A stability criterion for a class of discrete nonlinear systems with random parameters

In this paper, discrete nonlinear models with random parameters are studied. A new frame to classify and analyze discrete stochastic nonlinear systems has been developed from deterministic nonlinear systems to stochastic nonlinear systems. This frame is broad and includes a large class of stochastic nonlinear systems. A stability criterion developed for this frame is a non-Lyapunov method of stability analysis and is easily applied. In addition, this derived sufficient condition of stability is obtained without the assumption of stationarity for the random noise as frequently assumed in the literature.     

Control of nonlinear systems with time-varying output constraints

This paper presents control design for strict feedback nonlinear systems with time-varying output constraints. An asymmetric time-varying Barrier Lyapunov Function (BLF) is employed to ensure constraint satisfaction. By allowing the barriers to vary with the desired trajectory in time, the initial condition requirements are relaxed. Through a change of tracking error coordinates, we eliminate the explicit dependence of the BLF on time, thereby simplifying the analysis of constraint satisfaction. We show that asymptotic output tracking is achieved without violation of the output constraint, and also quantify the transient performance bound as a function of time that converges to zero. To handle parametric model uncertainty, we present an adaptive controller that ensures constraint satisfaction during the transient phase of online parameter adaptation. The performance of the proposed control is illustrated through a simulation example.     

Adaptive variable structure control of MIMO nonlinear systems with time-varying delays and unknown dead-zones

In this paper, adaptive variable structure neural control is presented for a class of uncertain multi-input multi-output （MIMO） nonlinear systems with state time-varying delays and unknown nonlinear dead-zones. The unknown time-varying delay uncer- tainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The approach removes the assumption of linear function outside the deadband without necessarily constructing a dead-zone inverse as an added contribution. By utilizing the integral-type Lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded. In addition, a modified adaptive control algorithm is given in order to avoid the high-frequency chattering phenomenon. Simulation results demonstrate the effectiveness of the approach.     

Fuzzy adaptive output feedback control for a class of switched non-triangular structure nonlinear systems with time-varying delays

This paper investigates an adaptive fuzzy output feedback control design problem for switched nonlinear system in non-triangular structure form. The discussed system contains unknown nonlinear dynamics, unmeasured states and unknown time-varying delays under a batch of switching signals. Fuzzy logic systems are utilised to learn unknown nonlinear dynamics and construct a fuzzy switched nonlinear observer. By combining the property of fuzzy basis function with Lyapunov–Krasovskii functional and the command filter, a novel observer-based fuzzy adaptive backstepping schematic design algorithm is presented. Furthermore, the stability of the closed-loop control system is proved via Lyapunov stability theory and average dwell time method. The simulation results are presented to verify the validity of the proposed control scheme.     

Adaptive neural control for MIMO nonlinear systems with state time-varying delay

In this paper,adaptive neural control is proposed for a class of multi-input multi-output(MIMO)nonlinear unknown state time-varying delay systems in block-triangular control structure.Radial basis function(RBF)neural networks (NNs)are utilized to estimate the unknown continuous functions.The unknown time-varying delays are compensated for using integral-type Lyapunov-Krasovskii functionals in the design.The main advantage of our result not only efficiently avoids the controller singularity,but also relaxes the restriction on unknown virtual control coefficients.Boundedness of all the signals in the closed-loop of MIMO nonlinear systems is achieved,while The outputs of the systems are proven to converge to a small neighborhood of the desired trajectories.The feasibility is investigated by two simulation examples.     

Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay

This paper investigates output-feedback control for a class of stochastic high-order nonlinear systems with time-varying delay for the first time. By introducing the adding a power integrator technique in the stochastic systems and a rescaling transformation, and choosing an appropriate Lyapunov-Krasoviskii functional, an output-feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability and the output can be regulated to the origin almost surely. A simulation example is provided to show the effectiveness of the designed controller.     

Robust predictive extended state observer for a class of nonlinear systems with time-varying input delay

ABSTRACT

This paper deals with asymptotic stabilisation of a class of nonlinear input-delayed systems via dynamic output feedback in the presence of disturbances. The proposed strategy has the structure of an observer-based control law, in which the observer estimates and predicts both the plant state and the external disturbance. A nominal delay value is assumed to be known and stability conditions in terms of linear matrix inequalities are derived for fast-varying delay uncertainties. Asymptotic stability is achieved if the disturbance or the time delay is constant. The controller design problem is also addressed and a numerical example with an unstable system is provided to illustrate the usefulness of the proposed strategy.     

Simple stability criteria for nonlinear time-varying discrete systems

We present two sufficient conditions for asymptotic stability of nonlinear time-varying discrete systems. Our main results generalize Mori's result for linear discrete time-invariant systems to nonlinear time-varying systems.     

Self-tuning type variable structure control method for a class of nonlinear systems

In this paper we propose a new self-tuning type Variable Structure Control (VSC) method for a class of nonlinear dynamical systems with parametric uncertainties. The controller is designed to satisfy the sliding mode condition; mean-while the on-line parameter identification is incorporated in the control system. Necessary modifications are made for the parameter identification to avoid the control singularity problem. By virtue of the sliding mode, the proposed identification algorithm can be applied to those nonlinear systems which may not be linear in parametric space but are linear while in the sliding mode. A model-based strategy is further introduced to estimate the uncertainty bound. The new approach attains the gain scheduling property by tuning the switching gain in accordance with the estimated system uncertainties, that is, the switching gain decreases asymptotically while the sliding mode condition is still maintained. © 1998 John Wiley & Sons, Ltd.     

一类非线性系统的积分变结构模糊自适应跟踪控制

针对一类具有未知常数控制增益的不确定非线性系统,基于变结构控制原理,并利用具有非线性可调参数的模糊系统逼近等价控制,提出一种具有监督控制器的积分变结构模糊自适应跟踪控制策略.该策略通过监督控制器保证闭环系统所有信号有界.进一步,通过引入最优逼近误差的自适应补偿项来消除建模误差的影响.理论分析证明了跟踪误差能够收敛到零.仿真结果表明了该方法的有效性.     

Adaptive fuzzy output-feedback control for a class of nonlinear pure-feedback systems with time delays

This paper investigates observer-based adaptive fuzzy control for a class of delayed nonlinear systems in pure-feedback form. We first proposed a linear observer to get the estimation of the system's state. And then utilise fuzzy logic systems to model those nonlinearities. Further, adaptive fuzzy approach and backstepping technique are combined to develop the desired controller via Lyapunov analysis. The suggested adaptive fuzzy control scheme ensures that all the signals of the resulting nonlinear system converge to a small neighbourhood of the origin. Then a real simulation is used to illustrated the effectiveness of our results.     

Observers for discrete-time nonlinear systems

The problem of observers for discrete-time nonlinear systems has been considered and a simple, easy-to-implement algorithm is given whose convergence properties are guaranteed for autonomous and forced systems. Some numerical examples show the effectiveness of the proposed observer.     

一类由偏微分方程描述时滞随机系统的变结构控制

研究了一类由偏微分方程描述的Ito型时变时滞随机系统的变结构控制问题．首先构造了系统的滑动流形,设计了变结构控制律;然后证明T系统的滑动模具有次可达性,并且利用Halanay不等式的方法给出了系统滑动模运动为均方稳定运动的一个充分条件．     

Improved robust backstepping adaptive control for nonlinear discrete-time systems without overparameterization

This paper reports a robust backstepping adaptive controller for output tracking of nonlinear discrete-time systems. The result improves the previous one in Zhang, Wen, and Soh [(2001). Robust adaptive control for nonlinear discrete-time systems without overparameterization. Automatica, 37, 551-558] by removing the lower bound constraints on the system nonlinearities.     

非线性DEDS的标准结构

非线性DEDS是指由极大极小函数描述的系统, 常见于计算机科学、控制论、运筹学等领域, 考虑非自治非线性DEDS的结构问题, 通过引入白色图和凝白色图, 得到了系统能达和能观的两个充要条件以及系统的标准结构, 同时还给出了它们的矩阵表示.     

A sufficient condition for asymptotic stability for a class of time-varying parameterized systems

We derive sufficient conditions for local asymptotic stability for a class of parameterized time-varying systems, whose dynamics are in general unbounded in time. Our main result generalizes a well known limiting-dynamics based approach due to Peuteman and Aeyels (1999) in [9] for fast time-varying systems whose dynamics are bounded in time. Its proof is based on a new result providing a Lyapunov characterization for exponential stability.     

An adaptive variable structure control for a class of nonlinear systems

Motivated by the recent advance in adaptive output-feedback control for a class of nonlinear systems which can be transformed into the so-called output-feedback form [7,10,11], an adaptive structure controller is proposed in this paper to solve the nonlinear model reference adaptive control problem. It is shown that an asymptotic output tracking performance can be achieved for this class of nonlinear system even if some nonlinearity is not available or some unknown parameters are fast time-varying.     

具有时变状态滞后的非线性2-D 离散系统的稳定性与控制

考虑一类由局部状态空间Fornasini-Marchesini(FM LSS)第二模型描述的,具有时变状态滞后非线性二维(2-D)离散系统的稳定性分析和控制问题.时变状态滞后项的上、下界为正整数,非线性项满足Lipschitz条件.首先,通过引入一个含有时滞上、下界的新Lyapunov函数,给出了系统的稳定性准则;然后设计了状态反馈控制器以保证系统的稳定性,进而,状态反馈控制律可由线性矩阵不等式求得;最后通过数值算例表明了所得结果的有效性.