Strong stability radii of positive linear time‐delay systems

In this paper, we study robustness of the strong delay‐independent stability of linear time‐delay systems under multi‐perturbation and affine perturbation of coefficient matrices via the concept of strong delay‐independent stability radius (shortly, strong stability radius). We prove that for class of positive time‐delay systems, complex and real strong stability radii of positive linear time‐delay systems under multi‐perturbations (or affine perturbations) coincide and they are computed via simple formulae. Apart from that, we derive solution of a global optimization problem associated with the problem of computing of the strong stability radii of a positive linear time‐delay system. An example is given to illustrate the obtained results. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust Mixed Performance of Continuous Switched Systems with Time Delay

In this paper, the robust mixed H₂ / H_∞ performance analysis of switched time‐delay systems with linear fractional perturbations and distributed delay via a switching signal selection is considered. Some delay‐dependent LMI‐based criteria are proposed to achieve the design of the switching signal. Our approach is guaranteed by the new proposed inequality in recent years. Finally, some numerical examples are illustrated to show the main results.     

Hybrid‐impulsive second‐order sliding mode control: Lyapunov approach

Dynamic system of relative degree two controlled by discontinuous‐hybrid‐impulsive feedback in the presence of bounded perturbations is considered. The state feedback impulsive‐twisting control exhibits a uniform exact finite time convergence to the second‐order sliding mode with zero convergence time. The output feedback discontinuous control augmented by a simplified hybrid‐impulsive functions provides uniform exact convergence with zero convergence time of the system's states to a real second‐order sliding mode in the presence of bounded perturbations. Only ‘snap’ knowledge of the output derivative, that is, the knowledge of the output derivative in isolated time instants, is required. The output feedback hybrid‐impulsive control with practically implemented impulsive actions asymptotically drives the system's states to the origin. The Lyapunov analysis of the considered hybrid‐impulsive‐discontinuous system proves the system's stability. The efficacy of the proposed control technique is illustrated via computer simulations. Copyright © 2016 John Wiley & Sons, Ltd.     

Simulated time for host‐based testing with TTCN‐3

Prior to testing embedded software in a target environment, it is usually tested in a host environment used for developing the software. When a system is tested in a host environment, its real‐time behaviour is affected by the use of simulators, emulation and monitoring. In this paper, the authors provide a semantics for host‐based testing with simulated time and propose a simulated‐time solution for distributed testing with TTCN‐3, which is a standardized language for specifying and executing test suites. The paper also presents the application of testing with simulated time to two real‐life systems. Copyright © 2007 John Wiley & Sons, Ltd.     

On l∞ and l2 robustness of spatially invariant systems

We consider spatiotemporal systems and study their l_∞ and l₂ robustness properties in the presence of spatiotemporal perturbations. In particular, we consider spatially invariant nominal models and provide necessary and sufficient conditions for system robustness for the cases when the underlying perturbations are linear spatiotemporal varying, and nonlinear spatiotemporal invariant, unstructured or structured. It turns out that these conditions are analogous to the scaled small gain condition (which is equivalent to a spectral radius condition and a linear matrix inequality for the l_∞ and l₂ cases, respectively) derived for standard linear time‐invariant models subject to time‐varying linear and time‐invariant nonlinear perturbations. Copyright © 2009 John Wiley & Sons, Ltd.     

State and Unknown Input H∞ Observers for Discrete‐Time LPV Systems

This paper proposes state and unknown input (UI) observers for linear parameter varying (LPV) systems affected by UI and perturbations in both state and measurement equations. The estimation is done by minimizing the L₂ transfer between the perturbations and the state estimation error (H_∞‐observation). The originality of the paper is to provide a generalization of existing works, specially by relaxing an assumption on systems matrices, widely used for UI decoupling. After giving the main results, some examples illustrate the theoretical contributions and give comparisons to former publications.     

Composite disturbance‐observer‐based control and H ∞ control for nonlinear time‐delay systems

A novel type of control scheme combined the distance‐observer‐based control (DOBC) with H_∞ control is proposed for a class of nonlinear time‐delay systems subject to disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other is supposed to have the bounded H₂ norm. The disturbance observers based on regional pole placement and D‐stability theory are presented, which can be designed separately from the controller design. By integrating disturbance‐observer‐based control with H_∞ control laws, the disturbances can be rejected and attenuated, simultaneously, the desired dynamic performances can be guaranteed for nonlinear time‐delay systems with unknown nonlinear dynamics. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Gain‐Scheduled Control via Switching of LTI Controllers and State Reset

This paper proposes a synthesis method of gain‐scheduled control systems that switch linear time‐invariant controllers according to hysteresis of the scheduling parameter. Stability and L₂‐gain analysis and synthesis methods for switched systems are applied to the switched gain‐scheduled control synthesis using reset of the controller state, where also the reset law is computed via linear matrix inequalities (LMIs). In addition to optimization of an upper bound of L₂‐gain, we reduce jumps of control input via an auxiliary optimization. Numerical examples are presented to illustrate the switched gain‐scheduled controller.     

Teaching and learning high school physics in Kenyan classrooms using analogies

Abstract

This study provides insights into the nature of the analogies deployed by Kenyan physics teachers and generated by students in class. The analogies looked at (both teacher‐ and student‐generated) were largely environmental (drawn from students’ socio‐cultural environment), anthropomorphic (life and human characteristics ascribed to analogues), and to a limited extent, scientific (analogue and target are science concepts). In some cases, anthropomorphic analogies proved problematic for students, sometimes resulting in serious misconceptions. Good analogy use is based on clear identification of matching and non‐matching features of the analogue‐target structure. Several models, including the General Model for Analogy Teaching (GMAT), Teaching with Analogy (TWA) and Working with Analogies (WWA) are discussed in this paper, with a view to providing a lens through which analogies can be understood. To transform students’ understanding from cultural belief systems to the science system of thinking, while respecting their socio‐cultural backgrounds, can be a daunting task. Where it proves problematic for the students to ‘decamp’ from indigenous ways of reasoning, then collateral learning may be considered.     

Output‐based H2 optimal controllers for a class of discrete‐time stochastic linear systems with periodic coefficients

The aim of the paper is to present a design procedure of the optimal controller minimizing the H₂‐type norm of discrete‐time stochastic linear systems with periodic coefficients simultaneously affected by a nonhomogeneous but periodic Markov chain and state and control multiplicative white noise perturbations. Firstly, two H₂‐type norms for the linear stochastic systems under consideration were introduced. These H₂‐type norms may be viewed as measures of the effect of the additive white noise perturbations on the regulated output of the considered system. Before deriving of the state space representation of the optimal controller, some useful formulae of the two H₂‐type norms were obtained. These formulae are expressed in terms of periodic solutions of some suitable linear equations and are derived in the absence of some additional assumptions regarding the Markov chain other than the periodicity of the sequence of the transition probability matrices. Further, it is shown that the optimal H₂ controller depends on the stabilizing solutions of some specific systems of coupled Riccati equations, which generalize the well‐known control and filtering equations from linear time invariant case. For the readers convenience, the paper presents iterative numerical algorithms for the computations of the stabilizing solutions of these Riccati type systems. The theoretical developments are illustrated by numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite‐time stabilization of Markovian jump delay systems – a switching control approach

In this paper, a finite‐time stabilization problem is considered for a class of continuous‐time Markovian jump delay systems (MJDSs). A switching controller, which only depends on the average dwell time (ADT) switching laws, is proposed to make a trade‐off between robustness and adaptiveness when the design complexity of mode‐independent, mode‐dependent, and mode‐dependent and variation‐dependent control strategies is considered. First, the stochastic finite‐time boundedness for an MJDS is analyzed by an ADT approach. Second, the disturbance attenuation capability of MJDS is studied via a finite‐time weighted L₂ gain, which depends on the switching numbers. The impacts of finite‐time interval and L₂ gain acting on the ADT are also thoroughly discussed. Then, a switching controller is designed such that the resulting closed‐loop MJDS is stochastically finite‐time bounded and has a guaranteed disturbance attenuation level. Finally, a numerical example is provided to verify the effectiveness of the developed results. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust Exponential Stability of Discrete‐Time Delay Impulsive Systems with Parametric Uncertainties

This paper investigates robust exponential stability for discrete‐time delay impulsive systems with parametric uncertainties. The parametric uncertainties in the systems are assumed to be time varying and norm bounded. Using Lyapunov functionals, some robust exponential stability criteria are given. It is shown that the time interval between the nearest two impulses should be small enough, i.e., impulses must act frequently, when the impulses are employed to stabilize the original impulse‐free system that is not robustly stable. Conversely, when the original system without impulses is robustly stable, the time interval between the nearest two impulses should be large enough to let the system with impulsive perturbations retain its stability property. It should be noted that this is the first time that impulsive robust exponential stabilization results are given via Lyapunov functionals for discrete‐time uncertain delay impulsive systems. Some examples, including an example which cannot be studied by the existing results, are also presented to illustrate the effectiveness of the obtained results.     

Robustness of Exact p‐Controllability and Exact p‐Observability to q‐Type of Perturbations of the Generator

In Mei and Peng, Systems & Control Letters, 59 (2010) 470–475, the authors have proved in general setting that p‐admissibilities of control operators and observation operators are invariant to any q‐type of perturbations of generator of C₀‐semigroups on Banach space. In this paper, under the p‐admissibility invariance premise, the robustness of the exact p‐controllability as well as the exact p‐observability to q‐type of perturbations is verified.     

Stability and l2‐gain of discrete‐time switched systems with unstable modes

This paper addresses stability and l₂‐gain for discrete‐time switched systems with unstable modes based on slow/fast mode‐dependent average dwell time (MDADT) switching strategies. Firstly, by employing a class of multiple discontinuous Lyapunov functions (MDLFs) and developing a kind of alternative switching signals, the sufficient conditions on stability are established for the system without external disturbances under a slow/fast MDADT switching scheme with a tighter bounds on the dwell time. Furthermore, by defining indicator functions and exploring the features of slow/fast MDADT switching, the weighted l₂‐gain conditions are achieved for the system with external disturbances. Particularly, the criteria of stability and l₂‐gain are also established for the corresponding discrete‐time switched linear systems with unstable modes via the MDLFs method and the slow/fast MDADT switching strategy. Finally, two numerical examples are presented to illustrate the advantages of the proposed methods.     

Generalised multivariable supertwisting algorithm

The purpose of this paper is to present an extension of the generalised supertwisting algorithm (STA) to the multivariable framework. We begin by introducing an algorithm that may be deemed as a linear, quasicontinuous, or discontinuous multivariable system, depending on the functions that define them. For the class represented by such an algorithm we prove the robust, Lyapunov stability of the origin and characterise the perturbations that preserve its stability. In particular, when its vector field is discontinuous or quasicontinuous our algorithm is endowed with finite‐time stability. Due to its resemblance to the scalar case, we denote such finite‐time stable systems as generalised multivariable STA. Furthermore, the class of finite‐time stable systems comprise the currently available versions of STAs. To finalise, by means of simulation examples, we show that our proposed finite‐time stable algorithms are well suited for signals online differentiation and highlight their dynamical traits.     

Resilient control for wireless networked control systems under DoS attack via a hierarchical game

In this paper, the resilient control problem is investigated for a wireless networked control system (WNCS) under denial‐of‐service (DoS) attack via a hierarchical game approach. In the presence of a wireless network, a DoS attacker leads to extra packet dropout in the cyber layer of WNCS by launching interference power. A zero‐sum Markov game is exploited to model the interaction between the transmitter and the DoS attacker under dynamic network environment. Additionally, with the attack‐induced packet loss, an H_∞ minimax controller is designed in the physical layer by using a delta operator approach. Both value iteration and Q‐learning methods are used to solve the hierarchical game problem for the WNCS. The proposed method is applied to a load frequency control system to illustrate the effectiveness.     

Design of Adaptive Block Backstepping Controllers with Perturbations Estimation for Nonlinear State‐Delayed Systems in Semi‐Strict Feedback Form

This paper is an extended study of an existing block backstepping control scheme designed for a class of perturbed multi‐input systems with multiple time‐varying delays to solve regulation problems, where the time‐varying delays must be linear with state variables. A new control scheme is proposed in this research where all the unknown multiple time‐varying delay terms in the dynamic equations can be nonlinear state functions in non‐strict feedback form, and the upper bounds of the time‐delays as well as their derivatives need not to be known in advance. Another improvement is to further alleviate the problem of “explosion of complexity,” i.e., to reduce the number of time derivatives of virtual inputs that the designers have to compute in the design of controllers. This is done by utilizing an existent derivative estimation algorithm to estimate the perturbations in the designing of proposed controllers. Adaptive mechanisms are also embedded in the controllers so that the upper bounds of perturbations and perturbation estimation errors are not required to be known beforehand. The resultant controlled systems guarantee asymptotic stability in accordance with the Lyapunov stability theorem. Finally, a numerical example and a practical application are demonstrated to verify the merits and feasibility of the proposed control scheme.     

Robust graph convolutional networks with directional graph adversarial training

Graph convolutional networks (GCNs), an emerging type of neural network model on graphs, have presented state-of-the-art performance on the node classification task. However, recent studies show that neural networks are vulnerable to the small but deliberate perturbations on input features. And GCNs could be more sensitive to the perturbations since the perturbations from neighbor nodes exacerbate the impact on a target node through the convolution. Adversarial training (AT) is a regularization technique that has been shown capable of improving the robustness of the model against perturbations on image classification. However, directly adopting AT on GCNs is less effective since AT regards examples as independent of each other and does not consider the impact from connected examples. In this work, we explore AT on graph and propose a graph-specific AT method, Directional Graph Adversarial Training (DGAT), which incorporates the graph structure into the adversarial process and automatically identifies the impact of perturbations from neighbor nodes. Concretely, we consider the impact from the connected nodes to define the neighbor perturbation which restricts the perturbation direction on node features towards their neighbor nodes, and additionally introduce an adversarial regularizer to defend the worst-case perturbations. In this way, DGAT can resist the impact of worst-case adversarial perturbations and reduce the impact of perturbations from neighbor nodes. Extensive experiments demonstrate that DGAT can effectively improve the robustness and generalization performance of GCNs. Specially, GCNs with DGAT can provide better performance when there are rare few labels available for training.

     

Networked‐based stabilization via discontinuous Lyapunov functionals

This paper presents a new stability and L₂‐gain analysis of linear Networked Control Systems (NCS). The new method is inspired by discontinuous Lyapunov functions that were introduced by Naghshtabrizitextitet al. (Syst. Control Lett. 2008; 57 :378–385; Proceedings 26th American Control Conference, New York, U.S.A., July 2007) in the framework of impulsive system representation. Most of the existing works on the stability of NCS (in the framework of time delay approach) are reduced to some Lyapunov‐based analysis of systems with uncertain and bounded time‐varying delays. This analysis via time‐independent Lyapunov functionals does not take advantage of the sawtooth evolution of the delays induced by sample‐and‐hold. The latter drawback was removed by Fridman (Automatica 2010; 46 :421–427), where time‐dependent Lyapunov functionals for sampled‐data systems were introduced. This led to essentially less conservative results. The objective of the present paper is to extend the time‐dependent Lyapunov functional approach to NCS, where variable sampling intervals, data packet dropouts, and variable network‐induced delays are taken into account. The Lyapunov functionals in this paper depend on time and on the upper bound of the network‐induced delay, and these functionals do not grow along the input update times. The new analysis is applied to the state‐feedback and to a novel network‐based static output‐feedback H_∞ control problems. Numerical examples show that the novel discontinuous terms in Lyapunov functionals essentially improve the results. Copyright © 2011 John Wiley & Sons, Ltd.