A comparative study on time-delay estimation for time-delay nonlinear system control

The problem of adaptive output tracking is researched for a class of nonlinear network control systems with parameter uncertainties and time-delay. In this paper, a new program is proposed to design a state-feedback controller for this system. For time-delay and parameter uncertainties problems in network control systems, applying the backstepping recursive method, and using Young inequality to process the time-delay term of the systems, a robust adaptive output tracking controller is designed to achieve robust control over a class of nonlinear time-delay network control systems. According to Lyapunov stability theory, Barbalat lemma and Gronwall inequality, it is proved that the designed state feedback controller not only guarantees the state of systems is uniformly bounded, but also ensures the tracking error of the systems converges to a small neighborhood of the origin. Finally, a simulation example for nonlinear network control systems with parameter uncertainties and time-delay is given to illustrate the robust effectiveness of the designed state-feedback controller.

Six different time-delayed controllers are introduced within this article to explore their efficiencies in suppressing the nonlinear oscillations of a parametrically excited system. The applied control techniques are the linear and nonlinear versions of the position, velocity, and acceleration of the considered system. The time-delay of the closed-loop control system is included in the proposed model. As the model under consideration is a nonlinear time-delayed dynamical system, the multiple scales homotopy method is utilized to derive two nonlinear algebraic equations that govern the vibration amplitude and the corresponding phase angle of the controlled system. Based on the obtained algebraic equations, the stability charts of the loop-delays are plotted. The influence of both the control gains and loop-delays on the steady-state vibration amplitude is examined. The obtained results illustrated that the loop-delays can play a dominant role in either improving the control efficiency or destabilizing the controlled system. Accordingly, two simple objective functions are introduced in order to design the optimum values of the control gains and loop-delays in such a way that improves the controllers’ efficiency and increases the system robustness against instability. The efficiency of the proposed six controllers in mitigating the system vibrations is compared. It is found that the cubic-acceleration feedback controller is the most efficient in suppressing the system vibrations, while the cubic-velocity feedback controller is the best in bifurcation control when the loop-delay is neglected. However, the analytical and numerical investigations confirmed that the cubic-acceleration controller is the best either in vibration suppression or bifurcation control when the optimal time-delay is considered. It is worth mentioning that this may be the first article that has been dedicated to introducing an objective function to optimize the control gains and loop-delays of nonlinear time-delayed feedback controllers.

In this chapter, optimal state feedback control problems of nonlinear systems with time delays are studied. In general, the optimal control for time-delay systems is an infinite-dimensional control problem, which is very difficult to solve and there is presently no good method for dealing with this problem. In this chapter, the optimal state feedback control problems of nonlinear systems with time delays both in states and controls are investigated. By introducing a delay matrix function, the explicit expression of the optimal control function can be obtained. Next, for nonlinear time-delay systems with saturating actuators, we further study the optimal control problem using a nonquadratic functional, where two optimization processes are developed for searching the optimal solutions. The above two results are for the infinite-horizon optimal control problem. To the best of our knowledge, there are no results on the finite-horizon optimal control of nonlinear time-delay systems. Hence, in the last part of this chapter, a novel optimal control strategy is developed to solve the finite-horizon optimal control problem for a class of time-delay systems.KeywordsOptimal ControllerDiscrete Nonlinear Time-delay SystemFinite Horizon Optimal Control ProblemActuator SaturationInfinite Dimensional Control ProblemsThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The Hopf bifurcation in a time-delayed nonlinear closed-loop control system is studied, where the nonlinear system has a linear dynamic plant represented by a feedforward transfer function and a nonlinear feedback controller represented by a Taylor series about an equilibrium operating point. The time delays occurred in the system are contained not only in the linear plant but also in the nonlinear feedback controller. The effective harmonic balance method is modified and applied to calculating the amplitude and frequency of the periodic solution emerging from the Hopf bifurcation of the dynamic system. Some new formulas containing up to an eighth-order harmonic balance approximation are derived, and two interesting examples are analyzed using the new results.

Matrix pseudoinverses producing necessary and sufficient conditions for positive and nonnegative definiteness

Tracking control of nonlinear automobile idle-speed time-delay system via differential geometry approach

Optimal tuning of composite nonlinear feedback control in time-delay nonlinear systems

This article proposes a state feedback controller synthesis for nonlinear time-delay distributed control systems subjected to input saturation nonlinearity and disturbances. Nonlinear time-delay distributed control system individual states are without time-delay and the states coming from other subsystems have the communication link time-delay. The coupling states time-delay is presumed to be time-varying within a predefined bound. First, we suggest global state feedback controller design and then, we extend the proposed global design technique to more general local state feedback controller scheme by using an auxiliary region of attraction. Linear matrix inequality (LMI)-based solution is anticipated to synthesis global and local state feedback controller by using global and local sector bounded condition, Lyapunov–Krasovskii function, and Lipschitz condition. Which guarantee global and local asymptotic stability of the complete closed-loop system and $$ L_{2} $$ gain reduction of the mapping from $$ d_{p} (t) $$ to $$ z_{p} (t) $$ . Application results are presented to validate the benefits and effectiveness of the anticipated controller design schemes.

The structure of nonlinear time-delay control systems is analyzed thanks to a sequence of delay free extended systems. Each of these extended systems is viewed as an approximation of the original time-delay system. Whether the trajectories can be recovered via a suitable initialization of the extended system is argued as well.

Time Delay Control(TDC) is a robust nonlinear control scheme using Time Delay Estimation(TDE) and also has a simple structure. To apply TDC to a real system, we must design Time Delay Controller to guarantee stability. The earlier research stated sufficient stability condition of TDC for general plants. In that research, it was assumed that time delay is infinitely small. But, it is impossible to implement infinitely small time delay in a real system. So, in this research we propose a new sufficient stabil ity condition of TDC for general plants with finite time delay. And the simulation results indicate that the previous sufficient stability condition does not work even for small time delay, while our proposed condition works well.

Time-delay frequently occurs in many practical systems, such as chemical processes, manufacturing systems, long transmission lines, telecommunication and economic systems, etc. Since time-delay is a main source of instability and poor performance, the control problem of time-delay systems has received considerable attentions in literature, such as [1][9]. The design approaches adopt in these literatures can be divided into the delaydependent method [1]-[5] and the delay-independent method [6]-[9]. The delay-dependent method needs an exactly known delay, but the delay-independent method does not. In other words, the delay-independent method is more suitable for practical applications. Nevertheless, most literatures focus on linear time-delay systems due to the fact that the stability analysis developed in the two methods is usually based on linear matrix inequality techniques [10]. To deal with nonlinear time-delay systems, the Takagi-Sugeno (TS) fuzzy model-based approaches [11]-[12] extend the results of controlling linear time-delay systems to more general cases. In addition, some sliding-mode control (SMC) schemes have been applied to uncertain nonlinear time-delay systems in [13]-[15]. However, these SMC schemes still exist some limits as follows: i) specific form of the dynamical model and uncertainties [13]-[14]; ii) an exactly known delay time [15]; and iii) a complex gain design [13]-[15]. From the above, we are motivated to further improve SMC for nonlinear timedelay systems in the presence of matched and unmatched uncertainties. The fuzzy control and the neural network control have attractive features to keep the systems insensitive to the uncertainties, such that these two methods are usually used as a tool in control engineering. In the fuzzy control, the TS fuzzy model [16]-[18] provides an efficient and effective way to represent uncertain nonlinear systems and renders to some straightforward research based on linear control theory [11]-[12], [16]. On the other hand, the neural network has good capabilities in function approximation which is an indirect compensation of uncertainties. Recently, many fuzzy neural network (FNN) articles are proposed by combining the fuzzy concept and the configuration of neural network, e.g., [19]-[23]. There, the fuzzy logic system is constructed from a collection of fuzzy If-Then rules while the training algorithm adjusts adaptable parameters. Nevertheless, few results using FNN are proposed for time-delay nonlinear systems due to a large computational load and a vast amount of feedback data, for example, see [22]-[23]. Moreover, the training algorithm is difficultly found for time-delay systems.

A event-based control problem is studied for a class of time-delayed nonlinear systems where partial state feedback and output feedback are considered respectively. The existence of unmeasurable states and time-delayed states may deteriorate the performance of the event-triggered system. An event trigger is designed with introducing a new variable to threshold function. It can be guaranteed that a positive value exists as the lower bound of the sampling intervals. What’s more, the globally asymptotic stabilization can be guaranteed under the nonlinear time-delay small-gain theorem by appropriately choosing the gains of measurable states and the estimator variable to the sampling error. Finally, the method is applied to a time-delayed nonlinear output-feedback control system to illustrate its effectiveness.

Stability of large scale measure and time-delay control systems with impulsive solutions which have not been studied up to now is presented and taken into account. By means of lumped Picard iteration method which avoids the difficulties of constructing Lyapunov function, the explicit algebraic criteria of the stability for nonlinear large scale measure and time-delay control systems are obtained.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In the space of system parameters, the closedform stability chart is determined for the delayed Mathieu equation defined as (t)(cost)x(t) bx(t2). This stability chart makes the connection between t...

On intermittent control of time delay system with actuator saturation