Exponential Estimation of the Lyapunov Function for Delay-Coupled Neural Networks with Integral Terms

This paper investigates a class of coupled neural networks with delays and ad-dresses the exponential synchronization problem using delay-compensatory impulsive control. Razumikhin-type inequalities involving some destabilizing delayed impulse gains are proposed, along with a new delay-compensatory concept demonstrating two crucial roles in system stability. Based on the constructed inequalities and the introduced delay-compensatory concept, sufficient stability and synchronization criteria for globally exponential synchronization of coupled neural networks are provided. To address the exponential synchronization problem in coupled neural networks. Utilizing delay-compensatory impulsive control and Razumikhin-type inequalities. The Lyapunov function for coupled neural networks with delays and integral terms exhibits exponential estimates.

Delayed feedback control experiments on some flexible structures

In recent decades,studies on delayed system dynamics have attracted increasing attention and advances have been achieved in stability,nonlinearity,delay identification, delay elimination and application.However,most of the existing work is on the theoretical basis and little is on the experiment.This paper presents our experimental studies on delayed feedback control conducted in recent years with the focus on the discussion of a DSP-based delayed experiment system.Some phenomena in our delay experiments are discussed and a few topics of interest for further research are brought forward.

Time delay control of hydraulic manipulators with continuous nonsingular terminal sliding mode

For the position tracking control of hydraulic manipulators,a novel method of time delay control(TDC) with continuous nonsingular terminal sliding mode(CNTSM) was proposed in this work.Complex dynamics of the hydraulic manipulator is approximately canceled by time delay estimation(TDE),which means the proposed method is model-free and no prior knowledge of the dynamics is required.Moreover,the CNTSM term with a fast-TSM-type reaching law ensures fast convergence and high-precision tracking control performance under heavy lumped uncertainties.Despite its considerable robustness against lumped uncertainties,the proposed control scheme is continuous and chattering-free and no pressure sensors are required in practical applications.Theoretical analysis and experimental results show that faster and higher-precision position tracking performance is achieved compared with the traditional CNTSM-based TDC method using boundary layers.

Bursting-like motion induced by time-varying delay in an internet congestion control model

Time delay is an problem of intemet congestion important parameter in the control. According to some researches, time delay is not always constant and can be viewed as a periodic function of time for some cases. In this work, an internet congestion control model is consid- ered to study the time-varying delay induced bursting-like motion, which consists of a rapid oscillation burst and quies- cent steady state. Then, for the system with periodic delay of small amplitude and low frequency, the method of multiple scales is employed to obtain the amplitude of the oscillation. Based on the expression of the asymptotic solution, it can be found that the relative length of the steady state increases with amplitude of the variation of time delay and decreases with frequency of the variation of time delay. Finally, an effective method to control the bursting-like motion is pro- posed by introducing a periodic gain parameter with appropriate amplitude. Theoretical results are in agreement with that from numerical method.

A survey on delayed feedback control of chaos

This paper introduces the basic idea and provides the mathematical formulation of the delayed feedback control （DFC） methodology, which has been widely used in chaos control. Stability analysis including the well-known odd number linfitation of the DFC is reviewed. Some new developments in characterizing the limitation of the DFC are presented. Various modified DFC methods, which are developed in order to overcome the odd number limitation, are also described. Finally, some open problems in this research field are discussed.

Identification and PID Control for a Class of Delay Fractional-order Systems

In this paper, a new model identification method is developed for a class of delay fractional-order system based on the process step response. Four characteristic functions are defined to characterize the features of the normalized fractional-order model. Based on the time scaling technology, two identification schemes are proposed for parameters U+02BC estimation. The scheme one utilizes three exact points on the step response of the process to calculate model parameters directly. The other scheme employs optimal searching method to adjust the fractional order for the best model identification. The proposed two identification schemes are both applicable to any stable complex process, such as higher-order, under-damped U+002F over-damped, and minimum-phase U+002F nonminimum-phase processes. Furthermore, an optimal PID tuning method is proposed for the delay fractional-order systems. The requirements on the stability margins and the negative feedback are cast as real part constraints U+0028 RPC U+0029 and imaginary part constraints U+0028 IPC U+0029. The constraints are implemented by trigonometric inequalities on the phase variable, and the optimal PID controller is obtained by the minimization of the integral of time absolute error U+0028 ITAE U+0029 index. Identification and control of a Titanium billet heating process is given for the illustration. © 2014 Chinese Association of Automation.

Stability analysis and design of fuzzy control system with bounded uncertain delays

Fuzzy control problems for systems with bounded uncertain delays were studied. Based on Lyapunov stability theory and matrix theory, a nonlinear state feedback fuzzy controller was designed by linear matrix inequalities （LMI） approach, and the global exponential stability of the closed-loop system was strictly proved. For a fuzzy control system with bounded uncertain delays, under the global exponential stability condition which is reduced to p linear matrix inequalities, the controller guarantees stability performances of state variables. Finally, the simulation shows the validity of the method in tiffs paper.

H_∞ Synchronization of Chaotic Systems via Delayed Feedback Control

The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are synchronized with a guaranteed H∞ performance. Based on the Lyapunov stability theory, a delay-dependent condition is derived and formulated in the form of linear matrix inequality （LMI）. A numerical simulation is also presented to validate the effectiveness of the developed theoretical results.

A new wide area damping controller design method considering signal transmission delay to damp interarea oscillations in power system

Wide area damping controller(WADC) is usually utilized to damp interarea low frequency oscillation in power system. However, conventional WADC design method neglects the influence of signal transmission delay and damping performance of WADC designed by the conventional method may deteriorate or even has no effect when signal transmission delay is beyond delay margin, an index that denotes delay endurance degree of power system. Therefore, a new design method for WADC under the condition of expected damping factor and required signal transmission delay is presented in this work. An improved delay margin with less conservatism is derived by adopting a new Lyapunov-Krasovskii function and more compact bounding technique on the derivative of Lyapunov-Krasovskii functional. The improved delay margin, which constructs the correlation of damping factor and signal transmission delay, can be used to design WADC. WADC designed by the proposed method can ensure that power system satisfies expected damping factor when WADC input signal is delayed within delay margin. Satisfactory test results demonstrate the effectiveness of the proposed method.

Input-to-state stability of Euler-Maruyama method for stochastic delay control systems

This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical methods is established.The conditions of the exact and EM method for an SDCS with the property of mean-square exp-ISS are obtained without involving control Lyapunov functions or functional.Under the global Lipschitz coefficients and mean-square continuous measurable inputs,it is proved that the mean-square exp-ISS of an SDCS holds if and only if that of the EM method is preserved for a sufficiently small step size.The proposed results are evaluated by using numerical experiments to show their effectiveness.

A multi-objective optimal PID control for a nonlinear system with time delay

It is generally difficult to design feedback controls of nonlinear systems with time delay to meet time domain specifications such as rise time, overshoot, and tracking error. Furthermore, these time domain specifications tend to be conflicting to each other to make the control design even more challenging. This paper presents a cell mapping method for multi-objective optimal feedback control design in time domain for a nonlinear Duffing system with time delay. We first review the multi-objective optimization problem and its formulation for control design. We then introduce the cell mapping method and a hybrid algorithm for global optimal solutions. Numerical simulations of the PID control are presented to show the features of the multi-objective optimal design. @ 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi：10.1063/2.1306306]

Adaptive sliding mode control of modular self-reconfigurable spacecraft with time-delay estimation

The reconstruction control of modular self-reconfigurable spacecraft (MSRS) is addressed using an adaptive sliding mode control (ASMC) scheme based on time-delay estimation (TDE) technology. In contrast to the ground, the base of the MSRS is floating when assembled in orbit, resulting in a strong dynamic coupling effect. A TED-based ASMC technique with exponential reaching law is designed to achieve high-precision coordinated control between the spacecraft base and the robotic arm. TDE technology is used by the controller to compensate for coupling terms and uncertainties, while ASMC can augment and improve TDE’s robustness. To suppress TDE errors and eliminate chattering, a new adaptive law is created to modify gain parameters online, ensuring quick dynamic response and high tracking accuracy. The Lyapunov approach shows that the tracking errors are uniformly ultimately bounded (UUB). Finally, the on-orbit assembly process of MSRS is simulated to validate the efficacy of the proposed control scheme. The simulation results show that the proposed control method can accurately complete the target module’s on-orbit assembly, with minimal perturbations to the spacecraft’s attitude. Meanwhile, it has a high level of robustness and can effectively eliminate chattering.

Exponential Synchronization of Master-Slave Lur'e Systems via Intermittent Time-Delay Feedback Control

This paper concerns with the master-slave exponential synchronization analysis for a class of general Lur'esystems with time delay.Different from the previous methods based on the differential inequality technique, a newapproach is proposed to derive some new exponential synchronization criteria.The restriction that the control widthhas to be larger than the time delay is removed.This leads to a larger application scope for our method.Moreover, notranscendental equation is involved in the obtained result, which reduces the computational burden.Two examples aregiven to validate the theoretical results.

Modified coupled map car-following model and its delayed feedback control scheme

A modified coupled map car-following model is proposed, in which two successive vehicle headways in front of the considering vehicle is incorporated into the optimal velocity function. The steady state under certain conditions is obtained. An error system around the steady state is studied further. Moreover, the condition for the state having no traffic jam is derived. A new control scheme is presented to suppress the traffic jam in the modified coupled map car-following model under the open boundary. A control signal including the velocity differences between the following and the considering vehicles, and between the preceding and the considering vehicles is used. The condition under which the traffic jam can be well suppressed is analysed. The results are compared with that presented by t^onishi et al. （the KKH model）. The simulation results show that the temporal behaviour obtained in our model is better than that in the KKH model. The simulation results are in good agreement with the theoretical analysis.

A Control Scheme Based on Online Delay Evaluation for a Class of Networked Control Systems

A control scheme that integrates control technology with communication technology to solve the delay problem is introduced for a class of networked control systems: Networked Half-Link Systems (NHLS). Concretely, we use the master-slave clock synchronization technology to evaluate the delays online, and then the LQ optimal control based on delays is adopted to stabilize the controlled plant. During the clock synchronization process, the error of evaluated delays is inevitably induced from the clock synchronization error, which will deteriorate the system performances, and even make system unstable in certain cases. Hence, the discussions about the clock error, and the related control analysis and design are also developed. Specifically, we present the sufficient conditions of controller parameters that guarantee the system stability, and a controller design method based on the error of delays is addressed thereafter. The experiments based on a CANbus platform are fulfilled, and the experimental results verify the previous analytic results finally.

THE OPTIMAL CONTROL OF DELAY CONTROL SYSTEMS WITH RESTRICTED STATE RIGHT ENDPOINT

In this paper, for the delay control system: (x) over dot (t)=f[x(t), x(t-1), u(t), t] t is an element of[t(0), t(1)] x(t)=psi(t) t is an element of[t(0), t(1)] with state right endpoint restricted by condition psi(k)[x(t(1))]=0 (k=1,2,..., l) a maximum principle is given. And as a specific example, this paper gives a maximum principle under the condition that partial stares right endpoints be completely fixed. Finally, this paper gives an example to explain the application of the main result of this paper. All the results are suitable for the control systems with multidelay as well.

CONTROLLABILITY OF DELAY DEGENERATE CONTROL SYSTEMS WITH INDEPENDENT SUBSYSTEMS

The controllability of delay degenerate differential control systems is discussed. Firstly, delay degenerate differential control system was transformed to be canonical form, and the connected terms were gotten rid of, had delay degenerate differential control systems with independent subsystems. For the general delay degenerate differnetial control systems, it was gotten that the necessary and sufficient condition of that they are controllable is that their reachable set is equal to the whole space. For the delay degenerate differential control systems with independent subsystems, it was gotten that the necessary and sufficient conditions of that they are controllable are that their reachable sets are equal to their corresponding subspaces. Then some algebra criteria were gotten. Finally, an example was given to illustrate the main results.

Discrete Quasi-Sliding Mode Tracking Controller with Time Delay Technique

Robust discrete quasi-sliding mode tracking controller is developed with discrete reaching law for trajectory tracking in the presence of modeling uncertainty and unknown disturbance. The conventional prior knowledge of uncertainty upper bounds being replaced by an on-line estimation used in the controller to cancel the slowly varying uncertainties by the mechanism of time delay. This method reduces the feedback gain substantially and improves tracking accuracy. The system behavior in the vicinity of the sliding surface is examined for the existence and bandwidth of quasi-sliding mode. Simulation results show the effectiveness of the strategy.

Orderly delay control technique for a new type of arthropod robot

The orderly delay control technique for a new type of arthropod robot is studied in this pa- per. The orderly delay controller is composed of three parts. The first part is a central pattern gener- ator （CPG） with periodical output. The second part is a neural pathway （NP） that generates the time delay characteristic of various gait patterns. The last part is a locomotion nerve center （ LNC ） that decides the frequency of the CPG output and generates orderly phase delay by changing the pa- rameters of NP. And then signals that fit for different gaits can be obtained through the regulation of LNC. Experiments are implemented with a robot following mathematical simulation of the controller. The experimental results show that various gait patterns can be realized successfully with the method proposed in this paper.

Experimental study of delayed positive feedback control for a flexible beam

Recently, some researches indicate that positive feedback can benefit the control if appropriate time delay is intentionally introduced into control system. However, most work is theoretical one but few are experimental. This paper presents theoretical and experimental studies of delayed positive feedback control technique using a flexible beam as research object. The positive feedback weighting coefficient is designed by using the optimal control method. The available time delay is determined by analyzing the maximal real part of characteristic roots of the system. A DSP-based experiment system is introduced. Simulation and experimental results indicate that the delayed positive feedback control may effectively reduce the beam vibration if time delay is appropriately selected.