Stochastic Models to Mitigate Sparse Sensor Attacks in Continuous-Time Non-Linear Cyber-Physical Systems

Cyber-Physical Systems are very vulnerable to sparse sensor attacks.But current protection mechanisms employ linear and deterministic models which cannot detect attacks precisely.Therefore,in this paper,we propose a new non-linear generalized model to describe Cyber-Physical Systems.This model includes unknown multivariable discrete and continuous-time functions and different multiplicative noises to represent the evolution of physical processes and randomeffects in the physical and computationalworlds.Besides,the digitalization stage in hardware devices is represented too.Attackers and most critical sparse sensor attacks are described through a stochastic process.The reconstruction and protectionmechanisms are based on aweighted stochasticmodel.Error probability in data samples is estimated through different indicators commonly employed in non-linear dynamics(such as the Fourier transform,first-return maps,or the probability density function).A decision algorithm calculates the final reconstructed value considering the previous error probability.An experimental validation based on simulation tools and real deployments is also carried out.Both,the new technology performance and scalability are studied.Results prove that the proposed solution protects Cyber-Physical Systems against up to 92%of attacks and perturbations,with a computational delay below 2.5 s.The proposed model shows a linear complexity,as recursive or iterative structures are not employed,just algebraic and probabilistic functions.In conclusion,the new model and reconstructionmechanism can protect successfully Cyber-Physical Systems against sparse sensor attacks,even in dense or pervasive deployments and scenarios.

Observer-based robust predictive control of singular systems with time-delay and parameter uncertainties

The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain ＂min-max＂ optimization problems are converted into convex optimization problems solving by the linear matrix inequality （LMI）, and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.

Robust Formation Maneuvers Through Sliding Mode for Multi-agent Systems With Uncertainties

This paper develops a robust control method for formation maneuvers of a multi-agent system. The multi-agent system is leader-follower-based, where the graph theory is utilized to describe the information exchange among the agents. The control method is exercised via sliding mode methodology where each agent is subjected to uncertainties. The technique of nonlinear disturbance observer is adopted in order to overcome the adverse effects of the uncertainties. Assuming that the uncertainties have an unknown bound, the formation stability conditions are investigated according to a given communication topology. In the sense of Lyapunov, not only the formation maneuvers of the multi-agent system have guaranteed stability, but the desired formations of the agents are also realized. Compared with other two control approaches, i.e., the basic sliding mode approach and the fuzzy sliding mode approach, some numerical results are presented to illustrate the effectiveness, performance and validity of the robust control method for formation maneuvers in the presence of uncertainties.

Integral sliding mode control of time-delay systems with mismatching uncertainties

A linear matrix inequality （LMI）-based sliding surface design method for integral sliding mode control of uncertain time- delay systems with mismatching uncertainties is proposed. The uncertain time-delay system under consideration may have mis- matching norm bounded uncertainties in the state matrix as well as the input matrix, A sufficient condition for the existence of a sliding surface is given to guarantee asymptotic stability of the full order slJdJng mode dynamics. An LMI characterization of the slid- ing surface is given, together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time. Finally, a simulation is given to show the effectiveness of the proposed method.

Robust model-reference control for descriptor linear systems subject to parameter uncertainties

Robust model-reference control for descriptor linear systems with structural parameter uncertainties is investigated. A sufficient condition for existing a model-reference zero-error asymptotic tracking controller is given. It is shown that the robust model reference control problem can be decomposed into two subproblems： a robust state feedback stabilization problem for descriptor systems subject to parameter uncertainties and a robust compensation problem. The latter aims to find three coefficient matrices which satisfy four matrix equations and simultaneously minimize the effect of the uncertainties to the tracking error. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, the robust compensation problem is converted into a minimization problem with quadratic cost and linear constraints. A numerical example shows the effect of the proposed approach.

Finite-time Control of Linear Singular Systems with Parametric Uncertainties and Disturbances

The concept of finite-time stability for linear singular system is induced in this paper.Finite-time control problem is considered for linear singular systems with time-varying parametricuncertainties and exogenous disturbances. The disturbance satisfies a dynamical system with para-metric uncertainties. A su?cient condition is presented for robust finite-time stabilization via statefeedback. The condition is translated to a feasibility problem involving restricted linear matrix in-equalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities.Finally, an example is given to show the validity of the results.

Distributed consensus algorithm for networked Euler-Lagrange systems with self-delays and uncertainties

A distributed coordinated consensus problem for multiple networked Euler-Lagrange systems is studied. The communication between agents is subject to time delays, unknown parameters and nonlinear inputs, but only with their states available for measurement. When the communication topology of the system is connected, an adaptive control algorithm with selfdelays and uncertainties is suggested to guarantee global full-state synchro-nization that the difference between the agent＇s positions and ve-locities asymptotically converges to zero. Moreover, the distributed sliding-mode law is given for chaotic systems with nonlinear inputs to compensate for the effects of nonlinearity. Finally, simulation results show the effectiveness of the proposed control algorithm.

Robust Feedback Controller for Exponential Stability of Nonlinear Systems with Mismatched Uncertainties

The robust stabilization of nonlinear systems with mismatched uncertainties is investigated. Based on the stability of the nominal system, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such feedback controllers, the exponential stability of uncertain nonlinear dynamical systems can be guaranteed. The approach can give a clear insight to system analysis. An illustrative example is given to demonstrate the utilization of the approach developed. Simulation results show that the method presented is practical and effective.

Robust H_∞ and H_2 Static Output Feedback Control of Discrete-time Piecewise Affine Singular Systems with Norm-bounded Uncertainties

This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncertainties. Based on a piecewise singular Lyapunov function combined with S-procedure,Projection lemma and some matrix inequality convexifying techniques,sufficient conditions in terms of linear matrix inequalities are given for the existence of an output-feedback controller for the discrete-time piecewiseaffine singular systems with a prescribed H∞disturbance attenuation level,and the H2norm is smaller than a given positive number. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. The numerical examples are given to illustrate the effectiveness of the proposed design methods.

Uncertainties of clock and shift operators for an electron in one-dimensional nonuniform lattice systems

The clock operator U and shift operator V are higher-dimensional Pauli operators. Just recently, tighter uncertainty relations with respect to U and V were derived, and we apply them to study the electron localization properties in several typical one-dimensional nonuniform lattice systems. We find that uncertainties △U^2 are less than, equal to, and greater than uncertainties △V^2 for extended, critical, and localized states, respectively. The lower bound LB of the uncertainty relation is relatively large for extended states and small for localized states. Therefore, in combination with traditional quantities,for instance inverse participation ratio, these quantities can be as novel indexes to reflect Anderson localization.

Decentralized robust stabilization of discrete-time fuzzy large-scale systems with parametric uncertainties: a LMI method

Decentralized robust stabilization problem of discrete-time fuzzy large-scale systems with parametric uncertainties is considered. This uncertain fuzzy large-scale system consists of N interconnected T-S fuzzy subsystems, and the parametric uncertainties are unknown but norm-bounded. Based on Lyapunov stability theory and decentralized control theory of large-scale system, the design schema of decentralized parallel distributed compensation （DPDC） fuzzy controllers to ensure the asymptotic stability of the whole fuzzy large-scale system is proposed. The existence conditions for these controllers take the forms of LMIs. Finally a numerical simulation example is given to show the utility of the method proposed.

STABILITY MARGIN OF SYSTEMS WITH MIXED UNCERTAINTIES UNDER THE IQC DESCRIPTIONS

Stability perturbation bounds problem for systems with mixed uncertainties is discussed. It is supposed that the linear part in the forward loop is of parametric uncertainties described by interval perturbation mode, and that the nonlinear part in the feedback loop is characterized by an integral quadratic constraint (IQC). The definition of stability margin under the interval perturbation mode is given by using the Minkowski functional. The infinite stability checking problem of the mixed uncertain system can be converted to finite or one dimensional stability checking for different structures of the IQC multipliers based on the concepts of biconvex and convex-concave junctions and their properties. The result is illustrated to be efficient through an example.

Stability Criteria for Large－Scale Linear Systems with Structured Uncertainties

The robust stability analysis for large scale linear systems with structured time varying uncertainties is investigated in this paper.By using the scalar Lyapunov functions and the properties of M matrix and nonnegative matrix,stability robustness measures are proposed.The robust stability criteria obtained are applied to derive an algebric criterion which is expressed directly in terms of plant parameters and is shown to be less conservative than the existing ones.A numerical example is given to demonstrate the stability criteria obtained and to compare them with the previous ones.

Robust Consensus Tracking Control of Uncertain Multi-Agent Systems With Local Disturbance Rejection

In this paper,a new distributed consensus tracking protocol incorporating local disturbance rejection is devised for a multi-agent system with heterogeneous dynamic uncertainties and disturbances over a directed graph.It is of two-degree-of-freedom nature.Specifically,a robust distributed controller is designed for consensus tracking,while a local disturbance estimator is designed for each agent without requiring the input channel information of disturbances.The condition for asymptotic disturbance rejection is derived.Moreover,even when the disturbance model is not exactly known,the developed method also provides good disturbance-rejection performance.Then,a robust stabilization condition with less conservativeness is derived for the whole multi-agent system.Further,a design algorithm is given.Finally,comparisons with the conventional one-degree-of-freedombased distributed disturbance-rejection method for mismatched disturbances and the distributed extended-state observer for matched disturbances validate the developed method.

Robust Stability Analysis of Smith Predictor Based Interval Fractional-Order Control Systems:A Case Study in Level Control Process

The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.

Optimized design of drilling and blasting operations in open pit mines under technical and economic uncertainties by system dynamic modelling

Drilling and blasting are the two most significant operations in open pit mines that play a crucial role in downstream stages. While previous research has focused on optimizing these operations as two separate parts or merely in a specific parameter, this paper proposes a system dynamic model(SDM) for drilling and blasting operations as an interactive system. In addition, some technical and economic uncertainties such as rock density, uniaxial compressive strength, bit life and operating costs are considered in this system to evaluate the different optimization results. For this purpose, Vensim simulation software is utilized as a powerful dynamic tool for both modelling and optimizing under deterministic and uncertain conditions. It is concluded that an integrated optimization as opposed to the deterministic approach can be efficiently achieved. This however is dependent on the parameters that are considered as uncertainties.

Numerical Experiments and Structural Transformation of Non-Linear Evolution in Ill-posed Systems

Numerical experiments on non-linear equations of the 1st-and 3rd-order derivatives have been carried out through structural analyses in the phase space according to the numerical instability of ill-posed systems,with changes of initial values and parameters,etc..The results show that the quantitative instability in an ill-posed system may reveal reversed transformation in system evolution by structural representation,and confirm A·Dauglas' theorem that "a non-linear equation does not satisfy the existence of the initial value in a linear well-posed system".

Robust H_∞ filtering for neutral jump system with time-delays and uncertainties

The problem of robust H∞ filtering for a class of neutral jump systems with time-delay and norm- bounded uncertainties is considered. By re-constructing the system, the dynamics of overall augmented error systems is obtained which involves unknown inputs represented by disturbances, model uncertainties and time-delays. As to the nominal system, sufficient conditions are provided for the existence of the mode-dependent H∞ filter by selecting the appropriate Lyapunov-Krasovskii function and the robust H∞ filter is proposed for the jump system while considering the time-delays and uncertainties. Both of above conditions for the existence of the H∞ filter and roust H∞ filter are presented in terms of linear matrix inequalities, and convex optimization problems are formulated to design the desired filters. By employing the proposed mode-dependent H∞ filter, the systems have the stochastic stability and better ability of restraining disturbances stochastically, and the given prescribed H∞ performance is guaranteed. Simulation resuhs illustrate the effectiveness of developed techniques.

Research on Uncertainties in Evaluation Indicator System for Ecological Residential Community

In the process of evaluating,the weights of indicators are firstly determined by AHP and Delphi methods;and the values of indicators are normalized by grey correlative coefficient method.A suit of means were put forward,by which a qualitative and quantitative evaluation indicator system suitable for the situation of China and uncertainties can be established.Both idiographic and operable methods and process were presented.Following the principle of elasticity,hiberarchy and maneuverability,a three-layer evaluation indicator system was established by AHP in Jiuyi ecological residential community,which includes 5 subsystems and 24 indicatiors.The weights of indicators are measured by AHP and expert estimate and their best indicators values up to par were determined by fuzzy mathematics and optimization.The whole evaluation indicator system not only has an active and practical effect on estimating ecological residential community,but also guides ecological residential community planning.