Finite-time H ∞ control for a class of Markovian jump delayed systems with input saturation

This work considers the finite-time control problem for a class Markovian jump delayed systems with partially known transition rates subject to saturating actuators. By employing local sector conditions and an appropriate Lyapunov–Krasovkii function, an observer-based state feedback controller is designed to guarantee that the resulted closed-loop constrained system is mean-square locally asymptotically finite-time stabilizable. Some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of proposed method.     

Finite-time output feedback control for a class of second-order nonlinear systems with application to DC–DC buck converters

The problem of output feedback control for a class of second-order nonlinear systems is investigated in this paper. Using the techniques of finite-time control and finite-time convergent observer, an observer-based finite-time output feedback controller is proposed which can guarantee that the system’s state converges to the equilibrium in a finite time. As an application of the proposed theoretical results, the problem of finite-time control without current signal for the DC–DC buck converters is solved. Simulation results are given to demonstrate the effectiveness of the proposed method.     

Finite-time non-fragile boundary feedback control for a class of nonlinear parabolic systems

In this paper, the finite-time non-fragile boundary feedback control problem is investigated for a class of nonlinear parabolic systems, where both the multiplicative and additive controller gain variations are considered to describe the actuator parameter perturbation. Non-fragile boundary control strategies are designed with respect to two controller gain variations via collocated or non-collocated boundary measurement, respectively. In light of the finite-time stability and Lyapunov-based techniques, some sufficient conditions are presented in terms of linear matrix inequalities such that the resulting closed-loop system is well-posedness and practically finite-time stable. Finally, numerical examples are given to verify the effectiveness of the proposed design method.

     

Double event-triggered leader-following consensus and fault detection for Lipschitz nonlinear multi-agent systems via periodic sampling strategy

This paper considers the problem of leader-following consensus and fault detection for a class of multi-agent systems with Lipschitz nonlinear dynamics. To reduce the amount of redundant information and avoid checking triggering conditions continually, this paper proposes an efficient network framework with a double periodic event-triggered mechanism. Based on the proposed framework, an improved fault detection observer and a consensus controller are designed. Then, the original problem is converted into a set of stability problems with constraints. According to Lyapunov–Krasovskii theorem and the free-weighting matrix technique, sufficient conditions for solving these stability problems are derived in the form of bilinear matrix inequalities (BMIs). Further, to eliminate the nonlinear terms of BMI and obtain optimal performance, two iterative algorithms based on linear matrix inequalities (LMIs) are developed. Two simulation examples are provided to verify the practicality and validity of the theoretical results.

     

Dissipative control of switched nonlinear systems with sliding mode: an event-triggered control scheme

This paper introduces the event-triggered scheme to study the problems of dissipative control and dissipativity-based sliding mode control (SMC) for switched nonlinear systems. Firstly, based on a designed event-triggered scheme, a piecewise continuous state feedback controller is constructed; sufficient conditions for \(\left( Q,S,R\right) \)-\(\alpha \)-dissipativity of the resulting system are derived by the approaches of a switched Lyapunov function and an average dwell time. Secondly, these two methods are extended to the study of \(H_\infty \) performance and passive performance; the corresponding sufficient conditions are provided. Thirdly, the dissipative control problem is solved by introducing an event-triggered scheme into SMC method. Sufficient conditions for dissipativity of the resulting system are derived, and an SMC law is designed to guarantee the reachability. At the end of this paper, the correctness of the proposed methods is proved by two numerical examples.

     

Fuzzy observer-based command filtered tracking control for uncertain strict-feedback nonlinear systems with sensor faults and event-triggered technology

For the trajectory tracking problem of nth-order uncertain nonlinear systems with sensor faults, a fuzzy controller based on command filtered and event-triggered technology is designed to improve the tracking error of the system. Concurrently, a fault-tolerant control scheme is introduced to effectively solve the problem of sudden output sensor failure. Additionally, the proposed controller can also greatly avoid complexity explosion problem of derivations of virtual control laws, which makes the design of the controller simpler. Furthermore, an effective observer is designed to solve the problem of system state immeasurability. Therefore, the proposed control scheme makes the design of the controller more convenient and flexible. According to Lyapunov stability theory, it is proved that all closed-loop signals are uniformly and ultimately bounded. Finally, two simulation examples of second-order nonlinear system and single-link robot show the effectiveness of the proposed scheme.

     

Property and evolution of the running-in attractor in an actual dynamic system

In this paper, the issue of adaptive neural tracking control for uncertain switched multi-input multi-output (MIMO) nonstrict-feedback nonlinear systems with average dwell time is studied. The system under consideration includes unknown dead-zone inputs and output constraints. The uncertain nonlinear functions are identified via neural networks. Also, neural networks-based switched observer is constructed to approximate all unmeasurable states. By means of the information for dead-zone slopes and barrier Lyapunov function (BLF), the problems of dead-zone inputs and output constraints are tackled. Furthermore, dynamic surface control (DSC) scheme is employed to ensure that the computation burden is greatly reduced. Then, an observer-based adaptive neural control strategy is developed on the basis of backstepping technique and multiple Lyapunov functions approach. Under the designed controller, all the signals existing in switched closed-loop system are bounded, and system outputs can track the target trajectories within small bounded errors. Finally, the feasibility of the presented control algorithm is proved via simulation results.

     

Observer-based sliding mode control for switched positive nonlinear systems with asynchronous switching

Nonlinear Dynamics - This paper investigates the problem of observer-based sliding mode control for switched positive nonlinear systems with asynchronous switching. The mode of controller is...     

Observer-based event-triggered control for semilinear time-fractional diffusion systems with distributed feedback

This paper is concerned with the observer-based distributed event-triggered feedback control for semilinear time-fractional diffusion systems under the Robin boundary conditions. To this end, an extended Luenberger-type observer is presented to solve the limitations caused by the impossible availability of full-state information that is needed for feedback control in practical applications due to the difficulties of measuring. With this, we propose the distributed output feedback event-triggered controllers via backstepping technique under which the considered systems admit Mittag–Leffler stability. It is shown that the given event-triggered control strategy could significantly reduce the amount of transmitted control inputs while guaranteeing the desired system performance with the Zeno phenomenon being excluded. A numerical illustration is finally presented to illustrate our theoretical results.     

Fuzzy speed control with an acceleration observer for a permanent magnet synchronous motor

Based on the Takagi–Sugeno fuzzy approach we design a fuzzy speed regulator as well as a fuzzy acceleration observer for a permanent magnet synchronous motor (PMSM). The proposed observer-based fuzzy speed regulator is independent of the load torque value. We derive the sufficient conditions for the existence of the regulator and the observer in terms of linear matrix inequalities (LMIs), and also give LMI parameterizations of the gain matrices. Simulation and experimental results are given to verify that the proposed control method can be used to accurately control the speed of a PMSM under model parameter and load torque variations.     

Integral-based event-triggered synchronization criteria for chaotic Lur’e systems with networked PD control

Integral-based event-triggered synchronization criteria are firstly presented for networked chaotic systems with proportional-derivative (PD) control. The event-triggered scheme effectively utilizes network resources; however, the PD-type control subject to the conventional triggering inequality may cause excessive triggering and have difficulty in obtaining a feasible solution. To solve these problems, the integrated event-triggering inequality is employed and the modified integral inequality with free-weighting matrix is proposed to fill the empty diagonal terms, which overcomes the difficulties of the integration of delayed signal vectors upon integral event-triggering condition. Based on Lyapunov stability, the synchronization criteria are derived as linear matrix inequalities. Finally, the effectiveness of the integral-based event-triggered synchronization method is demonstrated by numerical examples.     

Adaptive finite-time event-triggered command filtered control for nonlinear systems with unknown control directions

Nonlinear Dynamics - In this article, we study an adaptive finite-time event-triggered command filtered control problem based on output feedback for a class of nonstrict-feedback nonlinear systems...     

Observer-based adaptive fuzzy finite-time prescribed performance tracking control for strict-feedback systems with input dead-zone and saturation

This paper considers the problems of finite-time prescribed performance tracking control for a class of strict-feedback nonlinear systems with input dead-zone and saturation simultaneously. The unknown nonlinear functions are approximated by fuzzy logic systems and the unmeasurable states are estimated by designing a fuzzy state observer. In addition, a non-affine smooth function is used to approximate the non-smooth input dead-zone and saturated nonlinearity, and it is varied to the affine form via the mean value theorem. An adaptive fuzzy output feedback controller is developed by backstepping control method and Nussbaum gain method. It guarantees that the tracking error falls within a pre-set boundary at finite time and all the signals of the closed-loop system are bounded. The simulation results illustrate the feasibility of the design scheme.

     

Finite-time event-triggered sliding mode control for one-sided Lipschitz nonlinear systems with uncertainties

Nonlinear Dynamics - This paper investigates the problem of finite-time event-triggered sliding mode control for one-sided Lipschitz nonlinear systems with uncertainties. The system is subjected to...     

Event-triggered output-feedback tracking of a class of nonlinear systems with unknown time delays

A single function approximation (SFA) approach for event-triggered output-feedback tracker design is presented for uncertain nonlinear time-delay systems in lower-triangular form. Contrary to the existing event-triggered output-feedback control methods dependent on multiple function approximators in the presence of lower-triangular nonlinearities, the proposed SFA approach provides the following advantages: (i) the simple observer structure independent of function approximators; (ii) one event-triggering condition based on only a tracking error; and (iii) the simple control scheme using one function approximator. Thus, the structural simplicity is allowed for implementing the observer and the event-triggering law in the sensor part and the adaptive tracker in the control part. Under the proposed SFA-based event-triggered control scheme, it is shown that the boundedness of closed-loop signals and the existence of a minimum inter-event time are guaranteed regardless of unknown time-delay nonlinearities and unmeasurable state variables.

     

Finite-time stabilization of nonlinear systems using an event-triggered controller with exponential gains

Nonlinear Dynamics - This paper investigates the finite-time stabilization for a class of nonlinear systems by proposing a new event-triggered controller. The novelty lies in that, by introducing...     

Collective stochastic resonance behavior in the globally coupled fractional oscillator

This paper investigates the exponential synchronization of chaotic Lur’e systems (CLSs) with time-varying communication delays through event-triggered sampling control. Specially, first, a discrete event-triggered sampling control scheme, which only sends necessary sampling signal through the network, is designed for CLSs. By using this controller, the number of control updates could greatly reduce. Second, by getting utmost out of the usable information on the actual sampling pattern, some new sawtooth structure terms are introduced in the constructed Lyapunov–Krasovskii functional (LKF). It is worth mentioning that, different from some existing results to restrict the LKF to be positive define on the whole sampling intervals, the LKF is positive definite only needing at sampling times thanks to the use of the new inequality in Lemma 1. Third, less conservative synchronization criteria are established and the desired control gain matrix is obtained. Finally, two Chua’s circuit numerical simulations are presented to validate the feasibility and effectiveness of the theoretical results.     

Asynchronous observer-based finite-time control for nonlinear Markovian jump systems with time-varying delays

Nonlinear Dynamics - This paper addresses the problem of finite-time observer-based control for continuous-time nonlinear Markovian jump systems with time-varying delays. The existing studies about...     

$$H_\infty $$ switching synchronization for multiple time-delay chaotic systems subject to controller failure and its application to aperiodically intermittent control

This paper is concerned with the \(H_\infty \) synchronization control problem for a class of chaotic systems with multiple delays in the presence of controller temporary failure. Based on the idea of switching, the synchronization error systems with controller temporary failure are modeled as a class of switched synchronization error systems. Then, a switching condition that incorporates the controller failure time is constructed by using piecewise Lyapunov functional and average dwell-time methods, such that the switched synchronization error systems are exponentially stable and satisfy a weighted \(H_\infty \) performance level. In the meantime, a switching state feedback \(H_\infty \) controller is derived by solving a set of linear matrix inequalities. More incisively, the obtained results can also be applied to the issue of aperiodically intermittent control. Finally, three simulation examples are employed to illustrate the effectiveness and potential of the proposed method.     

Observer-based fault-tolerant control for an air-breathing hypersonic vehicle model

This paper focuses on controller and observer design for the longitudinal model of an air-breathing hypersonic vehicle (AHV) subject to actuator faults and limited measurements of the states. The feedback linearization method is firstly employed for a modified AHV model with actuator faults, and dynamic effect caused by the actuator faults on the linearized model is analyzed. Based on full state information, an adaptive controller is designed using the Lyapunov method, which guarantees reference command tracking of the AHV under actuator faults. Next, to estimate the unmeasurable states used in the adaptive controller, a sliding observer is designed based on the sliding control method and the Filippov’s construction of the equivalent dynamics (FCED). Finally, the adaptive controller is combined with the sliding observer to generate the observer-based adaptive controller, which relies only on partial state information. Simulations demonstrate that the observer-based adaptive controller achieves desired tracking performance and good robustness in the presence of actuator faults.