Controlling and synchronizing spatiotemporal chaos of the coupled Bragg acousto-optical bistable map system using nonlinear feedback

In this paper we present the control and synchronization of a coupled Bragg acousto-optic bistable map system using nonlinear feedback technology. This nonlinear feedback technology is useful to control a temporally chaotic system as well as a spatiotemporally chaotic system. It can be extended to synchronize the spatiotemporal chaos. It can work in a wide range of the controlled and synchronized signals, so it can decrease the sensitivity down to a noise level. The synchronization can be obtained by the analysis of the largest conditional Lyapunov exponent spectrum, and easily implemented in practical systems just by adjusting the coupled strength without any pre-knowledge of the dynamic system required.

Synchronization between two different chaotic systems with nonlinear feedback control

This paper presents chaos synchronization between two different chaotic systems by using a nonlinear controller, in which the nonlinear functions of the system are used as a nonlinear feedback term. The feedback controller is designed on the basis of stability theory, and the area of feedback gain is determined. The artificial simulation results show that this control method is commendably effective and feasible.

Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov expo- nents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k are studied. An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium. Furthermore, a circuit is designed to realize this new hyperchaotic system by electronic workbench （EWB）. Numerical simulations are presented to show these results.

Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.

Control algorithm of YUPENG ship autopilot based on tangent function nonlinear feedback

Autopilot is an important navigation instrument,and it plays an important role in safe navigation In order to further improve the performance of the autopilot,this paper adopts the first-order closed loop gain shaping algorithm(PID)to designautopilot control algo rithm with robustness and uses tangent function nonlinear feedback technology to replace the linear feedback to improve the energy saving effect of autopilot.Taking Dalian Maritime University’s newly-built YUPENG ship as anexample,the simulation research is carried out.The results show that the control effect is still satisfactory when the model parameterschange by25%,which suggests that the designed autopilot algorithm has good robustness.Compared with linearfeedback,nonlinear feedback can save7.9%of energy.The algo rithm proposed in this paper is simple and has obvious physicalmeaning.At the same time,the control algorithm is also helpful for the localization of controller design

Composite nonlinear feedback control for output regulation problem of linear discrete-time systems with input saturation

Transient performance for output regulation problems of linear discrete-time systems with input saturation is addressed by using the composite nonlinear feedback（CNF） control technique. The regulator is designed to be an additive combination of a linear regulator part and a nonlinear feedback part. The linear regulator part solves the regulation problem independently which produces a quick output response but large oscillations. The nonlinear feedback part with well-tuned parameters is introduced to improve the transient performance by smoothing the oscillatory convergence. It is shown that the introduction of the nonlinear feedback part does not change the solvability conditions of the linear discrete-time output regulation problem. The effectiveness of transient improvement is illustrated by a numeric example.

Application of composite nonlinear feedback control approach to linear and nonlinear systems

The objective of this research is to realize a composite nonlinear feedback control approach for a class of linear and nonlinear systems with parallel-distributed compensation along with sliding mode control technique.The proposed composite nonlinear feedback control approach consists of two parts.In a word,the first part provides the stability of the closed-loop system and the fast convergence response,as long as the second one improves transient response.In this research,the genetic algorithm in line with the fuzzy logic is designed to calculate constant controller coefficients and optimize the control effort.The effectiveness of the proposed design is demonstrated by servo position control system and inverted pendulum system with DC motor simulation results.

Tracking controller for robot manipulators viac omposite nonlinear feedback law

A composite nonlinear feedback tracking controller for motion control of robot manipulators is described. The structure of the controller is composed of a composite nonlinear feedback law plus full robot nonlinear dynamics compensation. The stability is carried out in the presence of friction. The controller takes advantage of varying damping ratios induced by the composite nonlinear feedback control, so the transient performance of the closed-loop is remarkably improved. Simulation results demonstrate the feasibility of the proposed method.

Parameterized design of nonlinear feedback controllers for servo positioning systems

To achieve fast, smooth and accurate set point tracking in servo positioning systems, a parameterized design of nonlinear feedback controllers is presented, based on a so-called composite nonlinear feedback （CNF） control technique. The controller designed here consists of a linear feedback part and a nonlinear part. The linear part is responsible for stability and fast response of the closed-loop system. The nonlinear part serves to increase the damping ratio of closed-loop poles as the controlled output approaches the target reference. The CNF control brings together the good points of both the small and the large damping ratio cases, by continuously scheduling the damping ratio of the dominant closed-loop poles and thus has the capability for superior transient performance, i.e. a fast output response with low overshoot. In the presence of constant disturbances, an integral action is included so as to remove the static bias. An explicitly parameterized controller is derived for servo positioning systems characterized by second-order model. Practical application in a micro hard disk drive servo system is then presented, together with some discussion of the rationale and characteristics of such design. Simulation and experimental results demonstrate the effectiveness of this control design methodology.

ABSOLUTE STABILITY OF CONTROL SYSTEM WITH MULTI-NONLINEAR FEEDBACK TERMS

In this paper, the absolute stability of control systems with multi nonlinear feedback terms are studied. The sufficient and necessary conditions of absolute stability are obtained. Some applied sufficient conditions of absolute stability are given.

Adaptive fuzzy compensation based composite nonlinear feedback controller design for robot manipulators

In order to suppress the influence of uncertain factors on robot system and enable an uncertain robot system to track the reference input accurately,a strategy of combining composite nonlinear feedback(CNF)control and adaptive fuzzy control is studied,and a robot CNF controller based on adaptive fuzzy compensation is proposed.The key of this strategy is to use adaptive fuzzy control to approach the uncertainty of the system online,as the compensation term of the CNF controller,and make full use of the advantages of the two control methods to reduce the influence of uncertain factors on the performance of the system.The convergence of the closed-loop system is proved by feedback linearization and Lyapunov theory.The final simulation results confirm the effectiveness of this plan.

Output regulation of singular linear systems with input saturation by composite nonlinear feedback control

Composite nonlinear feedback （CNF） control techniquefor tracking control problems is extended to the output regulationproblem of singular linear systems with input saturation. A statefeedback CNF control law and an output feedback CNF controllaw are constructed respectively for the output regulation problemof singular linear systems with input saturation. It is shown thatthe output regulation problem by CNF control is solvable underthe same solvability conditions of the output regulation problemby linear control. However, with the virtue of the CNF control, thetransient performance of the closed-loop system can be improvedby carefully designing the linear part and the nonlinear part of theCNF control law. The design procedure and the improvement ofthe transient performance of the closed-loop system are illustratedwith a numerical simulation.

Improved Composite Nonlinear Feedback Control for Robot Manipulators

External disturbances or inaccurate mathematical model built will inevitably impose a disadvantageous effect on the robot system,which generates positioning errors,vibrations,as well as weakening control performances of the system. The strategy of combining adaptive radial basis function( RBF) neural network control and composite nonlinear feedback( CNF) control is studied,and a robot CNF controller based on RBF neural network compensation is proposed. The core is to use RBF neural network control to approach the uncertainty of the system online,as the compensation term of the CNF controller,and make full use of the advantages of the two control methods to reduce the influence of uncertain factors on the performance of the system. The convergence of closed-loop system is proved. Simulation results demonstrate the effectiveness of this strategy.

Observer-Based Nonlinear Feedback Controls for Heartbeat ECG Tracking Systems

The analysis and design of observed-based nonlinear control of a heartbeat tracking system is investigated in this paper. Two of Zeeman’s heartbeat models are investigated and modified by adding the control input as a pacemaker, thereby creating the control-affine nonlinear system models that capture the general heartbeat behavior of the human heart. The control objective is to force the output of the heartbeat models to track and generate a synthetic electrocardiogram (ECG) signal based on the actual patient reference data, obtained from the William Beaumont Hospitals, Michigan, and the PhysioNet database. The formulations of the proposed heartbeat tracking control systems consist of two phases: analysis and synthesis. In the analysis phase, nonlinear controls based on input-output feedback linearization are considered. This approach simplifies the difficult task of developing nonlinear controls. In the synthesis phase, observer-based controls are employed, where the unmeasured state variables are estimated for practical implementations. These observer-based nonlinear feedback control schemes may be used as a control strategy in electronic pacemakers. In addition, they could be used in a software-based approach to generate a synthetic ECG signal to assess the effectiveness of diagnostic ECG signal processing devices.

Linearization of Multi-Valued Nonlinear Feedback Shift Registers

Nonlinear feedback shift registers(NFSRs) have been used in many stream ciphers for cryptographic security. The linearization of NFSRs is to describe their state transitions using some matrices. Such matrices are called their state transition matrices. Compared to extensive work on binary NFSRs, much less work has been done on multi-valued NFSRs. This paper uses a semi-tensor product approach to investigate the linearization of multi-valued NFSRs, by viewing them as logical networks. A new state transition matrix is found for a multi-valued NFSR, which can be simply computed from the truth table of its feedback function. The new state transition matrix is easier to compute and is more explicit than the existing results. Some properties of the state transition matrix are provided as well, which are helpful to theoretically analyze multi-valued NFSRs.

Integral sliding mode based optimal composite nonlinear feedback control for a class of systems

This paper presents an optimization method of designing the integral sliding mode （ISM） based composite nonlinear feedback （CNF） controller for a class of low order linear systems with input saturation. The optimal CNF control is first designed as a nominal control to yield high tracking speed and low overshoot. The selection of all the tuning parameters for the CNF control law is turned into a minimization problem and solved automatically by particle swarm optimization （PSO） algorithm. Subsequently, the discontinuous control law is introduced to reject matched disturbances. Then, the optimal ISM-CNF control law is achieved as the sum of the optimal CNF control law and the discontinuous control law. The effectiveness of the optimal ISM-CNF controller is verified by comparing with a step by step designed one. High tracking performance is achieved by applying the optimal ISM-CNF controller to the tracking control of the micromirror.

On observability of Galois nonlinear feedback shift registers over finite fields

Observability ensures that any two distinct initial states can be uniquely determined by their outputs,so the stream ciphers can avoid unobservable nonlinear feedback shift registers(NFSRs)to prevent the occurrence of equivalent keys.This paper discusses the observability of Galois NFSRs over finite fields.Galois NFSRs are treated as logical networks using the semi-tensor product.The vector form of the state transition matrix is introduced,by which a necessary and sufficient condition is proposed,as well as an algorithm for determining the observability of general Galois NFSRs.Moreover,a new observability matrix is defined,which can derive a matrix method with lower computation complexity.Furthermore,the observability of two special types of Galois NFSRs,a full-length Galois NFSR and a nonsingular Galois NFSR,is investigated.Two methods are proposed to determine the observability of these two special types of NFSRs,and some numerical examples are provided to support these results.

Absolute Stability of General Lurie Control Systems with Multi-Nonlinear Feedback Terms

In this paper, the problenl of absohlte stability for general Lurie control systems with multi- nonlinear feedback terms is investigated. From the Lyapunov function approach. new necessary and sufficient conditious and some practical sufficient conditions of absolute stability are derived. which improve the absolute stability for the set. A numerical examplc illustrates the effectiveness of the proposed results.

Composite nonlinear feedback control for cooperative output regulation of linear multi-agent systems by a distributed dynamic compensator

This paper investigates the cooperative output regulation problem of linear multi-agent systems with a linear exogenous system(exo-system).The network topology is described by a directed graph which contains a directed spanning tree with the exo-system as the root.Aiming at improving the transient performance of the multi-agent systems,a dynamic control law is developed by the composite nonlinear feedback(CNF)control technique.In particular,a distributed dynamic compensator independent of the interaction on the compensator states of agents among the network,is adopted.The solvability condition for the cooperative output regulation problem is obtained using the small-gain theory,which will not be destroyed by adding the nonlinear feedback part of the CNF control law.It is also shown that in the case with the exo-system not diverging exponentially,the small-gain condition can be guaranteed using the low-gain design.Finally,simulation results illustrate that the proposed CNF control law improves the transient performance for the cooperative output regulation of linear multi-agent systems.

Chaos and Nonlinear Feedback Control of the Arch Micro-Electro-Mechanical System

This paper addresses a nonlinear feedback control problem for the chaotic arch micro- electro-mechanical system with unknown parameters,immeasurable states and partial state-constraint subjected to the distributed electrostatic actuation.To reflect inherent properties and design controller, the phase diagrams,bifurcation diagram and Poincare section are presented to investigate the nonlinear dynamics.The authors employ a symmetric barrier Lyapunov function to prevent violation of constraint when the arch micro-electro-mechanical system faces some limits.An RBF neural network system integrating with an update law is adopted to estimate unknown function with arbitrarily small error. To eliminate chaotic oscillation,a neuro-adaptive backstepping control scheme fused with an extended state tracking differentiator and an observer is constructed to lower requirements on measured states and precise system model.Besides,introducing an extended state tracking differentiator avoids repeated derivative for the virtual control signal associated with conventional backstepping.Finally,simulation results are presented to illustrate feasibility of the proposed scheme.