Dissipative filtering for singular Markov jump systems with generally uncertain transition rates via new integral inequality approach

This paper considers the problem of dissipative filtering problem for singular Markov jump systems with time-varying delay and generally uncertain transition rates. Firstly, by tuning the improved integral inequality and Wirtinger-based integral inequalities, a sufficient condition is derived to guarantee that the considered system is regular, impulse-free, stochastically stable with the dissipation performance. Then, based on the derived condition, and applying linear matrix inequalities (LMIs) techniques, the filter is synthesized. Finally, some numerical examples are given to illustrate the effectiveness of the obtained theoretic results.     

Composite anti-disturbance control for uncertain Markovian jump systems with actuator saturation based disturbance observer and adaptive neural network

This paper studies the problem of composite control for a class of uncertain Markovian jump systems (MJSs) with partial known transition rates, multiple disturbances and actuator saturation. Compared with the existing results, a novel robust composite control scheme is put forward by virtue of adaptive neural network technique. For MJSs, the partial unknown information on transition rates and the actuator saturation influence the design of disturbance observer and the robust H_∞ controller. Firstly, without taking account of external disturbances, the network reconstruction error and saturation, a novel robust adaptive control strategy is established to ensure that all the signals of the closed-loop system are asymptotically bounded in mean square. Secondly, the solvability condition for ensuring the robust H_∞ performance is given by using a modified adaptive law, where the saturation is treated as a disturbance-like signal. Finally, the simulations for a numerical example and an application example are performed to validate the effectiveness of the proposed results.     

Non-fragile control of positive Markovian jump systems

This paper investigates the non-fragile control for positive Markovian jump systems both in continuous-time and discrete-time cases with actuator uncertainty. It is assumed that the coefficient matrices of the non-fragile controller is unknown and bounded. The state-feedback controller gain consists of nominal controller gain and gain perturbation. First, a set of state-feedback controllers for the considered system are designed by using a stochastic co-positive Lyapunov function integrated with linear programming approach. Under the designed controllers, the resulting closed-loop systems are positive and stochastically stable. Then, the proposed controller design approach is extended to discrete-time systems. Through comparisons, it is shown that existing results are special cases of the presented ones in the paper. Finally, two examples are given to illustrate the effectiveness of the proposed design.     

Sampled observer-based adaptive output feedback fault-tolerant control for a class of strict-feedback nonlinear systems

This paper studies the sampled outputs-based adaptive fault-tolerant control problem for a class of strict-feedback uncertain nonlinear systems, where the nonlinear functions are allowed to include the unmeasured system states. Within the framework, a sampled output observer is introduced to jointly estimate the system states and parameters. By combining the estimated states and the supervisory switching strategy, an adaptive fault-tolerant controller is designed to achieve the desirable tracking performance. By using Lyapunov stability theory, it is proved that all the signals of the closed-loop systems are bounded and the tracking error converges to an adjustable neighbourhood of the origin eventually both in the fault free and faulty cases. Especially, if the outputs are available all the time, the proposed output feedback fault-tolerant control method can ensure the tracking error satisfy the prescribed performance bounds regardless of the faults. Finally, two examples are used to illustrate the effectiveness of the proposed method.     

Asynchronous fault detection and robust control for switched systems with state reset strategy

This paper is concerned with the problem of simultaneous fault detection and control of switched systems under the asynchronous switching. A switching law and fault detection/control units called fault detector/controllers are designed to guarantee the fault sensitivity and robustness of the closed-loop systems. Different from the existing results, a state reset strategy is introduced in the process of fault detection/control, which reduces the conservatism caused by the jump of multiple Lyapunov functions at switching instants. Further, the proposed strategy is only dependent the state of fault detector/controllers, which is available when the system state is invalid. Finally, by using a performance gain transform technique, non-convex fault sensitivity conditions are converted into the convex error attenuation ones. This further improves the fault detection effect. A numerical example is given to demonstrate the effectiveness of the proposed results.     

Quantitative mean square exponential stability and stabilization of stochastic systems with Markovian switching

This paper is concerned with the quantitative mean square exponential stability and stabilization for stochastic systems with Markovian switching. First, the concept of quantitative mean square exponential stability(QMSES) is introduced, and two stability criteria are derived. Then, based on an auxiliary definition of general finite-time mean square stability(GFTMSS), the relations among QMSES, GFTMSS and finite time stochastic stability (FTSS) are obtained. Subsequently, QMSE-stabilization is investigated and several new sufficient conditions for the existence of the state and observer-based controllers are provided by means of linear matrix inequalities. An algorithm is given to achieve the relation between the minimum states’ upper bound and the states’ decay velocity. Finally, a numerical example is utilized to show the merit of the proposed results.     

Necessary conditions of exponential stability for a class of linear uncertain systems with a single constant delay

In this paper, we will investigate the necessary conditions, described by the Lyapunov matrix, for the robust exponential stability for a class of linear uncertain systems with a single constant delay and time-invariant parametric uncertainties, which are some generalizations of the existing results on uncertain linear time-delay systems. As a medium step, several pivotal properties of parameter-dependent Lyapunov matrix are proposed, which set up the relationships between fundamental matrix and Lyapunov matrix for the considered system. In addition, to calculate the parameter-dependent Lyapunov matrix, we introduce the differential equation method and the Lagrange interpolation method, respectively. Furthermore, it is noted that the proposed necessary conditions can be used to estimate the range of time delay, when the linear uncertain time-delay system is robust exponential stability. Finally, the validity of the obtained theoretical results is illustrated via numerical examples.     

Event-triggered decentralized output-feedback control for interconnected nonlinear systems with input quantization

In this paper, the event-triggered decentralized control problem for interconnected nonlinear systems with input quantization is investigated. A state observer is constructed to estimate the unmeasurable states, and the state-dependent interconnections are accommodated by presenting some smooth functions. Then by employing backstepping technique and neural networks (NNs) approximation capability, a novel decentralized output feedback control strategy and an event-triggered mechanism are designed simultaneously. It is proved through Lyapunov theory that the closed-loop system is stable and the tracking property of all subsystems is guaranteed. Finally, the effectiveness of the proposed scheme is illustrated by an example.     

Adaptive fault-tolerant control for continuous-time Markovian jump systems with signal quantization

This paper investigates the adaptive fault-tolerant control problem for a class of continuous-time Markovian jump systems with digital communication constraints, parameter uncertainty, disturbance and actuator faults. In this study, the exact information for actuator fault, disturbance and the unparametrisable time-varying stuck fault are totally unknown. The dynamical uniform quantizer is utilized to perform the design work and the mismatched initializations at the coder and decoder sides are also considered. In this paper, a novel quantized adaptive fault-tolerant control design method is proposed to eliminate the effects of actuator fault, parameter uncertainty and disturbance. Moreover, it can be proved that the solutions of the overall closed-loop system are uniformly bounded, which is asymptotically stable almost surely. Finally, numerical examples are provided to verify the effectiveness of the new methodology.     

Adaptive disturbance attenuation for a class of uncertain nonlinear systems: A double-gain nonlinear observer method

This paper is concerned with the problem of adaptive disturbance attenuation for a class of nonlinear systems. The traditional adaptive methods are almost impossible to compensate the time-varying unknown disturbance by designing parameter adaptive laws without a priori knowledge about the bounds of external disturbances. To solve the problem, a new strategy is proposed by constructing an augmented system where the external disturbance is considered as another component of the augmented state vector. Based on this, a double-gain nonlinear observer is employed to estimate the state of the augmented nonlinear system. Further, an output feedback control strategy is designed, and it is proved that the proposed strategy ensures that all the signals are bounded and the tracking error exponentially converges to an adjustable compact set. Finally, an example is performed to demonstrate the validity of the proposed scheme.     

Novel event-triggered filter design for nonlinear networked control systems

This paper investigates the problem of event-triggered filter design for nonlinear networked control systems (NCSs) in the framework of interval type-2 (IT2) fuzzy systems. A novel IT2 fuzzy filter for ensuring asymptotic stability and H_∞ performance of filtering error system is proposed, where the premise variables are different from those of the fuzzy model. Attention is focused on solving the problem of event-triggered filter design subject to parameter uncertainties, data quantization, and communication delay in a unified frame. It is shown that the proposed event-triggered filter design communication mechanism for IT2 fuzzy NCSs has the advantage of the existing event-triggered approaches to reduce the utilization of limited network resources and provides flexibility in balancing the tracking error and the utilization of network resources. Finally, simulation example is given to validate the advantages of the presented results.     

Periodic event-triggered resilient control for cyber-physical systems under denial-of-service attacks

This paper studies the problem of designing a resilient control strategy for cyber-physical systems (CPSs) under denial-of-service (DoS) attacks. By constructing an H_∞ observer-based periodic event-triggered control (PETC) framework, the relationship between the event-triggering mechanism and the prediction error is obtained. Then, inspired by the maximum transmission interval, the input-to-state stability of the closed-loop system is proved. Compared with the existing methods, a Zeno-free periodic PETC scheme is designed for a continuous-time CPS with the external disturbance and measurement noise. In particular, the objective of maximizing the frequency and duration of the DoS attacks is achieved without losing robustness. Finally, two examples are given to verify the effectiveness of the proposed approach.     

Finite-time control for periodic systems with Markov jump sensor nonlinearities and random input gains

Finite-time control for periodic systems with sensor nonlinearities and random input gains is addressed in this work. The variation of sensor nonlinearities is modeled by a Markov chain, and a stochastic variable is used to describe the influence of the actuator. A mode- and sensor nonlinearity-dependent non-fragile controller is designed to improve the performance and the non-fragility of the controller. The finite-time boundedness of the closed-loop system is ensured by a sufficient condition, the corresponding controller is then designed. Finally, the effectiveness of the developed results is illustrated by a numerical example.     

Distributed dynamic state estimation with parameter identification for large-scale systems

In this paper, we consider a distributed dynamic state estimation problem for time-varying systems. Based on the distributed maximum a posteriori (MAP) estimation algorithm proposed in our previous study, which studies the linear measurement models of each subsystem, and by weakening the constraint condition as that each time-varying subsystem is observable, this paper proves that the error covariances of state estimation and prediction obtained from the improved algorithm are respectively positive definite and have upper bounds, which verifies the feasibility of this algorithm. We also use new weighting functions and time-varying exponential smoothing method to ensure the robustness and improve the forecast accuracy of the distributed state estimation method. At last, an example is used to demonstrate the effectiveness of the proposed algorithm together with the parameter identification.     

Rapid Lyapunov control for decoherence-free subspaces of Markovian open quantum systems

A Lyapunov-based rapid control scheme is proposed to drive a Markovian open quantum system to a decoherence-free subspace by constructing the control Hamiltonians of the system. Based on Lyapunov theory, we design a general form of control laws, which includes the standard Lyapunov control law. The convergence of the control system to the decoherence-free subspace is strictly proved. By analyzing the relationship between the LaSalle invariant set and the decoherence-free subspace, we propose a construction method for the control Hamiltonians to further speed up the control process. Simulation experiments on a three-level quantum system demonstrate that the rapid Lyapunov control scheme proposed in this paper has a good control performance.     

Chaotification of a class of linear switching systems based on a Shilnikov criterion

This paper proposes an approach for constructing and generating chaos from a class of three-dimensional linear switching systems via a heteroclinic loop based on the Shilnikov criterion. First, the existence of a switching rule for the system is derived by utilizing the Shilnikov heteroclinic criterion. Then a general design philosophy and its procedure of switching rule are provided to ensure that the proposed approach is applicable to engineering. Two numerical examples are presented to validate the main principle and the implementability of the scheme. Theoretical analysis and numerical simulation are used to demonstrate the feasibility and effectiveness of developed techniques.     

Event-triggered fault estimation and fault-tolerant control for networked control systems

This paper is concerned with the event-triggered fault estimation and fault-tolerant control for continuous-time dynamic systems subject to system fault and external disturbance under network environment. Firstly, based on the event-triggered sampling, a fault diagnosis observer is constructed to estimate both the system state and the system fault simultaneously, and a multi-objective constraint is established to guarantee the estimation accuracy. Based on the estimated system state and fault signal, a fault-tolerant controller is proposed to compensate the influence of occurred faults and maintain the system performance. The event-triggered scheme and the fault-tolerant controller are co-designed to guarantee the required performance of faulty system and reduce the consumption of communication resources. Finally, simulation results of an F-404 aircraft engine system are provided to demonstrate the effectiveness of the proposed method.     

Robust adaptive control for prescribed performance tracking of constrained uncertain nonlinear systems

This paper proposes a robust adaptive control strategy for a class of state-constrained uncertain nonlinear systems with prescribed transient and steady-state behavior. The prescribed tracking performance can be characterized by constraints on an output tracking error. Both state and output constraints are achieved by bounding integral barrier Lyapunov functions in the backstepping procedure. A robust adaptive term is designed to compress auxiliary system uncertainties without the knowledge of their bounds. The satisfaction of control constraints and tracking error convergence are verified by theoretical analysis and are illustrated by simulation results.     

Fault-tolerant control for commercial aircraft with actuator faults and constraints

In this paper, a constrained control scheme based on model reference adaptive control is investigated for the longitudinal motion of a commercial aircraft with actuator faults and saturation nonlinearities. Actuator faults and constraints are both important factors adversely affecting the stability and performance of flight control systems. An adaptive adjustment law based on Lyapunov function is utilized to adjust the fault-tolerant control law. Both additive and multiplicative faults are considered in the designed controller to deal with the three types of actuator faults: locked in place, loss of effectiveness, and bias. Moreover, different techniques are implemented in the basic and fault-tolerant controller to anti-windup. Proofs for the stability of the two modified controllers which improve the performance of control system operating in the presence of actuator faults and saturations are proposed. Finally, a numerical example of the anti-windup fault-tolerant controller for a commercial aircraft is demonstrated. The stability and performance improvements can be accrued with the presented fault-tolerant control scheme.