Discontinuous Control Research Articles

Dynamic manipulation of graphene plasmonic skyrmions.

With the characteristics of ultrasmall, ultrafast, and topological protection, optical skyrmions are great prospects for applications in high intensity data stroage, high resolution microscopic imaging, and polarization sensing. Flexible control over the topology of optical skyrmions is required for practical implementation/application. At present, the manipulation of optical skyrmions usually relies upon the change of spatial structure, which results in a limited-tuning range and a discontinuous control in the parameter space. Here, we propose continuous manipulation of the graphene plasmon skyrmions based on the electrotunable properties of graphene. By changing the Fermi energy of one pair of the standing waves or the phase of incident light, one can achieve topological state transformation of graphene plasmon skyrmions, which is evident by the change of skyrmion number from 1 to 0.5. The direct manipulation of the graphene plasmon skyrmions is demonstrated by simulation results based on the finite element method. Our work suggests a feasible way to flexibly control the topology of an optical skyrmionic field, which can be used for novel integrated photonic devices in the future.

Design of improved direct torque control based on a five level torque controller and a new Sugeno-Takagi fuzzy super-twisting controller applied to an induction machine

This paper deals with the design and Hardware In Loop (HIL) verification of a novel intelligent Super-twisting Sliding Mode Speed Controller (STSMSC) based on a Sugeno-Takagi Fuzzy Logic System (STFLS) for an induction motor controlled by an improved Modified Direct Torque Control (MDTC) approach. Indeed, Conventional Super-twisting Sliding Mode Speed Controller (CSTSMSC) is chosen as an alternative solution for attenuating the chattering phenomenon brought on by the discontinuous control law of the First Order Sliding Mode Speed Control (FOSMSC) and maintaining its advantages like simplicity, robustness and accuracy. Moreover, the STSMSC is a type of a second order sliding mode control technique that needs only the information about the sliding surface, not its time derivative. However, the choice parameters of the CSTSMSC existing in the control law effects the tracking accuracy, the overshoot and the amplitude of the chattering. Therefore, an STSMSC based on an STFLS (STFLS-STSMSC) is proposed for online tuning of these parameters in transient and steady state operations. In fact, the STFLS is considered as an intelligent supervisor to adjust these parameter values according to the system state, which consequently provides excellent performance consisting in a higher robustness rate under disturbances and uncertainties, tracking with excellent accuracy and reduced chattering in steady state and transient operations. Numerous simulation and HIL co-simulation results are presented to demonstrate the effectiveness of the suggested STFLS-STSMSC based MDTC implemented on a Xilinx FPGA Zynq 7000 SoC ZC702.

Comparisons of Loss Reduction Techniques Based on Pulsewidth Modulation and Model Predictive Control for Three-Phase Voltage Source Inverters

Due to the lack of comparative studies between discontinuous pulse-width modulation and model predictive control methods for reducing switching losses in two-level three-phase voltage source inverter, a comparative analysis of a generalized discontinuous pulse-width modulation and two model predictive control approaches for reducing switching losses is studied in this paper. Both generalized discontinuous pulse-width modulation and two model predictive control approaches are described and conducted in the simulation and experiment. The output performance is obtained by these methods after conducting in various conditions, including switching frequency, output power, and load conditions. It is validated that the generalized discontinuous pulse-width modulation control scheme achieves a better control performance at steady-state, while two model predictive control schemes have better transient-state performance with a superior dynamic. Additionally, the generalized discontinuous pulse-width modulation approach achieves better reducing switching losses performance and has slightly higher efficiency than that of two model predictive control approaches.

Methods for Damping Payload Oscillations and Robust Control of an Overhead Crane Trolley Considering the Dynamics of the Electric Drive

The control plant is a trolley of a single-girder overhead crane designed to move a suspended payload along the span. Features of the plant: one control with two degrees of freedom, the uncertainty of mass-inertial characteristics, and the action of non-smooth uncontrolled disturbances. We consider the reduced dynamics of the DC motor in the mathematical model, where the power supply voltage of the armature circuit is a control. Here, parametric and external disturbances affecting the mechanical subsystem become unmatched (i.e., they act through different channels with control) and cannot be directly compensated. This paper considers two main problems, each of which uses S-shaped smooth sigmoid functions with saturation. The first problem is to design the trajectory of the trolley considering the design constraints on its velocity and acceleration. Tracking such a trajectory should ensure the smooth transfer of the payload in a given time and the damping of its oscillations. For this purpose, a reference trajectory has been developed in the form of the sum of a sigmoid function and an integral of the swing angle. The proposed solution is not inferior in the efficiency to existing analogs, while its implementation requires less computational costs. The second problem is to develop a robust tracking system. For this purpose, a procedure for block synthesis of discontinuous true control and sigmoid fictitious controls (local feedbacks) has been developed. The latter are smooth analogs of discontinuous control and make it possible to suppress unmatched disturbances with a given accuracy without identifying them. In contrast to standard linear local feedbacks, the boundness of sigmoid fictitious controls does not lead to a large overshoot of state variables, which is critical in the presence of design constraints. In addition, such fictitious controls are implemented in mechanical plants and do not contribute to the wear of the actuator, which inevitably occurs when discontinuous fictitious controls are used. We presented the results of numerical simulation and carried out a comparative analysis of closed-loop systems with various fictitious controls: linear, discontinuous, and sigmoid. The results of the numerical simulation demonstrated the effectiveness of the developed approach.

An Adaptive Continuous Approach to Consensus Tracking of Nonlinear Multiagent Systems With a Nonautonomous Leader

It is challenging and critical to achieve zero error consensus tracking in multiagent systems (MASs) with nonautonomous leaders (i.e., leaders with nonzero inputs). The traditional approach is to use discontinuous controllers which may cause a chattering phenomenon. How to achieve zero error consensus tracking via a chattering-free controller is still open. We propose a class of adaptive continuous controllers to achieve zero error consensus tracking for Lipschitz nonlinear MASs with a nonautonomous leader and directed communication topology. Unlike existing works that use discontinuous functions to eliminate the impacts of leaders’ inputs, we use a continuous function by introducing an exponential decay function into the denominator. First, we design a continuous controller with fixed coupling strengths and prove that zero error consensus tracking can be achieved if the coupling strengths are greater than some positive constants. Second, we design a continuous controller with dynamic coupling strengths under which fully distributed zero error consensus tracking can be achieved. Moreover, the case with undirected communication topology is studied. Finally, three examples are given to verify the theoretical results. Specifically, convergence results between the continuous controller here and that is developed via the boundary layer technique are compared. Compared with existing works, the designed adaptive continuous controllers here can not only achieve zero error consensus tracking but also is chattering free.

Finite-Time Stochastic Synchronization of Multiweighted Directed Complex Networks via Intermittent Control

In this paper, finite-time synchronization (FTS) is addressed for directed multiweighted complex networks (MWCNs) with stochastic perturbations via intermittent control. Different from the previous FTS of single-weight networks, FTS of directed MWCNs is considered by introducing the allowable deviation synchronization bound. In synchronization analysis, a novel Lyapunov function is constructed by selecting a vector where the Chebyshev distance between this vector and their corresponding vectors for coupling matrices satisfies the allowable deviation synchronization bound. Furthermore, continuous control is not realistic due to limited resources. Accordingly, by discontinuous intermittent control, some suitable criteria can be derived to achieve FTS of directed MWCNs with stochastic perturbations. Finally, examples show the validity of the provided theoretical results.

Discontinuous control for exponential synchronization of complex-valued stochastic multi-layer networks

This article is concerned with the exponential synchronization issue of complex-valued stochastic multi-layer networks (CVSMLNs) via two discontinuous control approaches. At first, a new network model of complex-valued multi-layer network is built by integrating stochastic disturbances, intra-layer and inter-layer couplings. Different from previous aperiodic intermittent control (APIC) approaches, under the framework of APIC, novel impulsive feedback control (IFC) (IFC is executed at the activation time of APIC) and universal adaptive feedback control (adaptive control gain is different in different layers) are both developed to realize the exponential synchronization of CVSMLNs. Subsequently, some simple sufficient criteria are derived by virtue of Lyapunov method, graph theory and complex generalized Itô’s formula. Ultimately, the theoretical results are used in a practical complex-valued neural network and the availability of the obtained results is verified by giving some numerical examples.

Predefined-time synchronization of fractional-order memristive competitive neural networks with time-varying delays

This article focuses on the predefined-time synchronization (PTS) of fractional-order memristive competitive neural networks (FMCNNs) with time-varying delays. According to the two-layer structural characteristics of CNNs, two kinds of distinctive discontinuous bilayer predefined-time control schemes with the fractional integrals are proposed: one is the double controllers based on piecewise Lyapunov function and the other is a controller with Lyapunov function and exponential function. Using the predefined-time stability theorems and applying fractional-order differential inequalities and other inequality techniques, some effective criteria are obtained to assure the PTS of two FMCNNs in terms of algebraic inequalities, which are very succinct and avert complicated calculations. Besides, the predefined time (PT) is set to an arbitrary positive parameter in these controllers and is entirely irrelevant to the initial values. Finally, two concrete examples are given to verify the theoretical results.

An Improved Finite-Time and Fixed-Time Stable Synchronization of Coupled Discontinuous Neural Networks.

This article focuses on the finite-time and fixed-time synchronization of a class of coupled discontinuous neural networks, which can be viewed as a combination of the Hindmarsh-Rose model and the Kuramoto model. To this end, under the framework of Filippov solution, a new finite-time and fixed-time stable theorem is established for nonlinear systems whose right-hand sides may be discontinuous. Moreover, the high-precise settling time is given. Furthermore, by designing a discontinuous control law and using the theory of differential inclusions, some new sufficient conditions are derived to guarantee the synchronization of the addressed coupled networks achieved within a finite-time or fixed-time. These interesting results can be seemed as the supplement and expansion of the previous references. Finally, the derived theoretical results are supported by examples with numerical simulations.

Discontinuous Speed Control of PMDC Motors with Chattering Attenuation

In most applications, electric drives are actuated using on/off devices due to their low cost and also due to the relatively high power consumption of the electric drives which make applying linear power amplifiers very costly. In this paper, the operation of PMDC motors under discontinuous control action is analyzed. In addition, to reduce chattering, boundary layer solution has been addressed. Both suggested control techniques have been applied to a PMDC motor model in a software simulation using MATLAB. The results show better performance of boundary layer technique due to the reduced chattering. Index Terms— PMDC Motor, Discontinuous Control, Boundary Layer.

Observer based fixed-time integral sliding mode tracking control for underactuated AUVs via an event-triggered mechanism

In this paper, a fixed-time control scheme is presented for trajectory tracking of underactuated autonomous underwater vehicles (AUVs) subject to external disturbances. An adaptive fixed-time disturbance observer (AFDO) is developed to estimate the external disturbances in fixed time without the prior knowledge of external disturbances. An event-triggered mechanism is introduced to save the bandwidth resources and reduce the communication burden. By synthesizing the developed AFDO and the event-triggered mechanism, an AFDO based event-triggered fixed-time integral sliding mode control (AFDO-EFISMC) scheme is proposed to force the AUV to track the reference trajectory in fixed time. With the aid of the developed AFDO, the gain of discontinuous control part of the designed control scheme is reduced, and therefore the control chattering is alleviated. Stability analysis is given to show that the designed AFDO-EFISMC scheme can make the tracking errors of the AUV converge to arbitrarily small neighborhood of the origin within a fixed-time independent of the initial conditions. The effectiveness of the proposed control scheme is proven by comparative numerical simulations.

Global Finite-Time Stabilization of Spacecraft Attitude With Disturbances via Continuous Nonlinear Controller

In this paper, a robust continuous controller is investigated to solve the global finite-time attitude stabilization problem of rigid spacecraft system subject to multiple disturbances. The system order is firstly increased by derivation and the derivative of the actual torque is regarded as the virtual control law to be designed. Then, a super-twisting differentiator is constructed to provide finite-time angular acceleration estimations. Finally, based on the estimated angular accelerations, a discontinuous set stabilization control law is designed as the virtual controller. The actual continuous controller is obtained by integrating the discontinuous one. Rigorous proof and stability analysis are presented based on Lyapunov analysis. Compared with most of the existing finite-time control approaches in spacecraft systems, the proposed continuous control scheme guarantees the finite-time set stability of the closed-loop system. Moreover, the system states can converge to the equilibria even in the presence of derivative-bounded disturbances. Simulation studies of the proposed controller are illustrated to demonstrate the strong disturbance rejection ability, fast convergence rate, and high steady-state precision.

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.

Filippov's Solution and Finite-Time Stability of Stochastic Systems for Discontinuous Control

In this paper, a suite of theoretic tools is provided for discontinuous control design and finite-time stability analysis of a class of stochastic differential systems. The notion of Filippov&#x0027;s solutions for stochastic differential systems is proposed, and the corresponding solution existence problem is explored. The classical It&#x00F4; differentiation formula is generalized for quasi-<inline-formula><tex-math notation="LaTeX">$C_{0}^{2}(\mathbb {R}^{n},\mathbb {R})$</tex-math></inline-formula>-class functions along Filippov&#x0027;s solutions of stochastic differential systems, and two involved set-valued stochastic integrals are introduced with a study on their properties. Some finite-time stability results of stochastic differential systems are revealed with Filippov&#x0027;s solutions, and one of them is applied to neural synchronization, together with case simulations.

Finite-Time Discontinuous Control of Nonholonomic Chained-Form Systems

A finite-time discontinuous control method is proposed for controlling nonholonomic chained-form systems. Through a general discontinuous coordinate transformation, the nonholonomic system is transformed into two decoupled subsystems that are independently stabilized with control laws. Sufficient conditions for the existence of decoupled subsystems and finite-time convergence of system states are given. Furthermore, the finite-time discontinuous control laws are proposed to ensure that the system states reach the equilibrium in a finite time. Simulation results are presented to demonstrate the effectiveness and advantages of the proposed approach.

Event‐triggered adaptive control based on integral sliding mode surface for a class of linear systems with matched disturbance

AbstractIn this paper, we propose an event‐triggered adaptive integral sliding mode control scheme for a class of linear systems with external disturbance. In this method, the controller is designed using a triggered‐state‐dependent integral sliding mode, which can ensure the robustness and avoid the shortcomings of traditional sliding mode arrival stage. The triggering mechanism utilizes a time‐varying trigger threshold instead of a traditional fixed threshold, which not only realizes the dynamic update of the control law, reduces the overhead of network communication but also ensures that the system trajectory enters the bounded area. The lower bound of inter event time guarantees the avoidance of the Zeno phenomenon. Next, in order to reduce the impact of high‐frequency chattering of the control signal effectively and allow the gain of the discontinuous control term to be adjusted automatically according to the rate of change of the disturbance, a dual‐layer nested adaptive gain scheme based on equivalent control is considered. This scheme does not require a priori boundedness of the disturbance and its rate of change. Through Lyapunov stability analysis, the event‐triggered adaptive sliding mode controller can make the system trajectory converge in finite time and ensure the robustness of the control. Finally, the simulation results verify the effectiveness and simplicity of this method.

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-time synchronization of fractional-order delayed memristive fuzzy neural networks

This paper deals with the finite-time synchronization (FTS) for a class of fractional-order memristive fuzzy neural networks (FOMFNNs) with leakage and transmission delays. Two types of discontinuous control schemes with leakage and transmission delays are designed: one is the state feedback control and the other is the fractional-order adaptive control. Based on differential inclusion theory and fractional-order differential inequalities, several new delay-independent algebraic conditions are derived to guarantee the FTS of drive-response FOMFNNs with leakage and transmission delays. Moreover, the estimation of the upper bound of the settling time for the FTS is given as well. Ultimately, two numerical examples with simulations are furnished to demonstrate the feasibility and availability of the theoretical results.

Discontinuous control in problem of disturbance reduction for a linear dynamical system

In the paper, we study the problem of active reduction of the influence of a disturbance on the output of a linear controlled system. The problem is investigated on infinite time intervals. We consider a system of linear differential equations under the action of an unknown disturbance and a control to be formed. Our goal is to design an algorithm for reducing the disturbance by means of an appropriate control on the basis of inaccurate measurements of all (or a part of) phase coordinates of the system. This algorithm should form a feedback control that would guarantee that the trajectory of the given system and the velocity of its changing track the trajectory and the velocity of its changing of some reference system. We present two algorithms for solving this problem. These algorithms forming piece‐wise constant controls are based on the combination of constructions of the theory of dynamical inversion and the theory of feedback control. They are stable with respect to informational noises and computational errors.

Using the Whale Optimization Algorithm to Solve the Optimal Reactive Power Dispatch Problem

The optimal reactive power dispatch (ORPD) is a complex, optimal non-meritorious control issue with continuous and discontinuous control variables. This article exhibits a whale optimization algorithm (WOA) motivated by the whale’s bubble-net hunting tactic to resolve ORPD. The intention is to comply with certain constraints to promote the voltage transmission quality by adequately altering the parameters. The WOA not only equalizes exploitation and exploration to maximize the overall performance and eliminate search stagnation but also has remarkable sustainability and robustness to accomplish superior convergence speed and computation accuracy. The WOA is contrasted with MFO, BA, GOA, GWO, MDWA, SMA, SPBO and SSA by diminishing the fitness value to highlight the superiority and stability. The experimental results reveal that WOA exhibits a superior convergence level and computation precision to accomplish the minimum active power loss and superior control variables.