Discontinuous Feedback Control Research Articles

A stochastic rumor spreading model with event-triggered discontinuous feedback control in multilingual online networks

A stochastic rumor spreading model with event-triggered discontinuous feedback control in multilingual online networks

Finite-Time Stabilization of Inertial Memristive Neural Networks via Nonreduced Order Method.

This article investigates the finite-time stabilization problem of inertial memristive neural networks (IMNNs) with bounded and unbounded time-varying delays, respectively. To simplify the theoretical derivation, the nonreduced order method is utilized for constructing appropriate comparison functions and designing a discontinuous state feedback controller. Then, based on the controller, the state of IMNNs can directly converge to 0 in finite time. Several criteria for finite-time stabilization of IMNNs are obtained and the setting time is estimated. Compared with previous studies, the requirement of differentiability of time delay is eliminated. Finally, numerical examples illustrate the usefulness of the analysis results in this article.

Finite-Time Synchronization of Neural Networks With Infinite Discrete Time-Varying Delays and Discontinuous Activations.

This article investigates finite-time synchronization of neural networks (NNs) with infinite discrete time-varying delays and discontinuous activations (DDNNs). By virtue of theory of differential inclusions, comparison strategies, and inequality techniques, finite-time synchronization of the underlying DDNNs can be developed via a discontinuous state feedback control law, and the synchronous settling time can be estimated. The delayed state feedback controller and finite-time stability theorem are not employed during the analysis. As a special case, finite-time synchronization of NNs with bounded delays and discontinuous activations is given. Finally, two examples are provided to illustrate the validity of the theories.

Drive-Response Synchronization for Second-Order Memristor-Based Delayed Neural Networks with Settling Time Estimation via Discontinuous Feedback Control

In this paper, the settling time estimation of synchronization issues for inertial memristive neural networks (IMNNs) with mixed time-varying delays is investigated. First, by using a new reduced order approach and introducing free-weighted coefficients η i and ξ i into variable transformation, the original second-order derivative system is transformed into a first-order differential system. Second, appropriate controllers are designed for IMNNs to guarantee the system synchronization in a settling time. In addition, the settling time is explicitly estimated and dependent on time delays and the initial values of the coupled system. Finally, two numerical examples are presented to demonstrate the effectiveness of the theoretical results.

Finite/fixed-time synchronization control of fuzzy inertial cellular neural networks with mixed delays

In this paper, the finite-time (FT) and fixed-time synchronization (F-TS) problems of fuzzy inertial cellular neural networks (FICNNs) with mixed delays are discussed based on the Filippov solution theory and FT stability theory. Compared with related research, this paper considers the fuzzy inertial system combined with discontinuous activation of cellular neural networks (CNNs) for the first time. Then, by choosing appropriate variable transformation, the original system can be rewritten as a first-order differential system. Some novel and useful sufficient conditions for finite/fixed-time synchronization of FICNNs are established by applying three suitable discontinuous state feedback controllers. Finally, three numerical simulations are presented to elaborate the validity of the proposed methods.

A survey on High-Order Sliding-Mode control design using Lyapunov functions

A survey of (some) recent Lyapunov-based methods to analyze and design High-Order Sliding-Mode (HOSM) controllers and observers is presented. This overview includes also some novel algorithms, taking advantage of a discontinuous integral action, to attain a High-Order Sliding-Mode using a continuous control signal. This account starts presenting the design based on Lyapunov functions of classical sliding-mode controllers using a discontinuous state feedback control law to impose a high-order sliding-mode of arbitrary order. In order to estimate in finite-time the required derivatives of the measured signals for the implementation of the controllers, a Lyapunov-based design of the well-known robust and exact differentiator is shown. As a mechanism to reduce the effect of the undesirable chattering effect a recent method for higher-order sliding-mode controllers has been developed, using a continuous state feedback in conjunction with a discontinuous integral action to enforce a sliding-mode by means of a continuous control signal. The analysis and design tool for this integral controller is also an explicit, strict and particularly tailored Lyapunov function. In order to make this recount accessible to a wide audience the presentation is restricted to the main results, without giving proofs or design details, and leaving aside the rigorous mathematical machinery. For this the main references are provided.

Design of Super Twisting Integral Sliding Mode Control for Industrial Robot Manipulator

In the present work, integral sliding mode based continuous control algorithm is extended to multi input multi output system. The typical integral sliding mode control (ISMC) contains nominal control with discontinuous feedback control due to which overall control becomes discontinuous in nature. The proposed controller is a fusion of two continuous terms and one of which is able to handle, estimate and reject the disturbance successfully. A proposed robust ISMC technique is applied for industrial robot manipulators which utilizes interactive manipulation activity. Here, robust position tracking control obtained via ISMC principle for two link IRM scheme influenced by parametric uncertainties and external disturbances. The proposed ISMC design replaces the discontinuous part by continuous control, which super twisting control is able to handle the disturbance rejection completely. The effectiveness of the proposed control technique is tested under uncertain conditions and comparison study with other controllers has been done. The simulation result shows that the tracking error is effectively minimized by the proposed technique in presence of uncertain conditions.

Finite-Time Stabilization of Competitive Neural Networks With Time-Varying Delays.

This article investigates finite-time stabilization of competitive neural networks with discrete time-varying delays (DCNNs). By virtue of comparison strategies and inequality techniques, finite-time stabilization of the underlying DCNNs is analyzed by designing a discontinuous state feedback controller, which simplifies the controller design and proof processes of some existing results. Meanwhile, global exponential stabilization of the DCNNs is provided under a continuous state feedback controller. In addition, global exponential stability of the DCNNs is shown as an M-matrix, which contains some published outcomes as special cases. Finally, three examples are given to illuminate the validity of the theories.

Globally stable proportional‐integral‐derivative control for spacecraft pose tracking via dual quaternions

Due to the high reliability and simple adjustment, proportional-integral-derivative (PID) control is widely used in practical systems. However, intrinsic non-linearity of the pose dynamics hinders the design of a PID pose controller. Besides, topological constraints on the rigid body configuration space SE(3) prevent a continuous or a memoryless discontinuous state feedback control from achieving robust global stability. For these two issues, this paper develops a dual quaternion-based hybrid PID pose tracking control strategy, where the newly introduced integral term can compensate for constant disturbances, and the hysteretic switching-based hybrid feedback can avoid both unwinding phenomenon and noise sensitivity caused by the topological constraints. In addition, by adjusting the hysteresis width, the proposed hybrid PID controller can also become a continuous or a discontinuous PID controller. The global asymptotic stability in the presence of constant disturbance forces and torques, and robustness to measurement noises are proven by the hybrid system stability theory. Numerical simulations for an earth-orbiting spacecraft pose tracking mission are conducted to illustrate and compare the performances of the proposed hybrid, continuous and discontinuous PID pose tracking control laws.

Fixed-Time Synchronization Control of Delayed Dynamical Complex Networks.

Fixed-time synchronization problem for delayed dynamical complex networks is explored in this paper. Compared with some correspondingly existed results, a few new results are obtained to guarantee fixed-time synchronization of delayed dynamical networks model. Moreover, by designing adaptive controller and discontinuous feedback controller, fixed-time synchronization can be realized through regulating the main control parameter. Additionally, a new theorem for fixed-time synchronization is used to reduce the conservatism of the existing work in terms of conditions and the estimate of synchronization time. In particular, we obtain some fixed-time synchronization criteria for a type of coupled delayed neural networks. Finally, the analysis and comparison of the proposed controllers are given to demonstrate the validness of the derived results from one numerical example.

Exponential input-to-state stabilization of an ODE cascaded with a reaction–diffusion equation subject to disturbances

This paper addresses the exponential input-to-state stabilization of an ODE cascaded with a reaction–diffusion equation subject to disturbances appearing in all channels. By applying the backstepping method and the sliding mode control approach, the discontinuous boundary feedback controller is designed to reject the matched disturbance and achieve the exponential input-to-state stability of the closed-loop system. The existence of generalized solution to the closed-loop system is obtained using the Galerkin approximation scheme. The effectiveness of the proposed controller is illustrated by some numerical simulations.

Effects of mixed time delays and D operators on fixed-time synchronization of discontinuous neutral-type neural networks

Abstract In this paper, the fixed-time synchronization analysis is addressed for a class of discontinuous neutral-type neural networks. The focus is mainly on the design of useful control laws such that the constructed error system converges to zero in a fixed time. The major difficulty is to cope with the discontinuous neuron activations, D operators, time-varying discrete, and distributed delays simultaneously. To accomplish the target, a new and effective framework is firstly established. By means of functional differential inclusions theory, inequality technique and Lyapunov–Krasovskii functional, novel discontinuous feedback controllers are designed and some new verifiable algebraic criteria are derived to design the control gains. In contrast to the existed results on the neutral-type neural networks, the theoretical results of this paper are more general and rigorous. Finally, numerical examples and simulations are presented to illustrate the correctness of the main results.

A switching-based state-scaling design for prescribed-time stabilization of nonholonomic systems with actuator dead-zones

Nonholonomic constraint is widespread in many aerospace applications such as space robots, artificial satellites, aircrafts etc. In this paper, the problem of global prescribed-time stabilization is addressed for a category of uncertain nonholonomic constraint systems (namely, nonholonomic systems for short) with actuator dead-zones. To deal with the obstacle that the presence of input dead-zone nonlinearities renders the traditional discontinuous feedback control technique inapplicable to nonholonomic systems, a novel switching-based state-scaling transformation (switching-based-SST) is introduced. This transformation can change the original predefined-time stabilization into the asymptotic stabilization of the transformed one. Under such new framework, a state feedback controller that achieves the prescribed-time convergence performance is developed by using the recursive idea. Finally, a practical application to a unicycle-type mobile robot is presented to confirm the validity of the proposed method.

Arbitrary Configuration Stabilization Control for Nonholonomic Vehicle With Input Saturation: A c-Nonholonomic Trajectory Approach

This article addresses the saturated stabilization control problem for nonholonomic vehicles with a novel c-nonholonomic trajectory approach on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{SE}(2)$</tex-math></inline-formula> , with applications to automatic parking. First, by defining the c-nonholonomic configuration, a c-nonholonomic trajectory is obtained, which provides a novel approach to design stabilization controller to reach an arbitrary configuration. Second, a global discontinuous time-invariant feedback controller with input saturation is proposed, which does not involve time signal information, and its convergence is illustrated by a Lyapunov function approach. Thereafter, the motion trajectory of the proposed controller is analyzed, and the application scenario in automatic parking with the approximate desired trajectory is demonstrated. Finally, the performance of the proposed controller is validated by both numerical simulations and experiments.

Global dissipativity and exponential synchronization of mixed time-varying delays neural networks with discontinuous activations

Abstract In this paper, the matters of dissipativity and synchronization for non-autonomous Hopfield neural networks with discontinuous activations are investigated. Firstly, under the framework of extending Filippov differential inclusion theory, several effective new criteria are derived. The global dissipativity of Filippov solution to neural networks is proved by using generalized Halanay inequality and matrix measure method. Secondly, the global exponential synchronization of the addressed network drive system and the response system is realized by utilizing inequality and some analysis techniques and designing the discontinuous state feedback controller. Finally, several numerical examples are given to verify the validity of the theoretical results.

Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

In this research work, the finite-time synchronization and adaptive finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks (FCDNNs) are investigated under two different control strategies. By utilizing differential inclusion theory, Filippov framework, suitable Lyapunov functional, and graph theory approach, several sufficient criteria based on discontinuous state feedback control protocol and discontinuous adaptive feedback control protocol are established for ensuring the finite-time synchronization and adaptive finite-time synchronization of FCDNNs. Finally, two numerical cases illustrate the efficiency of the proposed finite-time synchronization results.

Robust stabilization of competing species in the chemostat

This work addresses the problem of robust stabilization of the concentrations of two different species of living organisms, which compete for a single limiting substrate in a bioreactor. This stabilization is performed using discontinuous feedback control laws that ensure the coexistence of all species. The control laws are designed considering bounded parametric uncertainties on the kinetic rates.

Fixed-Time Synchronization of Delayed Fractional-Order Memristor-Based Fuzzy Cellular Neural Networks

In this article, we discussed the fixed-time synchronization of fractional-order memristor-based fuzzy cellular neural networks (FMFCNNs) with time-varying delays. Based on the differential inclusion theory and discontinuous state feedback control technique, some useful novel criteria of the fixed-time synchronization for FMFCNNs are derived by constructing appropriate Lyapunov function. The results in our paper improve and generalize current literature research results significantly. Finally, the effectiveness of our control schemes for the fixed-time synchronization is demonstrated through numerical simulations.

Fixed-Time Synchronization of Fuzzy Cellular Neural Networks With Time-Varying Delays and Discontinuous Activations

The present paper investigates the fixed-time synchronization for fuzzy cellular neural networks with time-varying delays and discontinuous activations. In the framework of differential inclusions, new and useful fixed-time synchronization criteria for the networks considered are established by utilizing the discontinuous state feedback control and constructing Lyapunov functionals, which significantly generalize and improve recent works in the literature. Numerical simulations are given to show the effectiveness of the fixed-time synchronization schemes.

Finite-time synchronization of delayed fractional-order heterogeneous complex networks

This paper is devoted to exploring the finite-time (FET) synchronization problem of time-varying delay fractional-order (FO) coupled heterogeneous complex networks (TFCHCNs) with external interference via a discontinuous feedback controller. Firstly, we propose a novel Lemma which is useful for discussing the FET stability and synchronization problem of FO systems. Secondly, based on the proposed Lemma, a discontinuous feedback controller is designed to guarantee the FET synchronization of TFCHCNs with external interference. Moreover, the upper bound of settling-time function is obtained. Finally, two simulation examples are provided to verify the practicability of our findings.