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This article studies the output regulation problem (ORP) for nonlinear systems based on prescribed performance control (PPC). The items with the partial derivative of the virtual controller are combined together by using backstepping, and then the fuzzy logic systems (FLSs) are used to approximate these combined items, so that the designed virtual controller does not have the partial derivative of the previous virtual controllers. Therefore, this method not only reduces the calculation burden in the backstepping method, but also avoids the disadvantages of dynamic surface control (DSC). Finally, a function $\Theta $ is constructed such that the overall performance (dynamic performance and steady-state performance) of the tracking error (OPTE) is constrained by PP functions. The proposed control algorithm ensures that all the signals are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error achieves the PPC. Simulation examples are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article studies the adaptive finite-time quantized tracking control problem for a class of full state-constrained nonlinear systems with unknown control directions based on a modified fractional-order dynamic surface control (FODSC) technique. First, fractional calculus is introduced to filter design to avoid the issue of the “explosion of complexity” exposed in the traditional backstepping technique. To facilitate the control design, barrier Lyapunov functions and Nussbaum gain technique are utilized to handle full state-constrained problem and the unknown control directions, respectively. In addition, the fuzzy logic systems are employed to approximate the unknown nonlinearity of the system. By integrating with the approximation errors and compensating signals, a composite adaptive quantized controllers is designed to guarantee all the signals of the closed-loop systems are bounded and tracking error converges to an arbitrarily small neighborhood of the zero within a finite time. Finally, a mechanical horizontal platform model and a Brusselator model are carried out to verify the effectiveness of the presented control method. [ABSTRACT FROM AUTHOR]

This article addresses the adaptive event-triggered nonfragile state estimation for the fractional-order complex networked systems subject to randomly occurring nonlinearities and adversarial network attacks, in which the order of fractional derivative operator satisfies $0 < p < 1$. To reduce unnecessary transmission burden as much as possible in an allowable range, an adaptive event-triggered scheme (AETS) is introduced to determine whether the data released by the sensor should be transmitted to the nonfragile state estimator. First, based on the considerations of the designed AETS and stochastic cyber-attacks, one constructs a newly fractional-order estimation error system model. Then, by employing the Lyapunov functional approach and the properties of Mittag–Leffler (M–L) functions, a sufficient condition is obtained to ensure the augmented error system stochastic mean-square stability; moreover, by making use of matrix’s singular value decomposition (SVD), the desired nonfragile state estimator is designed, and the estimator gains can be obtained by finding the feasible solutions of linear matrix inequality (LMI). Finally, a numerical example and Chua’s circuit model example are given to illustrate the feasibility of the designed nonfragile estimator. [ABSTRACT FROM AUTHOR]

This article develops a generalized $\mathcal {H}$ -representation, which can transforms stochastic systems into deterministic systems. With the help of this new approach, the necessary and sufficient conditions of $p$ th moment asymptotic stability and stabilization of linear stochastic systems are addressed. Meanwhile, the generalized $\mathcal {H}$ -representation method is also applied to investigate $p$ th moment observability and $p$ th moment complete observability for the addressed systems. [ABSTRACT FROM AUTHOR]

This article studies the adaptive backstepping control problem for a class of fractional-order (FO) nonlinear systems subject to input quantization and unknown control directions by combining with an indirect FO Lyapunov stability method, and a command filter-based FO dynamic surface control (FODSC) technique. First, a modified FODSC method is utilized to reduce the computational complexity existing in the conventional recursive procedure in which an FO command filter is designed to obtain the command signals and their FO derivatives. Furthermore, the Nussbaum function and neuro-fuzzy networks (NFNs) are adopted to deal with the problem of the unknown control directions and unknown nonlinear functions existing in the system. Moreover, by introducing the compensation and prediction mechanism to controller design, the adaptive controllers, and adaptive laws are constructed to ensure that all the signals of the controlled systems are bounded. Finally, two examples are given to show the validity of the developed control method. [ABSTRACT FROM AUTHOR]

This article considers admissibility analysis and stabilization for implicit Markovian jump systems (IMJSs) with retarded discrete-distributed delays. Admissibility analysis is investigated for the unforced delay IMJSs by virtue of reciprocally convex integral inequality technique and Barbalat’s lemma. State feedback controller is designed via the matrix transformation technique to realize the stabilization of the delayed closed-loop IMJSs. By selecting comprehensive L-K functional with modes and delays information, admissibilization conditions are presented in terms of LMIs. Two illustrative examples including an inverted pendulum controlled by a direct current motor (DCMCIP) system are utilized to certify the effectiveness and practicality of the admissibilization technique. [ABSTRACT FROM AUTHOR]

This article investigates the issue of neuro-fuzzy-based adaptive dynamic surface control (DSC) for uncertain fractional-order (FO) nonlinear systems in strict-feedback form where input constraint is considered in the systems. In the recursive steps, the neuro-fuzzy network systems are employed to deal with the unknown nonlinear terms existing in systems. Furthermore, based on a DSC scheme, a modified FO filter is constructed to overcome the problem of explosion of complexity caused by the traditional backstepping design. Moreover, according to the FO Lyapunov stability theory, a neuro-fuzzy-based adaptive controller is designed to guarantee all the signals of FO closed-loop systems tend to be bounded. Finally, the three examples are provided to verify the validity and superiority of the presented control scheme. [ABSTRACT FROM AUTHOR]

This paper studies the resilient asynchronous ${H} _{\infty }$ control problem for slow sampling discrete-time uncertain Markov jump singularly perturbed systems (SPSs). Compared with slow state variables feedback controller, a new controller is proposed for slow sampling discrete-time SPSs, which has less conservatism. A more realistic situation, i.e., the system modes cannot be directly acquired for controller design, is considered with the help of hidden Markov model (HMM). The goal is to design a resilient asynchronous controller based on HMM such that the closed-loop system is stochastically stable while meeting an expected ${H}_{\infty }$ performance in the presence of random controller gain fluctuation and the system modes hiding for controller. By utilizing matrix inequality techniques and Lyapunov function method, some criteria are established for the existence of the resilient asynchronous controller. The superiority and practicability of the obtained theoretical results are demonstrated by a numerical example and an inverted pendulum system. [ABSTRACT FROM AUTHOR]

A fractional-order integral fuzzy sliding mode control scheme is proposed for a class of uncertain fractional-order nonlinear systems subject to uncertainties and external disturbances. First, in each step, a neuro-fuzzy network system is developed to approximate the uncertain nonlinear function existing in fractional-subsystem and a fractional sliding mode surface is presented. Second, based on the fractional Lyapunov stability theory and the finite-time stability theory, a fractional adaptive backstepping neuro-fuzzy sliding mode controller is designed to drive the state trajectories of fractional-order systems to the prescribed sliding mode surface. Meanwhile, the finite-time stability of the fractional-order closed-loop system is proved. At last, three numerical examples are given to illustrate the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper aims to design a dissipative fuzzy filter for a class of discrete-time nonlinear networked systems. In order to adopt the limited communication links, we employ an event-triggered scheme to reduce the number of transmitted data in the network by preventing the unnecessary ones from releasing. Due to the digital channel, the data to be transmitted should be quantized and a logarithmic quantizer is employed. Then, when the part of released data is transmitted in the network, data losses is captured by a Bernoulli process. Consequently, the uncomplete data sequence is compensated by the buffer and then send to the filter. During this process, a new random series is developed to help constructing the filtering systems. Thus, a novel method is presented to guarantee the filter error system to be dissipative based on the T–S fuzzy model approach. Finally, an example concerned with Henon mapping system is provided to verify the validity of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the practically finite-time (PFT) control problem for a class of more general nonlinear systems subject to mismatching time-varying disturbances. Without any extra assumptions on system nonlinearities, a composite controller is developed by introducing a disturbance observer and finite-time control technique. Based on the designed controller and Lyapunov stability theory, the PFT stability of the closed-loop system is strictly verified and proven to be a better convergence performance. Furthermore, as a byproduct of the proposed design method, the disturbance observer-based PFT control for high-order nonlinear systems is also shown to be possible. To the best of the authors’ knowledge, it is the first PFT control result for high-order nonlinear systems with external disturbances. Finally, an application example of a single-link robot system with disturbances and a numerical example are presented to demonstrate the effectiveness of the proposed scheme, respectively. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fuzzy controller is constructed to address the finite-time tracking control problem for a class of strict-feedback nonlinear systems, where the full state constraints are strictly required in the systems. Backstepping design with a tan-type barrier Lyapunov function is proposed. Meanwhile, fuzzy logic systems are used to approximate the unknown nonlinear functions. The addressed control scheme guarantees that the output is followed the reference signals within a bounded error, and all the signals in the closed-loop system are bounded. The simulation results demonstrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]