New advances in H∞ control and filtering for nonlinear systems

The main objective of this special issue is to summarise recent advances in H∞ control and filtering for nonlinear systems, including time-delay, hybrid and stochastic systems. The published papers provide new ideas and approaches, clearly indicating the advances made in problem statements, methodologies or applications with respect to the existing results. The special issue also includes papers focusing on advanced and non-traditional methods and presenting considerable novelties in theoretical background or experimental setup. Some papers present applications to newly emerging fields, such as network-based control and estimation

Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Robust Fault Detection of Switched Linear Systems with State Delays

This correspondence deals with the problem of robust fault detection for discrete-time switched systems with state delays under an arbitrary switching signal. The fault detection filter is used as the residual generator, in which the filter parameters are dependent on the system mode. Attention is focused on designing the robust fault detection filter such that, for unknown inputs, control inputs, and model uncertainties, the estimation error between the residuals and faults is minimized. The problem of robust fault detection is converted into an H infin-filtering problem. By a switched Lyapunov functional approach, a sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed method

Distributed Event-Triggered Control for Asymptotic Synchronization of Dynamical Networks

This paper studies synchronization of dynamical networks with event-based communication. Firstly, two estimators are introduced into each node, one to estimate its own state, and the other to estimate the average state of its neighbours. Then, with these two estimators, a distributed event-triggering rule (ETR) with a dwell time is designed such that the network achieves synchronization asymptotically with no Zeno behaviours. The designed ETR only depends on the information that each node can obtain, and thus can be implemented in a decentralized way.Comment: 8 pages, 2 figues, 1 tabl

A virtual actuator approach for the secure control of networked LPV systems under pulse-width modulated DoS attacks

In this paper, we formulate and analyze the problem of secure control in the context of networked linear parameter varying (LPV) systems. We consider an energy-constrained, pulse-width modulated (PWM) jammer, which corrupts the control communication channel by performing a denial-of-service (DoS) attack. In particular, the malicious attacker is able to erase the data sent to one or more actuators. In order to achieve secure control, we propose a virtual actuator technique under the assumption that the behavior of the attacker has been identified. The main advantage brought by this technique is that the existing components in the control system can be maintained without need of retuning them, since the virtual actuator will perform a reconfiguration of the plant, hiding the attack from the controller point of view. Using Lyapunov-based results that take into account the possible behavior of the attacker, design conditions for calculating the virtual actuators gains are obtained. A numerical example is used to illustrate the proposed secure control strategy.Peer ReviewedPostprint (author's final draft

Robust Stability Analysis for Uncertain Switched Discrete-Time Systems

This paper is concerned with the robust stability for a class of switched discrete-time systems with state parameter uncertainty. Firstly, a new matrix inequality considering uncertainties is introduced and proved. By means of it, a novel sufficient condition for robust stability of a class of uncertain switched discrete-time systems is presented. Furthermore, based on the result obtained, the switching law is designed and has been performed well, and some sufficient conditions of robust stability have been derived for the uncertain switched discrete-time systems using the Lyapunov stability theorem, block matrix method and inequality technology. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes

Advances In Internal Model Principle Control Theory

In this thesis, two advanced implementations of the internal model principle (IMP) are presented. The first is the identification of exponentially damped sinusoidal (EDS) signals with unknown parameters which are widely used to model audio signals. This application is developed in discrete time as a signal processing problem. An IMP based adaptive algorithm is developed for estimating two EDS parameters, the damping factor and frequency. The stability and convergence of this adaptive algorithm is analyzed based on a discrete time two time scale averaging theory. Simulation results demonstrate the identification performance of the proposed algorithm and verify its stability. The second advanced implementation of the IMP control theory is the rejection of disturbances consisting of both predictable and unpredictable components. An IMP controller is used for rejecting predictable disturbances. But the phase lag introduced by the IMP controller limits the rejection capability of the wideband disturbance controller, which is used for attenuating unpredictable disturbance, such as white noise. A combination of open and closed-loop control strategy is presented. In the closed-loop mode, both controllers are active. Once the tracking error is insignificant, the input to the IMP controller is disconnected while its output control action is maintained. In the open loop mode, the wideband disturbance controller is made more aggressive for attenuating white noise. Depending on the level of the tracking error, the input to the IMP controller is connected intermittently. Thus the system switches between open and closed-loop modes. A state feedback controller is designed as the wideband disturbance controller in this application. Two types of predictable disturbances are considered, constant and periodic. For a constant disturbance, an integral controller, the simplest IMP controller, is used. For a periodic disturbance with unknown frequencies, adaptive IMP controllers are used to estimate the frequencies before cancelling the disturbances. An extended multiple Lyapunov functions (MLF) theorem is developed for the stability analysis of this intermittent control strategy. Simulation results justify the optimal rejection performance of this switched control by comparing with two other traditional controllers

Distributed State Estimation for Linear Systems

This paper studies a distributed state estimation problem for both continuous- and discrete-time linear systems. A simply structured distributed estimator is first described for estimating the state of a continuous-time, jointly observable, input free, multi-channel linear system whose sensed outputs are distributed across a fixed multi-agent network. The estimator is then extended to non-stationary networks whose graphs switch according to a switching signal with a fixed dwell time or a variable but with fixed average dwell time, or switch arbitrarily under appropriate assumptions. The estimator is guaranteed to solve the problem, provided a network-widely shared gain is sufficiently large. As an alternative to sharing a common gain across the network, a fully distributed version of the estimator is thus studied in which each agent adaptively adjusts a local gain though the practicality of this approach is subject to a robustness issue common to adaptive control. A discrete-time version of the distributed state estimation problem is also studied, and a corresponding estimator is proposed for time-varying networks. For each scenario, it is explained how to construct the estimator so that its state estimation errors all converge to zero exponentially fast at a fixed but arbitrarily chosen rate, provided the network's graph is strongly connected for all time. This is accomplished by appealing to the ``split-spectrum'' approach and exploiting several well-known properties of invariant subspace. The proposed estimators are inherently resilient to abrupt changes in the number of agents and communication links in the inter-agent communication graph upon which the algorithms depend, provided the network is redundantly strongly connected and redundantly jointly observable.Comment: 17 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1903.0548

Fault detection for switched positive systems under successive packet dropouts with application to the Leslie matrix model

In this paper, the problem of fault detection filter design is dealt with for a class of switched positive systems with packet dropouts on the channel between the sensors and the filters. The phenomena of packet dropouts are governed by a Bernoulli process, and a stochastic switched positive system is established based on the augmented states of the plants and filters. Two criteria are developed to evaluate the performance of the fault detection for the system under investigation. Sufficient conditions are established on the existence of the desired filters for the mean-square stability with an L1 disturbance attenuation level, and an index for the L fault sensitivity is also derived through constructing a switched Lyapunov function in term of linear programming. Two illustrative examples, one of which is concerned with the Leslie matrix model, are provided to show the effectiveness and applicability of the proposed results. Copyright © 2015 John Wiley & Sons, Ltd.National Natural Science Foundation of China under Grants 61104114, 61201035, 61374070, 61473055. Fundamental Research Funds for the Central Universities in China under Grants DUT14QY14, DUT14QY31, and the Natural Science Foundation of Liaoning under Grants L2014026, 2015020075