Realization and canonical representation of linear systems through I/O maps

In this paper, we use input and output maps to develop simple procedures to obtain minimal realizations for linear continuous-time systems. The procedures developed are numerically efficient and yield explicit formulae for the state-space matrices of the realization in terms of the system parameters, notably the system eigenvalues. Both systems with distinct eigenvalues and repeated eigenvalues are treated. We also present a procedure for transforming a realization obtained through the input or output map to Jordan canonical form. The transformation matrices required to transform the realization to Jordan canonical form are specified entirely in terms of the system eigenvalues. We illustrate the results obtained with several examples.     

Event-based H∞ filtering for discrete-time Markov jump systems with network-induced delay

The problem of event-based H_∞ filtering for discrete-time Markov jump system with network-induced delay is investigated in this paper. For different jumping modes, different event-triggered communication schemes are constructed to choose which output signals should be transmitted. Through the analysis of network-induced delay’s intervals, the discrete-time system, the event-triggered scheme and network-induced delay are unified into a discrete-time Markov jump filter error system with time-delay. Based on time-delay system analysis method, criteria are derived to guarantee the discrete-time Markov jump error system stochastically stable with an H_∞ norm bound. The correspondent filter and the event-based parameters are also given. A numerical example is given to show that the proposed filter design techniques are effective and event-triggered communication scheme can save limited network resources greatly.     

Recursive state estimation based-on the outputs of partial nodes for discrete-time stochastic complex networks with switched topology

In this paper, the state estimation problem is studied for a class of discrete-time stochastic complex networks with switched topology. In the network under consideration, we assume that measurement outputs can be got from only partial nodes, besides, the switching rule of this network is characterized by a sequence of Bernoulli random variables. The aim of the presented estimation problem is to develop a recursive estimator based on the framework of extended Kalman filter (EKF), such that the upper bound for the filtering error convariance is optimized. In order to address the nonlinear functions, the Taylor series expansion is utilized and the high-order terms of linearization errors are expressed in an exact way. Furthermore, by solving two Ricatti-like difference equations, the gain matrix can be acquired at each time instant. It is shown that the filtering error is bounded in mean square under some conditions with the aid of stochastic analysis techniques. A numerical example is given to demonstrate the validity of the proposed estimator.     

Event-triggered interval-based state estimator for continuous-time linear systems

In this paper we propose an interval-based state estimator for continuous-time linear systems with discrete-time measurements using an event-triggered mechanism and an explicit reachability method. An output injection method combined with a state variables permutation procedure are applied to design the robust estimator. In addition, the convergence of the proposed set-membership state estimator and the existence of a lower bound on the inter-event times are shown. Throughout a numerical example, the performance of this estimator are illustrated and compared to related works.     

Global exact tracking for uncertain MIMO linear systems by output feedback sliding mode control

This paper presents a solution to the problem of global exact output tracking for uncertain MIMO (multiple-input–multiple-output) linear plants with non-uniform arbitrary relative degree using output feedback sliding mode control. The key idea to overcome the relative degree obstacle is to generalize our previous hybrid estimation scheme to a multivariable version by combining, through switching, a standard linear lead filter with a non-linear one based on robust exact differentiators, achieving uniform global exponential practical stability and exact tracking.     

Centralized security-guaranteed filtering in multirate-sensor fusion under deception attacks

In this paper, the centralized security-guaranteed filtering problem is studied for linear time-invariant stochastic systems with multirate-sensor fusion under deception attacks. The underlying system includes a number of sensor nodes with a centralized filter, where each sensor is allowed to be sampled at different rate. A new measurement output model is proposed to characterize both the multiple rates and the deception attacks. By exploiting the lifting technique, the multi-rate sensor system is cast into a single-rate discrete-time system. With a new concept of security level, the aim of this paper is to design a filter such that the filtering error dynamics achieves the prescribed level of the security under deception attacks. By using the stochastic analysis techniques, sufficient conditions are first derived such that the filtering error system is guaranteed to have the desired security level, and then the filter gain is parameterized by using the semi-definite programme method with certain nonlinear constraints. Finally, a numerical simulation example is provided to demonstrate the feasibility of the proposed filtering scheme.     

Event-triggered adaptive fault-tolerant control of uncertain non-affine systems with predefined performance

This paper is concerned with an event-triggered adaptive fault-tolerant problem for an uncertain non-affine system. The implicit function theorem and mean value theorem are utilized to transform a non-affine system into an affine one, and an extended state observer and a tracking differentiator are used to estimate unknown dynamics and the derivative of virtual control laws, respectively. Adaptive laws are designed for unknown faults, and an event-triggered control scheme with a time-varying threshold, based on a tracking error and adaptive parameters, is developed. The tracking error is steered to converge to a bounded set with the help of a predefined performance function, and its transient performance is improved despite of faults. The stability of the closed-loop system is analyzed by the theorem of the input-to-state practically stability, and the Zeno behavior is excluded. Finally, two examples are given to illustrate the effectiveness of the proposed scheme.     

Global consensus tracking of discrete-time saturated networked systems via nonlinear feedback laws

This paper revisits the coordinated tracking of networked systems in the presence of input saturation. For discrete-time networked systems with high-order integrator typed dynamics and input saturation, nonlinear feedback laws are constructed and then sufficient conditions are established to guarantee the global consensus tracking of the systems. Finally, numerical simulations are given to support the theoretical results.     

Exponential stabilization of switched linear systems subject to actuator saturation with stabilizable and unstabilizable subsystems

This paper is concerned with the exponential stabilization of switched linear systems subject to actuator saturation with both stabilizable subsystems and unstabilizable subsystems for continuous-time case and discrete-time case, respectively. Sufficient conditions for the exponential stabilization under dwell time switching under the cases of continuous-time and discrete-time are established by using a novel class of multiple time-varying Lyapunov function. The existence conditions for stabilizing controllers are presented in terms of linear matrix inequalities (LMIs) for the continuous-time case and the discrete-time case, respectively. Two optimization problems are proposed for obtaining the maximal attraction region. The problem of exponential stabilization for switched system subject to actuator saturation with asynchronous switching controller is also studied. Several numerical examples are presented to prove the validity of the obtained results.     

Predictive control of discrete-time high-order fully actuated systems with application to air-bearing spacecraft simulator

This paper addresses an output tracking problem for discrete-time high-order fully actuated (DHOFA) systems and its application in the control of air-bearing spacecraft (ABS) simulator. A HOFA system model, as a novel system representation, is applied to establish the dynamics of discrete-time control systems. Accordingly, a HOFA predictive control scheme is presented to deal with this problem, which is composed of a HOFA feedback for stabilization and a HOFA predictive control for tracking. In this scheme, a Diophantine equation is exploited to construct an incremental HOFA (IHOFA) prediction model to substitute a reduced-order prediction model, and then a cost function involving tracking performance is minimized by using multi-step output predictions. A sufficient and necessary condition is proposed to discuss the stability and tracking performance of the closed-loop DHOFA systems, it is simple to utilize in system analysis and extend in practice. Two experiments of the control of ABS simulator are shown to illustrate the feasibility of the presented HOFA predictive control scheme.     

Sliding mode control for uncertain discrete-time systems with Markovian jumping parameters and mixed delays

This paper is concerned with the robust sliding mode control (SMC) problem for a class of uncertain discrete-time Markovian jump systems with mixed delays. The mixed delays consist of both the discrete time-varying delays and the infinite distributed delays. The purpose of the addressed problem is to design a sliding mode controller such that, in the simultaneous presence of parameter uncertainties, Markovian jumping parameters and mixed time-delays, the state trajectories are driven onto the pre-defined sliding surface and the resulting sliding mode dynamics is stochastically stable in the mean-square sense. A discrete-time sliding surface is firstly constructed and an SMC law is synthesized to ensure the reaching condition. Moreover, by constructing a new Lyapunov–Krasovskii functional and employing the delay-fractioning approach, a sufficient condition is established to guarantee the stochastic stability of the sliding mode dynamics. Such a condition is characterized in terms of a set of matrix inequalities that can be easily solved by using the semi-definite programming method. A simulation example is given to illustrate the effectiveness and feasibility of the proposed design scheme.     

Event-triggered filtering for uncertain semi-Markov jump systems with time-varying delay by using quantized measurement

This paper focuses on the extended dissipative filter design problem for a class of uncertain semi-Markov jump systems in the discrete-time context, where the parameter uncertainties are assumed to be occurred in a special probabilities way. The aim of this paper is to design a mode-dependent filter ensuring the stochastic stability of the resulting filtering error system. To reduce the burden of communication network, the event-triggered scheme and quantized measurement are employed. By constructing a new Lyapunov functional, the filter design methodology is put forward. Finally, two numerical examples are proposed to demonstrate the usefulness of the filter design methodology.     

Disturbance rejection and control system design based on a high-order equivalent-input-disturbance estimator

This paper presents an improved equivalent-input-disturbance (EID) approach to deal with exogenous disturbances. A high-order filter is newly used to construct an improved EID estimator. The parameters of the filter are selected to improve the disturbance-rejection performance without changing the bandwidth of an EID-based control system. The stability and disturbance-rejection mechanism of the system are analyzed using the transfer function from the EID to the output. The high-order filter is designed using the loop-shaping method. Simulation results of a rotational control system demonstrate the validity of the approach and superiority over other methods.     

Flocking of the hybrid Cucker–Smale model

In recent years, both the continuous-time and discrete-time Cucker–Smale models have been widely studied. However, in the practical systems, the dynamics of the agents coupled with each others can be hybrid. Thus, we consider the asymptotic flocking behavior of the hybrid Cucker–Smale model, which is composed of continuous-time dynamic agents and discrete-time dynamic agents. Firstly by some technical lemmas, a super-linear inequality of the derivative of velocity variance is established. Then, we eventually show that the hybrid model can achieve asymptotic flocking for the long-range communication weight¹ case. At last, the simulation examples are given to verify the theoretical results.     

Recurrent neural dynamics for handling linear equation system with rank-deficient coefficient and disturbance existence

In this paper, for handling discrete-form time-variant linear equation system (DF-TV-LES) with rank-deficient coefficient and disturbance existence, a luminous discrete-time recurrent neural dynamics (DTRND) method is presented. Firstly, the continuous-time recurrent neural dynamics (CTRND) method can be discretized to the DTRND method by using recently-developed 5-instant discretization formula. Secondly, aiming at the situations of rank-deficient coefficient and disturbance existence, corresponding handling methods are presented, respectively. Specifically, on the one hand, under the situation of rank-deficient coefficient, we present an effective method to compute the least-squares solution of DF-TV-LES; on the other hand, under the situation of disturbance existence, integral state of error function is introduced, and then the presented DTRND method possesses a certain performance for restraining different types of disturbances. Finally, comparative numerical experiment substantiates the superiority of the presented DTRND method for handling DF-TV-LES.     

Output reversibility in linear discrete-time dynamical systems

Output reversibility involves dynamical systems where for every initial condition and the corresponding output there exists another initial condition such that the output generated by this initial condition is a time-reversed image of the original output with the time running forward. Through a series of necessary and sufficient conditions, we characterize output reversibility in linear discrete-time dynamical systems in terms of the geometric symmetry of its eigenvalue set with respect to the unit circle in the complex plane. Furthermore, we establish that output reversibility of a linear continuous-time system implies output reversibility of its discretization. In addition, we present a control framework that allows to alter the system dynamics in such a way that a discrete-time system, otherwise not output reversible, can be made output reversible. Finally, we present numerical examples involving a discretization of a Hamiltonian system that exhibits output reversibility and an example of a controlled system that is rendered output reversible.     

Implicit media frames: automated analysis of public debate on artificial sweeteners

The framing of issues in the mass media plays a crucial role in the public understanding of science and technology. This article contributes to research concerned with the analysis of media frames over time by making an analytical distinction between implicit and explicit media frames, and by introducing an automated method for the analysis of implicit frames. In particular, we apply a semantic maps method to a case study on the newspaper debate about artificial sweeteners, published in the New York Times between 1980 and 2006. Our results show that the analysis of semantic changes enables us to filter out the dynamics of implicit frames, and to detect emerging metaphors in public debates. Theoretically, we discuss the relation between implicit frames in public debates and the codification of meaning and information in scientific discourses, and suggest further avenues for research interested in the automated analysis of frame changes and trends in public debates.     

High-order command filtered adaptive backstepping control for second- and high-order fully actuated strict-feedback systems

In this paper, a high-order command filtered adaptive backstepping (HOCFAB)-based approach is proposed in order to track a given reference signal for the second- and high-order strict-feedback systems (SFSs) with parametric uncertainties, where both their subsystems hold a common full-actuation structure, namely, high-order fully actuated (HOFA) SFSs. Unlike the prevailing traditional first-order state-space backstepping approach which suffers from the problem of “explosion of terms”, the proposed HOCFAB approach circumvents the complexity arising owing to differentiating the virtual controllers repeatedly, and does not need to convert the high-order systems into first-order forms which is easier to carry out and demands fewer steps. Meanwhile, an error-compensating mechanism is constructed to reduce filtering errors. A critical analysis is theoretically proven which indicates that in both cases the entire system states are uniformly ultimately bounded under the proposed high-order controller, and the tracking error could be made arbitrarily small with predesigned parameters. Finally, the effectiveness of the proposed scheme is verified by a benchmark application in the robotic manipulator.     

A dynamically event-triggered approach to recursive filtering with censored measurements and parameter uncertainties

In this paper, a dynamically event-triggered filtering problem is investigated for a class of discrete time-varying systems with censored measurements and parameter uncertainties. The censored measurements under consideration are described by the Tobit measurement model. In order to save the communication energy, a dynamically event-triggered mechanism is utilized to decide whether the measurements should be transmitted to the filter or not. The aim of this paper is to design a robust recursive filter such that the filtering error covariance is minimized in certain sense for all the possible censored measurements, parameter uncertainties as well as the effect induced by the dynamically event-triggered mechanism. By means of the mathematical induction, an upper bound is firstly derived for the filtering error covariance in terms of recursive matrix equations. Then, such an upper bound is minimized by designing the filter gain properly. Furthermore, the boundedness is analyzed for the minimized upper bound of the filtering error covariance. Finally, two numerical simulations are exploited to demonstrate the effectiveness of the proposed filtering algorithm.