Fault-tolerant safe control design of switched and interconnected nonlinear systems

This paper provides novel fault-tolerant safe control (FTSC) strategies for switched and interconnected nonlinear systems. With several switching and interconnection situations considered, the proposed corresponding strategies ensure that the state never enters the unsafe set and asymptotically converges to the origin in the presence of faults. This relies on a proposed concept named “fault-tolerant control Lyapunov-Barrier functions (FTCLBF)”. Two practical examples are taken to demonstrate the efficiency of the proposed method.     

Adaptive fuzzy tracking control for switched uncertain strict-feedback nonlinear systems

This paper concerns an adaptive fuzzy tracking control problem for a class of switched uncertain nonlinear systems in strict-feedback form via the modified backstepping technique. The unknown nonlinear functions are approximated by the generalized fuzzy hyperbolic model (GFHM). It is shown that if the designed parameters in the controller and adaptive laws are appropriately selected, then all closed-loop signals are bounded and the stability of the system can be kept under average dwell time methods. In the end, simulation studies are presented to illustrate the effectiveness of the proposed method.     

Sampled-data control of a class of switched nonlinear systems under asynchronous switching

This paper focuses on an output feedback stabilization problem for a class of switched nonlinear systems in non-strict feedback form under asynchronous switching via sampled-data control. Since the output of the considered systems is measurable only at the sampling instants, an observer is designed with a tunable scaling gain to estimate the state, and then a sampled-data controller is constructed with the sampled estimated state. As a distinctive feature, a merging virtual switching signal is introduced to describe the asynchronous switching generated by detecting the activation of the subsystem. By choosing an appropriate Lyapunov function, it is proved that the constructed controller with dwell time constraint can globally stabilize the considered systems under asynchronous switching. Finally, the effectiveness of the proposed method is illustrated by two examples.     

Finite-time adaptive control for a class of switched stochastic uncertain nonlinear systems

This paper addresses the problem of global finite-time adaptive control for a class of switched stochastic uncertain nonlinear systems under arbitrary switchings. By applying the delicate introduction of coordinate transformations and adding a power integrator technique, an adaptive controller is constructed to guarantee that the system state is regulated to the origin almost surely in a finite time while maintaining the boundedness of the resulting closed-loop systems in probability. Two examples are given to illustrate the effectiveness of the proposed control scheme.     

Adaptive fault-tolerant control with prescribed performance for switched nonlinear pure-feedback systems

In this paper, the problem of adaptive fuzzy fault-tolerant control is investigated for a class of switched uncertain pure-feedback nonlinear systems under arbitrary switching. The considered actuator failures are modeled as both lock-in-place and loss of effectiveness. By utilizing mean value theorem, the considered pure-feedback systems are transformed into a class of switched nonlinear strict-feedback systems. Under the framework of backstepping design technique and common Lyapunov function (CLF), an adaptive fuzzy fault-tolerant control (FTC) method with predefined performance bounds is developed. It is proved that under the proposed controller, all the signals of the close-loop systems are bounded and the state tracking error for each step remains within the prescribed performance bound (PPB) regardless of actuator faults and the system switchings. In addition, the tracking errors and magnitudes of control inputs can be reduced by adjusting the PPB parameters of errors in the first and last steps. The simulation results are provided to show the effectiveness of the proposed control scheme.     

Model reference adaptive control for switched linear systems using switched multiple models control strategy

In this paper, the multiple model strategy is applied to the adaptive control of switched linear systems to improve the transient performance. The solvability of the adaptive stabilization problem of each subsystem is not required. Firstly, the two-layer switching mechanism is designed. The state-dependent switching law with dwell time constraint is designed in the outer-layer switching to guarantee the stability of the switched systems. During the interval of dwell time constraint, the parameter resetting adaptive laws are designed in the inner-layer switching to improve the transient performance. Secondly, the minimum dwell time constraint providing enough time for multiple model adaptive control strategy to work fully and maintaining the stability of the switched systems is found. Finally, the proposed switched multiple model adaptive control strategy guarantees that all the closed-loop system signals remain bounded and the state tracking error converges to zero.     

Synchronization of switched logical control networks via event-triggered control

This paper investigates the event-triggered control design for state/output synchronization of switched k-valued logical control networks (SKVLCNs). Firstly, based on the algebraic form of SKVLCNs, some necessary and sufficient conditions are presented for the event-triggered state/output synchronization of SKVLCNs. Secondly, using the partitioning technique of matrix, a constructive procedure is proposed to design state feedback event-triggered controllers for the synchronization of SKVLCNs. Finally, an illustrative example is worked out to show the effectiveness of the obtained new results.     

Finite-time stabilization of a class of upper-triangular switched nonlinear systems

This paper investigates the finite-time stabilization for a class of upper-triangular switched nonlinear systems, where nonlinearities are allowed to be lower-order growing. Due to the special structure of the considered system, the presented methods for lower-triangular switched nonlinear systems in the literature can not be directly utilized. To solve the problem, a state feedback control law with a new structure is designed to guarantee the global finite-time stability of the closed-loop system under arbitrary switching signals by using the recursive design approach and the nested saturation method. A simulation example is provided to show the effectiveness of the proposed method.     

Robust simultaneous fault detection and control for a class of nonlinear stochastic switched delay systems under asynchronous switching

This paper concerns the simultaneous fault detection and control (SFDC) problem for a class of nonlinear stochastic switched systems with time-varying state delay and parameter uncertainties. The switching signal of detector/controller unit (DCU) is assumed to be with switching delay, which results in the asynchronous switching between the subsystems and DCU. By constructing a switching strategy depending on the state and switching delays, new sufficient conditions expressed by a set of linear matrix inequalities (LMIs) is derived to design DCU gains. This problem is formulated as an H_∞ optimization problem and both mean square exponential stability and fault detection of augmented system are considered. A numerical example is finally exploited to verify the effectiveness and potential of the achieved scheme.     

Stabilization of artificial gas-lift process using nonlinear predictive generalized minimum variance control

Artificial gas-lift (AGL) is one of the most widely used methods in oil production to maintain acceptable oil flow to the processing equipment and sales when the reservoir pressure is not high enough. In spite of its popularity, the AGL process is prone to casing-heading instability, which is revealed as significant flow oscillation. This is undesirable as it results in production losses and unstable behavior that has negative impact on the downstream equipment. Controller design for such a process is very challenging as it exhibits highly nonlinear dynamics. In this work, the predictive generalized minimum variance control (NPGMV) is employed to derive a robust controller based on the state estimation to stabilize AGL process when casing-heading phenomenon occurs. A closed-form optimal control law is obtained based on the Taylor series approximation. Further, a nonlinear state observer is produced and combined with the controller to ensure closed-loop control through variables that are most beneficial to the system performance, which are unmeasurable and can be obtained only via estimation. Through simulation studies, the effectiveness of the proposed controller is demonstrated.     

Adaptive practical finite-time stabilization for switched nonlinear systems in pure-feedback form

This paper investigates adaptive practical finite-time stabilization for a class of switched nonlinear systems in pure-feedback form. Under some appropriate assumptions, a controller and adaptive laws are designed by using adding a power integrator technique, and neural networks are employed to approximate unknown nonlinear functions. It is proved that all states of the closed-loop system converge to a small neighborhood of the origin in finite time. Finally, two simulations are provided to show the feasibility and validity of the proposed control scheme.     

Asynchronous switching for switched nonlinear input delay systems with unstable subsystems

We study the input-to-state stability (ISS) of switched nonlinear input delay systems under asynchronous switching. Our results apply to cases where some subsystems of the switched systems are not necessarily stable under the influence of input delay. By making a compromise among the matched-stable period, the matched-unstable period, and the unmatched period and allowing the increase of the Lyapunov–Krasovskii functional (LKF) on all the switching times, the extended stability criteria for switched delay systems in generally nonlinear setting are derived first. Then, we focus on switched nonlinear input delay systems where the presence of the input delay leads to the instability of some subsystems of it. By explicitly constructing input-to-state stable LKF, the sufficient conditions for ISS of switched nonlinear input delay systems under asynchronous switching are presented. Finally, two examples are given to illustrate the effectiveness of the proposed theory.     

Global finite-time stabilization for switched stochastic nonlinear systems via output feedback

This paper is concerned with the problem of global finite-time stabilization via output feedback for a class of switched stochastic nonlinear systems whose powers are dependent of the switching signal. The drift and diffusion terms satisfy the lower-triangular homogeneous growth condition. Based on adding a power integrator technique and the homogeneous domination idea, output-feedback controllers of all subsystems are constructed to achieve finite-time stability in probability of the closed-loop system. Distinct from the existing results on switched stochastic nonlinear systems, the delicate change of coordinates are introduced for dominating nonlinearities. Moreover, by incorporating a multiplicative design parameter into the coordinate transformations, the obtained control method can be extended to switched stochastic nonlinear systems with nonlinearities satisfying the upper-triangular homogeneous growth condition. The validity of the proposed control methods is demonstrated through two examples.     

Impulsive observer design for a class of switched nonlinear systems with unknown inputs

This paper investigates hybrid observer design of a class of unknown input switched nonlinear systems. The distinguishing feature of the proposed method is that the stability of all subsystems of the error switched systems is not necessarily required. First, an output derivative-based method and time-varying coordinate transformation are considered to eliminate the unknown input. Then in order to maintain a satisfactory estimation performance, an impulsive full-order and switched reduced-order observer are developed with a pair of upper and lower dwell time bounds and constructing time-varying Lyapunov functions combined with convex combination technique. In addition, the time-varying Lyapunov functions method is also used to analyze the stability of a class of error switched nonlinear systems with stable subsystems. Finally, two examples are presented to demonstrate the effectiveness of the proposed method.     

Uniform exponential stability of periodic discrete switched linear system

Let {Π_τ(m, n): m?≥?n?≥?0} be the family of periodic discrete transition matrices generated by bounded valued square matrices Λ_τ(n), where $\tau :[0,1,2,?)\to \Omega$ is an arbitrary switching signal. We prove that the family {Π_τ(m, n): m?≥?n?≥?0} of bounded linear operator is uniformly exponentially stable if and only if the sequence $n?{\sum }_{k=0}^n{e}^{i\alpha k}{\Pi }_{\tau }(n,k)w\left(k\right):{\mathbb{Z}}_{+}\to \mathbb{R}$ is bounded.     

Observer-based fuzzy adaptive stabilization of uncertain switched stochastic nonlinear systems with input quantization

This paper proposes an observer-based fuzzy adaptive output feedback control scheme for a class of uncertain single-input and single-output (SISO) nonlinear stochastic systems with quantized input signals and arbitrary switchings. The SISO system under consideration contains completely unknown nonlinear functions, unmeasured system states and quantized input signals quantized by a hysteretic quantizer. By adopting a new nonlinear disposal of the quantized input, the relationship between the control input and the quantized input is established. The hysteretic quantizer that we take can effectively avoid the chattering phenomena. Furthermore, the introduction of a linear observer makes the estimation of the states possible. Based on the universal approximation ability of the fuzzy logic systems (FLSs) and backstepping recursive design with the common stochastic Lyapunov function approach, a quantized output feedback control scheme is constructed, where the dynamic surface control (DSC) is explored to alleviate the computation burden. The proposed control scheme cannot only guarantee the boundedness of signals but also make the output of the system converge to a small neighborhood of the origin. The simulation results are exhibited to demonstrate the validity of the control scheme.     

Event-triggered sliding mode control of uncertain switched systems under denial-of-service attacks

This study is concerned with the event-triggered sliding mode control problem for a class of cyber-physical switched systems, in which the Denial-of-Service (DoS) attacks may randomly occur according to the Bernoulli distribution. A key issue is how to design the output feedback sliding mode control (SMC) law for guaranteeing the dynamical performance of the closed-loop system under DoS attacks. To this end, an event-triggered mechanism is firstly introduced to reduce the communication load, under which the measurement signal is transmitted only when a certain triggering condition is satisfied. An usable output signal for the controller is constructed to compensate the effect of unmeasured states and DoS attacks. And then, a dynamic output feedback sliding mode controller is designed by means of the attack probability and the compensated output signals. Both the reachability and the mean-square exponential stability of sliding mode dynamics are investigated and the corresponding sufficient conditions are obtained. Finally, some numerical simulation results are provided.     

On stability for sampled-data nonlinear ADRC-based control system with application to the ball-beam problem

This paper mainly concerns with the stability analysis of the sampled-data nonlinear active disturbance rejection control (ADRC)-based control system. Firstly, a class of single-input-single-output (SISO) continuous plant is discretized using zero-order-hold (ZOH), and several kinds of digital implementation methods for the nonlinear extended state observer (NLESO) are newly proposed. Then the sampled-data nonlinear ADRC (NLADRC) based closed-loop system is transformed into a discrete-time Lurie-like system, to which linear matrix inequality (LMI)-based sufficient conditions for absolute stability and robust absolute stability are obtained. The sufficient conditions provide convenient and effective methods for determining the stability and its relationship with the parameters of the controller, the plant and the sampling period. Using the ball-beam system as an example, the proposed results are verified in both simulations and experiments.     

Robust packet-based nonlinear fuzzy networked control systems

A class of networked nonlinear control systems with norm-bounded uncertainties is presented in this paper. The class is represented by Takagi–Sugeno (T-S) fuzzy models with packet processing. The network loop delay is considered either as known delay or random delay. For the former case, we develop conditions that guarantee the robust asymptotic stability and state-feedback stabilization with strict dissipativity and cast the results in linear matrix inequality (LMI) framework. Next employing a probabilistic-based delay partitioning method to deal with random delay, we establish novel LMI criteria for strict dissipative stability analysis and feedback synthesis. The efficacy of the ensuing techniques is demonstrated by numerical solution of typical examples and Mont Carlo simulation.