of linear discrete time-varying systems with non-Gaussian stochastic parameters and intermittent measurements. In order to improve the filtering performance, a buffer-aided strategy is used to store the historical measurement data which is sent to the filter via a shared communication channel at each transmission instant. The main objective of this paper is to design a quadratic filter to estimate the states of the considered non-Gaussian stochastic systems by using the buffer-aided strategy. Specifically, an augmented system is constructed by combining the original system states and their second-order Kronecker powers. As such, the considered quadratic filtering problem amounts to the Kalman filtering problem for the augmented system. The filtering error covariance (FEC) conditioned on the transmission intervals is firstly derived recursively and then is minimized by choosing the suitable filtering gains. Moreover, sufficient conditions are deduced to guarantee the boundedness of both the FEC and the conditional FEC. Finally, two illustrative examples are provided to demonstrate the effectiveness of the proposed filtering method.

Novel Discrete-Time Recurrent Neural Network for Robot Manipulator: A Direct Discretization Technical Route.

Controlling and processing of time-variant problem is universal in the fields of engineering and science, and the discrete-time recurrent neural network (RNN) model has been proven as an effective method for handling a variety of discrete time-variant problems. However, such model usually originates from the discretization research of continuous time-variant problem, and there is little research on the direct discretization method. To address the aforementioned problem, this article introduces a novel discrete-time RNN model for solving the discrete time-variant problem in a pioneering manner. Specifically, a discrete time-variant nonlinear system, which originates from the mathematical modeling of serial robot manipulator, is presented as a target problem. For solving the problem, first, the technique of second-order Taylor expansion is used to deal with the discrete time-variant nonlinear system, and the novel discrete-time RNN model is proposed subsequently. Second, the theoretical analyses are investigated and developed, which shows the convergence and precision of the proposed discrete-time RNN model. Furthermore, three distinct numerical experiments verify the excellent performance of the proposed discrete-time RNN model. In addition, a robot manipulator example further verifies the effectiveness and practicability of the proposed novel discrete-time RNN model.

Finite-Horizon $H_{\infty }$ Filtering via a High-Rate Network With the FlexRay Protocol

This paper addresses the finite-horizon <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> filtering problem for a class of discrete time-varying nonlinear systems over high-rate networks whose signal exchanges are scheduled by the FlexRay protocol. To improve the efficiency of the data transmission, a high-rate network is deployed for the measurement signals to be broadcasted from the sensors to the filter. The FlexRay protocol is embedded into the high-rate network to orchestrate the transmission rule of the signals with different attributes, thereby further enhancing the transmission flexibility. On the basis of the Round-Robin and Try-Once-Discard protocols, a novel FlexRay-protocol-based measurement model is proposed by using certain data holding strategies. A sufficient condition is provided to guarantee that the filtering error dynamics meets the desirable disturbance attenuation level against exogenous disturbances over a finite horizon. The parameterized form of the filter gain is attained by the solutions to some matrix inequalities. Numerical simulation is carried out to substantiate the proposed filter design algorithm.

Probability-guaranteed state estimation for nonlinear delayed systems under mixed attacks

In this paper, the problem of the networked set-membership state estimation is discussed for a class of nonlinear discrete time-varying systems subject to cyber attacks and time delays. Two forms of malicious attacks (i.e. Denial-of-Service (DoS) attack and bias injection attack) are taken into account to describe the adversary's attempt to destroy/deteriorate the system performance via communication network. It is the aim of the investigated issue to propose a set-membership state estimator ensuring the required estimation performance despite the existence of both the external mixed attacks and internal time delays. By resorting to the feasibility of a series of matrix inequalities, sufficient conditions are provided for the solvability of the addressed state estimator design problem. Furthermore, an optimisation strategy is developed with the purpose of seeking the local optimal estimator parameters. At last, a numerical simulation example is presented to demonstrate the effectiveness of the proposed theoretical algorithm.

A component-based coding–decoding approach to set-membership filtering for time-varying systems under constrained bit rate

This paper is concerned with the set-membership filtering (SMF) problem for a class of discrete time-varying systems with unknown-but-bounded noises under bit rate constraints. The communication between sensor nodes and filters is implemented through a wireless digital communication network with limited bandwidth. A bit rate constraint is first established to quantify the extent to which the network is constrained. A component-based coding–decoding procedure is proposed that enables individual decoder to decode messages from different components scattering in different physical locations. Based on this procedure, a decoded-measurement-based recursive SMF scheme with a prediction–correction structure is put forward. The desired parameters of the set-membership filter can be calculated recursively by the proposed recursive SMF scheme. Furthermore, the co-design issue of the bit rate allocation protocol and the filter gain is converted into the mixed-integer nonlinear programming problem that is solved by means of the particle swarm optimization and the recursive filtering algorithms. Finally, numerical simulations on two scenarios are conducted to validate the effectiveness of the proposed SMF approach.

Protocol-based zonotopic state and fault estimation for communication-constrained industrial cyber-physical systems

This paper is concerned with the communication protocol-based zonotopic state and fault estimation issue for a class of discrete time-varying industrial cyber-physical systems under bounded disturbances and constrained communication resources. First, in order to alleviate resource consumption, a round-robin protocol is developed to schedule the data transmission between the local sensor and the remote estimator. Second, a zonotopic set-membership estimation algorithm is developed to guarantee that the unavailable system state and fault signals could be simultaneously estimated and enclosed in a zonotope at every instant of time. Subsequently, the size of such a zonotope is minimized at each iteration by appropriately selecting a correlation matrix. Furthermore, the rigorous stability and performance analysis for the developed zonotopic estimation algorithm is provided. Finally, two simulation examples are provided to verify the obtained theoretical results.

Policy Iteration for Optimal Control of Discrete-Time Time-Varying Nonlinear Systems

Aimed at infinite horizon optimal control problems of discrete time-varying nonlinear systems, in this paper, a new iterative adaptive dynamic programming algorithm, which is the discrete-time time-varying policy iteration (DTTV) algorithm, is developed. The iterative control law is designed to update the iterative value function which approximates the index function of optimal performance. The admissibility of the iterative control law is analyzed. The results show that the iterative value function is non-increasingly convergent to the Bellman-equation optimal solution. To implement the algorithm, neural networks are employed and a new implementation structure is established, which avoids solving the generalized Bellman equation in each iteration. Finally, the optimal control laws for torsional pendulum and inverted pendulum systems are obtained by using the DTTV policy iteration algorithm, where the mass and pendulum bar length are permitted to be time-varying parameters. The effectiveness of the developed method is illustrated by numerical results and comparisons.

Design of distributed recursive filters based on data compression for sensor networks

This paper is concerned with the distributed filtering problem based on data compression for linear discrete time-varying systems over sensor networks. Two kinds of sensors are considered: one kind only has a measuring capability and communicates measurements, while the other adds a calculating capability and communicates estimates. At each sensor node with calculating capability, a weighted measurement fusion algorithm is employed to compress the measurements of the sensor and its neighbor nodes with only measuring capability; and a weighted state fusion algorithm is employed to compress the estimates from neighbor nodes with calculating capability. Using compressed data, an optimal distributed recursive filter with a Kalman consensus filter form is devised in the linear unbiased minimum variance (LUMV) criterion. Cross-covariance matrices (CCMs) of the filtering errors between sensor nodes are derived. To avoid calculating CCMs, a suboptimal distributed recursive filter is presented, where a covariance intersection fusion algorithm is employed to compress the estimates from neighbor nodes with calculating capability. The filtering and consensus gains are solved to minimize an upper bound of covariance matrix (CM) of the filtering error. It is proved that the filtering error is exponentially bounded in the mean square. Simulations illuminate the effectiveness of proposed algorithms.

An anti-windup control strategy for discrete time-delay system based on triple Lyapunov functional

This paper addresses the design of a dynamic output feedback-based anti-windup compensator to mitigate the windup phenomenon for a discrete time-varying delayed system with input saturation to establish the asymptotic stability. Linear matrix inequalities–based stability conditions are derived locally and globally. The controller for the closed-loop system is designed to reduce the effect of external bounded disturbances by utilizing the linear matrix inequality approach. The novel triple Lyapunov–Krasovskii functional along with reciprocal convex inequality is used to solve the expressions contained in the forward difference of the functional and to maximize the basin of attraction. Finally, industrial examples are simulated to prove the effectiveness of the proposed criterion.

H∞ Filtering Controller for Discrete Time-Varying Delay System with Missing Measurements

The aim of this paper is to address the analysis and design problem of [Formula: see text] filtering for discrete time-varying delay systems with missing measurements. Our attention is focused on the filter design, using Scaled Small Gain (SSG) approach, guaranteeing the asymptotic stability of the augmented system. A transformation model is obtained via three-term approximation method and Input–Output (IO) approach based on the SSG theorem. The use of SSG theorem for the stability of discrete time-varying delayed systems with missing measurements has not been studied elsewhere in the literature. This represents the main innovation of this paper. Less conservative results are obtained, compared with previous results, and are established in terms of LMIs. Numerical examples illustrate the applicability of the proposed methodology.