Discrete Time-varying Systems Research Articles

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.

Distributed consensus of discrete time-varying linear multi-agent systems with event-triggered intermittent control.

The consensus problem of discrete time-varying linear multi-agent systems (MASs) is studied in this paper. First, an event-triggered intermittent control (ETIC) protocol is designed, aided by a class of auxiliary functions. Under this protocol, some sufficient conditions for all agents to achieve consensus are established by constructing an error dynamical system and applying the Lyapunov function. Second, in order to further reduce the communication burden, an improved event triggered intermittent control (I-ETIC) strategy is presented, along with corresponding convergence analysis. Notably, the difference between the two control protocols lies in the fact that the former protocol only determines when to control or not based on the trigger conditions, while the latter, building upon this, designs new event trigger conditions for the update of the controller during the control stage. Finally, two numerical simulation examples are provided to demonstrate the effectiveness of the theoretical results.

Input-Output Finite-Time Sliding Mode Control of Discrete Time-Varying Systems Under an Adaptive Event-Triggered Mechanism

This paper is concerned with the issue of input-output finite-time stability (IO-FTS) for a class of nonlinear discrete time-varying systems. A time-varying observer-based sliding mode control method is proposed. In order to mitigate the transmission burden, an adaptive event-triggered mechanism is proposed by adjusting the threshold. Taking consideration of the effect of time-delay phenomenon and time-varying system matrices, a time-varying Lyapunov functional is designed. Based on the designed Lyapunov functional and IO-FTS theory, sufficient conditions are established for the error estimation system and closed-loop state estimation system. Moreover, the proposed observer-based sliding mode control method makes sure the reachability of the quasi-sliding mode surface in finite steps. And conditions in terms of recursive linear matrix inequalities (RLMIs) are attained to ensure IO-FTS during both reaching phase and sliding mode phase. An algorithm is provided to solve the RLMIs and obtain the time-varying observer gains. Finally, the effectiveness and superiority of the proposed method is demonstrated by an industrial continuous-stirred tank reactor system.

Overlapping Fusion Estimation for Discrete Time-Varying Interconnected Systems

Overlapping Fusion Estimation for Discrete Time-Varying Interconnected Systems

Recursive Distributed Filtering for Time-Varying Systems Over Sensor Network via Rayleigh Fading Channels: Tackling Binary Measurements

This paper is concerned with the distributed filtering problem for a class of discrete time-varying stochastic systems over binary sensor networks with the Rayleigh fading channels. Both the system state and measurement are subject to random noises with known statistical information, where the distribution function of measurement noise is employed to extract the functional information for state estimation purposes. The communication between a sensor node and its neighboring ones is implemented over a Rayleigh fading channel. For each binary sensor, a distributed filter is constructed by virtue of the available information from itself and its neighboring nodes, and the overall filtering error dynamics is guaranteed to be exponentially ultimately bounded in the mean square sense. By resorting to a local performance analysis method, sufficient criteria are established for ensuring the existence of the desired distributed filter in terms of a set of recursive linear matrix inequalities. The desired filter parameters are recursively calculated on every node by solving an optimization problem at each time instant with the aim of improving the estimation accuracy. Finally, some comparative results are presented to demonstrate the applicability and effectiveness of the developed distributed filtering scheme.

Distributed State and Input Estimation Over Sensor Networks Under Deception Attacks

This paper is concerned with the joint state and input estimation problem for linear discrete time-varying systems over peer-to-peer sensor networks, in which deception attacks are taken into account. By resorting to singular value decomposition, a local estimator structure is proposed to jointly estimate the system states and unknown inputs. Then, a distributed state estimator is constructed by fusing local estimates and covariance matrices. In addition, a sufficient condition is provided to ensure the uniformly bounded estimation error (in mean square) in each node. Finally, a numerical example is provided to show the effectiveness of the proposed estimation algorithm.

An approximate minimum mean-square error estimator for linear discrete time-varying systems: Handling Try-Once-Discard protocol

This paper is concerned with the remote state estimation problem for a class of linear discrete time-varying stochastic systems under communication constraints. In order to mitigate the undesired phenomena of data collisions, a Try-Once-Discard (TOD) protocol is utilized to regulate the signal transmissions over the sensor-to-estimator communication channel, where the TOD protocol is based on the scheduling rule described by a specific switching function. Under the introduced TOD protocol, the approximate minimum mean-square error (MMSE) state estimation problem is investigated and a recursive algorithm is developed for the MMSE estimator design whose computational complexity is comparable to that of the conventional Kalman filter. Furthermore, some conditions are established for the boundedness of the estimation error covariance. A numerical example is presented to illustrate the effectiveness of the proposed MMSE estimator.

Set-membership state and parameter estimation for discrete time-varying systems based on the constrained zonotope

In this paper, the set-membership state and parameter estimation problems are considered for linear time-varying systems. The noises in the system are unknown but bounded and the variation of parameters is considered as a bounded expansion. The entire estimator is an interactive estimation of parameters and states. In parameter estimation, the exact set of parameter estimates may be non-convex because of the uncertain states. A polytopic linear parameter varying (LPV) enclosure of the system regression expression is constructed as a convex relaxation. The result of parameter estimation is a set to include the true parameter of the model. Meanwhile, in the state estimation, a similar LPV enclosure of the state-space model is also used to bound the state matrix uncertainties. This LPV enclosure in the state estimation is narrowed by the parameter estimation, and then the set of state estimates is computed to include the true state. The constrained zonotope (CZ) is used to describe sets of interest and the necessary set operations are expanded to LPV mapping. Because of the highly adjustable accuracy of CZ, the proposed algorithm can make a better trade-off between computational accuracy and efficiency. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm.

Distributed Recursive Filtering Over Sensor Networks With Nonlogarithmic Sensor Resolution

Sensor resolution, which is one of the most important parameters/specifications for almost all kinds of sensors, plays an important role in any signal processing problems. This article deals with the distributed filtering problem for a class of discrete time-varying stochastic systems subject to nonlogarithmic sensor resolution and stochastic nonlinearities. The soft measurement technique is exploited in the filter design to overcome the difficulties resulting from the sensor-resolution-induced (SRI) uncertainty. The aim of the presented filtering problem is to construct the distributed filter over a sensor network such that in the presence of SRI uncertainty and stochastic nonlinearity, an upper bound on the filtering error covariance is guaranteed and subsequently minimized by appropriately designing the filer parameters at each time instant. Moreover, a matrix simplification method is utilized to tackle the difficulties stemming from the sparsity of sensor networks. Finally, a numerical example is employed to illustrate the effectiveness of the proposed filtering scheme.

Swarm Intelligence Based Model Predictive Control Strategy for Optimal State Control of Discrete Time-varying MIMO Linear Systems

Swarm Intelligence Based Model Predictive Control Strategy for Optimal State Control of Discrete Time-varying MIMO Linear Systems

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

In this note, a formula for the Bohl exponent of a discrete system with slowly varying coefficients was proved. This formula expresses the Bohl exponent through the eigenvalues of the coefficients. Based on these formulae a necessary and sufficient condition for uniform exponential stability of such systems are also presented.

Predictive control of uncertain systems over networks with redundant link

Networked systems using redundant channels to transmit data can effectively reduce the probability of data loss and improve system reliability and control margin. However, the structural complexity and economic cost of the system are also increased. To balance the redundancy and feasibility, the ratio of attraction domain to packet loss rate is defined as a balanced feasibility index. In this paper, single-channel packet loss is considered as Bernoulli distribution and a bounded packet loss network system control model is constructed as the arbitrary bounded packet loss control problem for redundant channel transmission network system. Therefore, the robust conditions of the closed-loop system and the constraints of the input and state are established under the framework of robust predictive control to construct the linear matrix inequality (LMI) optimization problem. Finally, to verify the effectiveness of the design method proposed in this paper, the discrete time-varying linear system and the main steam control system with redundant channels are used as study cases.

Secure Finite-Horizon Consensus Control of Multiagent Systems Against Cyber Attacks.

The problem of secure finite-horizon consensus control for discrete time-varying multiagent systems (MASs) with actuator saturation and cyber attacks is addressed in this article. A random attack model is first proposed to account for randomly occurring false data injection attacks and denial-of-service attacks, whose dynamics are governed by the random Markov process. The hybrid secure control scheme is developed to mitigate the influence of arbitrary cyber attacks on system performance. Specifically, this article proposes a hybrid control law containing multiple controllers, each of which is designed to counter different types of cyber attacks. By using the stochastic analysis approach, two sufficient criteria are provided to guarantee that the time-varying MASs satisfy the finite horizon H∞ consensus performance. Then, the controller parameters are obtained by solving the recursive linear matrix inequality. The usefulness of the theoretic results presented is demonstrated via a numerical example that contains a performance comparison of different secure control schemes.

Novel Unbiased Optimal Receding-Horizon Fixed-Lag Smoothers for Linear Discrete Time-Varying Systems

This paper proposes novel unbiased minimum-variance receding-horizon fixed-lag (UMVRHF) smoothers in batch and recursive forms for linear discrete time-varying state space models in order to improve the computational efficiency and the estimation performance of receding-horizon fixed-lag (RHF) smoothers. First, an UMVRHF smoother in batch form is proposed by combining independent receding-horizon local estimators for two separated sub-horizons. The local estimates and their error covariance matrices are obtained based on an optimal receding horizon filter and the smoother in terms of the unbiased minimum variance; they are then optimally combined using Millman’s theorem. Next, the recursive form of the proposed UMVRHF smoother is derived to improve its computational efficiency and extendibility. Additionally, we introduce a method for extending the proposed recursive smoothing algorithm to a posteriori state estimations and propose the Rauch–Tung–Striebel receding-horizon fixed-lag smoother in recursive form. Furthermore, a computational complexity reduction technique that periodically switches the two proposed recursive smoothing algorithms is proposed. The performance and effectiveness of the proposed smoothers are demonstrated by comparing their estimation results with those of previous algorithms for Kalman and receding-horizon fixed-lag smoothers via numerical experiments.