Bounded control of feedforward time‐delay systems with linearized systems consisting of chain of oscillators

For the global stabilization of a family of feedforward nonlinear time‐delay systems whose linearized systems consist of a chain of identical oscillators, a saturated feedback control is established based on a special canonical form. The proposed control laws use not only the current states but also the delayed states for feedback, which helps maintain the decoupling property in the recursive design. Moreover, explicit conditions guaranteeing the stability of the closed‐loop system are provided. When the nonlinear terms vanish and even the oscillators are distinct, a modified saturated feedback control can still be established for the corresponding global stabilization problem. Two numerical examples are given to illustrate the effectiveness of the proposed approaches.     

Global adaptive stabilization for high‐order uncertain time‐varying nonlinear systems with time‐delays

This paper focuses on the adaptive stabilization problem for a class of high‐order nonlinear systems with time‐varying uncertainties and unknown time‐delays. Time‐varying uncertain parameters are compensated by combining a function gain with traditional adaptive technique, and unknown multiple time‐delays are manipulated by the delicate choice of an appropriate Lyapunov function. With the help of homogeneous domination idea and recursive design, a continuous adaptive state‐feedback controller is designed to guarantee that resulting closed‐loop systems are globally uniformly stable and original system states converge to zero. The effectiveness of the proposed control scheme is illustrated by the stabilization of delayed neural network systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Decentralized stabilization of large-scale feedforward systems using saturated delayed controls

This paper investigates the problem of decentralized stabilization via saturated delayed feedback. First, a new class of saturated delayed feedback controllers is proposed for a class of single-input feedforward nonlinear systems. Then, this design scheme is generalized for the setting of decentralized feedforward systems using saturated time-delayed feedback. The stability analysis for the closed-loop decentralized systems is rather simple based on the proposed feedback structure.     

Observer based output feedback regulation of a class of feedforward nonlinear systems with uncertain input and state delays using adaptive gain

We consider a global regulation problem of a class of feedforward nonlinear systems with uncertain delays by output feedback. The considered system is a generalized feedforward time-delay nonlinear system in the sense that an additional uncertain constant delay exists in the main control input to the system and feedforward nonlinearity includes states and input which have uncertain time-varying delays. Moreover, when feedforward nonlinearity satisfies some restrictive condition, we extend our control problem to the case such that the delay in the main control input is also a time-varying delay. To globally regulate the considered system, we develop an output feedback controller whose gain-scaling factor involves an adaptive dynamic. Two examples are given for illustration.     

Global stabilization for a class of stochastic nonlinear systems with SISS‐like conditions and time delay

The global stabilization problem for a class of stochastic time‐delay nonlinear systems with stochastic‐input‐to‐state‐stable–like conditions is investigated. Different from the existing results, the nonlinear growing conditions are more general, and the existences of the state and input time delays make the work more challenging in the control design and stability analysis. By introducing an appropriate gain‐scaling method and using a homogeneous domain control strategy, a delay‐independent controller is constructed to ensure that the equilibrium at the origin of the closed‐loop system is globally asymptotically stable in probability. Examples are given to show the validness of the proposed method.     

Global stabilization via nested saturation function for high‐order feedforward nonlinear systems with unknown time‐varying delays

We consider the global stabilization problem for a class of high‐order feedforward time‐delay nonlinear systems. The nested saturation function method is inherently improved to develop a continuous controller, without the requirements on the memory of the past input and the prior information of the time‐varying delays. The proposed controller is less conservative in terms of the level of nonlinearities whose upper bounds include high‐order, low‐order, and linear terms. The design procedures are provided based on the sign function technique, the homogeneous domination idea, and the search of Lyapunov function. Finally, a simulation example is used to demonstrate the application of the obtained theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Asymptotic stabilization of high‐order feedforward systems with delays in the input

This paper deals with the state feedback controller design for a class of high‐order feedforward (upper‐triangular) nonlinear systems with delayed inputs. The uncertainties in the systems are assumed to be dominated by higher‐order nonlinearities multiplying by a constant growth rate. The designed controller, which is a continuous but not smooth feedback, could achieve global asymptotical stability. Based on the appropriate state transformation of time‐delay systems, the problem of controller design can be converted into the problem of finding a parameter, which can be obtained by appraising the nonlinear terms of the systems. The nonlinear systems considered here are more general than conventional feedforward systems and they could be viewed as generalized feedforward systems. Two examples are given to show the effectiveness of the proposed design procedure. Copyright © 2009 John Wiley & Sons, Ltd.     

Global stabilization of discrete‐time feedforward time‐delay systems by bounded controls

This paper studies the problem of global stabilization of a family of discrete‐time feedforward time‐delay systems with bounded controls. Two classes of nonlinear control laws are established based on a special canonical form of the considered system. The proposed control laws use not only the current states but also the delayed states for feedback and, moreover, contain some free parameters. These advantages can help to improve the transient performance of the closed‐loop system significantly. A practical example is given for illustration.     

Adaptive control for a class of nonlinear systems with time-varying delays in state and input

This paper is concerned with the adaptive stabilization problem of uncertain input delayed systems.A solution to this problem is given for a class of uncertain nonlinear systems with time-varying delays in both state and input.An adaptive asymptotically stabilizing controller,which can guarantee the stability of the closed-loop system and the convergence of the original system state,is designed by means of the Lyapunov-Krasovskii functional stability theory combined with linear matrix inequalities (LMIs) an...     

Memoryless State Feedback Controller Design for Time Delay Systems With Matched Uncertain Nonlinearities

The robust control problem for a class of uncertain time-delay systems is investigated. The systems include multiple time delays and uncertain nonlinear functions. To our best knowledge, no controller design method for the systems is reported in the literature except for sliding mode control (SMC). However, the sliding mode controller must use the delayed state of the system, so that the precise time delays have to be known, and also a large memory is needed for controller implementation. To overcome the shortcomings, we employ the backstepping method to design a memoryless state feedback controller. By constructing a novel Lyapunov-Krasovskii functional, we show that the resulting closed-loop system is asymptotically stable. Simulations are done to verify the effectiveness of the proposed method.     

带有输入和状态时滞的高阶非线性前馈系统的自适应控制

本文考虑了一类高阶不确定非线性前馈系统的自适应镇定问题.将高阶非线性进一步放宽到不仅允许状态时滞,而且还具有未知增长率.通过将自适应方法、动态增益控制方法和增加幂次积分器法结合,设计了一个状态反馈控制器.所设计的控制器保证了闭环系统的所有信号有界,平衡点全局稳定,并且原状态收敛到0.     

Aggressive Longitudinal Aircraft Path Tracking Using Nonlinear Control

We study the problem of converting a trajectory tracking controller to a path tracking controller for a nonlinear non-minimum phase longitudinal aircraft model. The solution of the trajectory tracking problem is based on the requirement that the aircraft follows a given time parameterized trajectory in inertial frame. In this paper we introduce an alternative nonlinear control design approach called path tracking control. The path tracking approach is based on designing a nonlinear state feedback controller that maintains a desired speed along a desired path with closed loop stability. This design approach is different from the trajectory tracking approach where aircraft speed and position are regulated along the desired path. The path tracking controller regulates the position errors transverse to the desired path but it does not regulate the position error along the desired path. First, a trajectory tracking controller, consisting of feedforward and static state feedback, is designed to guarantee uniform asymptotic trajectory tracking. The feedforward is determined by solving a stable noncausal inversion problem. Constant feedback gains are determined based on LQR with singular perturbation approach. A path tracking controller is then obtained from the trajectory tracking controller by introducing a suitable state projection.     

Global stabilization of stochastic high-order feedforward nonlinear systems with time-varying delay

In this paper, we consider the problem of global stabilization for a class of stochastic high-order feedforward nonlinear systems with time-varying delay. By introducing the homogeneous domination design method and constructing the appropriate Lyapunov–Krasovskii functional, a state feedback controller is constructed to drive the closed-loop system to be globally asymptotically stable in probability.     

惯性轮倒立摆的鲁棒镇定

用一个时滞状态反馈控制律镇定惯性轮倒立摆,不仅保证闭环系统全局渐近稳定,还允许闭环系统承受一定的时滞.将惯性轮倒立摆转化为存在高阶非线性的4维积分器链,然后设计一个明确规定了饱和度和时滞参数的饱和控制律.用简单方式证明了闭环的全局渐近稳定性.仿真表明设计是有效的.     

Stabilization by forwarding design for switched feedforward systems with unstable modes

The problem of global stabilization is investigated for a class of switched nonlinear feedforward systems in this paper where the solvability of the stabilization problem for individual subsystem is not assumed. Some sufficient condition for the stabilization problem to be solvable is derived for the first time by exploiting the multiple Lyapunov functions method and the forwarding technique. Also, we design a switching law and construct bounded state feedback controllers of subsystems explicitly by a recursive design algorithm to achieve global asymptotic stability. The provided technique permits removal of a common restriction in which all subsystems in switched nonlinear feedforward systems are globally asymptotically stable. Finally, a numerical example is provided to demonstrate the feasibility of the theoretical result. Copyright © 2017 John Wiley & Sons, Ltd.     

多变量非线性动态系统的全局稳定化控制器

对可化为Bymes-Isidori正规型的多变量非线性系统,仅利用线性组成部分的状态设计了全局稳定化控制器。引入了有限时间滑动模态的概念,其优点是线性部分的状态在有限时间内趋近于零。当非线性系统是最小相位时,所设计的控制器保证了系统的全局稳定性。     

Global sampled-data output feedback control for a class of feedforward nonlinear systems

This paper investigates the problem of global output feedback stabilization for a class of feedforward nonlinear systems via linear sampled-data control. To solve the problem, we first construct a linear sampled-data observer and controller. Then, a scaling gain is introduced into the proposed observer and controller. Finally, we use the sampled-data output feedback domination approach to find the explicit formula for choosing the scaling gain and the sampling period which renders the closed-loop system globally asymptotically stable. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.     

Finite‐time output feedback stabilization of nonlinear high‐order feedforward systems

This paper considers the global finite‐time output feedback stabilization of a class of nonlinear high‐order feedforward systems. By using the homogeneous domination method together with adding a power integrator method and overcoming several troublesome obstacles in the design and analysis, a global finite‐time output feedback controller with reduced‐order observer is recursively designed to globally finite‐time stabilize nonlinear high‐order feedforward systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Feedback stabilisation of time-delay nonlinear systems with continuous time-varying output function

This paper investigates the problem of global output feedback stabilisation for a class of uncertain nonlinear systems, where output function is time-varying and continuous, and multiple time delays exist in system state at the same time. A double-domination method is used to capture time-varying measurement error and delayed states. The control strategy is presented based on the choice of Lyapunov–Krasovskii functionals and the construction of a novel state observer without using the information on the output function and nonlinearities. A simulation example is given to show the efficiency of the proposed control scheme.     

一类非仿射非线性时滞系统的动态状态反馈镇定

本文讨论了一类非仿射非线性时滞系统的全局镇定问题.通过引入辅助积分系统和构造合适的LyapunovKrosovskii泛函,提出了一种基于反推法的时滞无关动态状态反馈控制器,所提控制方法无需时滞的任何先验知识.利用Lyapunov稳定性理论证明了该控制策略能够保证非仿射时滞系统状态渐近收敛于原点,且所有闭环信号全局有界.一个仿真实例进一步验证了所得控制方案的可行性与有效性.