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.     

Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints

In this paper, adaptive tracking control is proposed for a class of uncertain multi-input and multi-output nonlinear systems with non-symmetric input constraints. The auxiliary design system is introduced to analyze the effect of input constraints, and its states are used to adaptive tracking control design. The spectral radius of the control coefficient matrix is used to relax the nonsingular assumption of the control coefficient matrix. Subsequently, the constrained adaptive control is presented, where command filters are adopted to implement the emulate of actuator physical constraints on the control law and virtual control laws and avoid the tedious analytic computations of time derivatives of virtual control laws in the backstepping procedure. Under the proposed control techniques, the closed-loop semi-global uniformly ultimate bounded stability is achieved via Lyapunov synthesis. Finally, simulation studies are presented to illustrate the effectiveness of the proposed adaptive tracking control.     

控制增益符号未知的MIMO时滞系统自适应控制

针对一类带有死区模型并具有未知函数控制增益的不确定MIMO非线性时滞系统,基于滑模控制原理和Nussbaum函数的性质,提出了一种稳定的自适应神经网络控制方案.该方案放宽了对函数控制增益上界为未知常数的假设,并通过使用Lyapunov-Krasovskii泛函抵消了因未知时变时滞带来的系统不确定性.理论分析证明,闭环系统是半全局一致终结有界.仿真结果表明了该方法的有效性.     

具有输入齿隙的一类非线性不确定系统自适应鲁棒控制

针对一类具有未知输入齿隙、参数不确定以及未建模动态和干扰的非线性系统,设计了自适应鲁棒控制器.将齿隙非线性模型等价表示为具有有界建模误差的全局线性化模型,在此基础上设计了包含自适应模型补偿、反馈稳定和鲁棒反馈3部分的自适应鲁棒控制器,并给出了系统动态跟踪误差和稳态误差指标.理论分析证明,闭环控制系统信号有界且跟踪误差在任意期望的精度范围内,仿真研究验证了所提出方法的有效性.     

Adaptive control of a class of slowly time-varying plants

An adaptive control system of the type considered earlier by the author, which is designed to be stable under the assumption that the unknown plant parameters are constant, is shown to maintain stability when the plant parameters are slowly time varying.     

Adaptive neural network predictive control for nonlinear pure feedback systems with input delay

This paper presents an adaptive neural control design for nonlinear pure-feedback systems with an input time-delay. Novel state variables and the corresponding transform are introduced, such that the state-feedback control of a pure-feedback system can be viewed as the output-feedback control of a canonical system. An adaptive predictor incorporated with a high-order neural network (HONN) observer is proposed to obtain the future system states predictions, which are used in the control design to circumvent the input delay and nonlinearities. The proposed predictor, observer and controller are all online implemented without iterative predictive calculations, and the closed-loop system stability is guaranteed. The conventional backstepping design and analysis for pure-feedback systems are avoided, which renders the developed scheme simpler in its synthesis and application. Practical guidelines on the control implementation and the parameter design are provided. Simulation on a continuous stirred tank reactor (CSTR) and practical experiments on a three-tank liquid level process control system are included to verify the reliability and effectiveness.     

Set-based adaptive estimation for a class of nonlinear systems with time-varying parameters

In this paper, an adaptive estimation technique is proposed for the estimation of time-varying parameters for a class of continuous-time nonlinear system. A set-based adaptive estimation is used to estimate the time-varying parameters along with an uncertainty set. The proposed method is such that the uncertainty set update is guaranteed to contain the true value of the parameters. Unlike existing techniques that rely on the use of polynomial approximations of the time-varying behaviour of the parameters, the proposed technique does require a functional representation of the time-varying behaviour of the parameter estimates. A simulation example and a building systems estimation example are considered to illustrate the developed procedure and ascertain the theoretical results.     

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...     

An LPV approach to the robust control of a class of quasi-linear propagation processes

In this paper the trajectory tracking control problem for a certain class of propagation processes modeled as quasi-linear parameter varying systems is considered. The propagation physical models are generally described by means of partial differential equations (PDEs). However in real world control problems the PDE models are usually converted into ordinary differential equations (ODEs) models adopting numerical and/or physical approximations. In many practical problems it happens that the propagation dynamics are linear, while the boundary conditions are described by nonlinear algebraic equations. A trajectory following control scheme is proposed for this class of systems together with a robust performance analysis based on the concept of quadratic stability with an H_∞ norm bound. An LMI based observer synthesis procedure is also proposed to increase the closed loop system performance.     

基于观测器的非线性时变时滞系统自适应重复控制

针对一类未知时变时滞非线性系统,提出一种基于观测器的重复控制方案．采用线性矩阵不等式设计非线性观测器,所设计的控制律含有ＰＩＤ 反馈项,常值参数自适应律是微分差分型的,时变参数学习律是差分型的．在假设未知时变时滞、时变参数和参考输出的周期有已知的最小公倍数下,通过构造一个Ｌｙaｐｕｎｏｖ-Ｋｒａｓｏｖｓｋｉｉ型复合能量函数,证明了所有闭环信号有界且输出跟踪误差收敛．仿真实例表明了算法的有效性．     

Global observability of a class of nonlinear discrete time systems

It is shown that discrete time systems whose dynamics are governed by piecewise monotone maps of the interval are globally observable under a general class of observations. The results rest on the fact that the dynamics are ergodic.     

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.     

Truncated predictor feedback control for exponentially unstable linear systems with time-varying input delay

The stabilization of exponentially unstable linear systems with time-varying input delay is considered in this paper. We extend the truncated predictor feedback (TPF) design method, which was recently developed for systems with all poles on the closed left-half plane, to be applicable to exponentially unstable linear systems. Assuming that the time-varying delay is known and bounded, the design approach of a time-varying state feedback controller is developed based on the solution of a parametric Lyapunov equation. An explicit condition is derived for which the stability of the closed-loop system with the proposed controller is guaranteed. It is shown that, for the stability of the closed-loop system, the maximum allowable time-delay in the input is inversely proportional to the sum of the unstable poles in the plant. The effectiveness of the proposed method is demonstrated through numerical examples.     

一类非线性时滞过程的自适应控制

通过结合非线性过程的一般模型控制(GMC)、强跟踪预测器(STP)和强跟踪滤波器(SIF),提出了一类具有输入时滞非线性时变过程的自适应一般模型控制(AGMC)方法.基于强跟踪预测器对未来状态的预测,传统的一般模型控制被扩展到一类具有输入时滞的非线性过程.通过强跟踪滤波器估计非线性过程的时变参数,对STP和GMC进行在线参数修正.对三容水箱系统DTS200进行计算机仿真,仿真结果表明,该自适应控制策略是令人满意的,其状态跟踪能力强,对于模型失配也具有较强的鲁棒性.     

一类非线性系统的自适应预测函数控制

针对一类具有输出反馈耦合的离散非线性系统,将过程的非线性状态空间模型等效为线性时变状态空间模型;然后利用最小二乘法辨识系统参数,并通过在目标函数中引入系统状态的变化给出一种具有类似离散PI最优调节器结构的新型自适应预测函数控制器．由于引入了新的优化目标函数,该控制器控制效果与鲁棒性要优于仅考虑预测输出误差的传统预测函数控制器．仿真结果表明,该控制器优于经典离散PI最优调节器．     

Adaptive fuzzy dynamic surface control for a class of perturbed nonlinear time-varying delay systems with unknown dead-zone

In this paper,adaptive dynamic surface control(DSC) is developed for a class of nonlinear systems with unknown discrete and distributed time-varying delays and unknown dead-zone.Fuzzy logic systems are used to approximate the unknown nonlinear functions.Then,by combining the backstepping technique and the appropriate Lyapunov-Krasovskii functionals with the dynamic surface control approach,the adaptive fuzzy tracking controller is designed.Our development is able to eliminate the problem of "explosion of complexity" inherent in the existing backstepping-based methods.The main advantages of our approach include:1) for the n-th-order nonlinear systems,only one parameter needs to be adjusted online in the controller design procedure,which reduces the computation burden greatly.Moreover,the input of the dead-zone with only one adjusted parameter is much simpler than the ones in the existing results;2) the proposed control scheme does not need to know the time delays and their upper bounds.It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error is smaller than a prescribed error bound,Finally,simulation results demonstrate the effectiveness of the proposed approach.     

Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs

In this paper, adaptive neural control is proposed for a class of uncertain multi-input multi-output (MIMO) nonlinear state time-varying delay systems in a triangular control structure with unknown nonlinear dead-zones and gain signs. The design is based on the principle of sliding mode control and the use of Nussbaum-type functions in solving the problem of the completely unknown control directions. The unknown time-varying delays are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The approach removes the assumption of linear functions outside the deadband as an added contribution. By utilizing the integral 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. Simulation results demonstrate the effectiveness of the approach.     

Adaptive control of a class of nonlinear time-varying systems with multiple models

The adaptive control of nonlinear systems that are linear in the unknown but time-varying parameters are treated in this paper. Since satisfactory transient performance is an important factor, multiple models are required as these parameters change abruptly in the parameter space. In this paper we consider both the multiple models with switching and tuning methodology as well as multiple models with second level adaptation for this class of systems. We demonstrate that the latter approach is better than the former.     

Iterative learning control with Smith time delay compensator for batch processes

How to improve the control of batch processes is not an easy task because of modeling errors and time delays. In this work, novel iterative learning control (ILC) strategies, which can fully use previous batch control information and are attached to the existing control systems to improve tracking performance through repetition, are proposed for SISO processes which have uncertainties in modeling and time delays. The dynamics of the process are represented by transfer function plus pure time delay. The stability properties of the proposed strategies for batch processes in the presence of uncertainties in modeling and/or time delays are analyzed in the frequency domain. Sufficient conditions guaranteeing convergence of tracking error are stated and proven. Simulation and experimental examples demonstrating these methods are presented.