Robust adaptive control for uncertain nonlinear systems with unknown control directions and actuator nonlinearity

A robust adaptive control scheme is proposed for a class of uncertain nonlinear systems in strict feedback form with both unknown control directions and non-symmetric dead-zone nonlinearity based on backstepping design.The conditions that the dead-zone slopes and the boundaries are equal and symmetric are removed by simplifying nonlinear dead-zone input model,the assumption that the priori knowledge of the control directions to be known is eliminated by utilizing Nussbaum-type gain technique and neural networks(NN) approximation capability.The possible controller singularity problem and the effect of dead-zone input nonlinearity are avoided perfectly by combining integral Lyapunov design with sliding mode control strategy.All the signals in the closed-loop system are guaranteed to be semi-globally uniformly ultimately bounded and the tracking error of the system is proven to be converged to a small neighborhood of the origin.Simulation results demonstrate the effectiveness of the proposed control scheme.     

Adaptive Iterative Learning Control for a Class of Nonlinear Time-varying Systems with Unknown Delays and Input Dead-zone

This paper presents an adaptive iterative learning control (AILC) scheme for a class of nonlinear systems with unknown time-varying delays and unknown input dead-zone. A novel nonlinear form of dead-zone nonlinearity is presented. The assumption of identical initial condition for iterative learning control (ILC) is removed by introducing boundary layer function. The uncertainties with time-varying delays are compensated for by using appropriate Lyapunov-Krasovskii functional and Young0s inequality. Radial basis function neural networks are used to model the time-varying uncertainties. The hyperbolic tangent function is employed to avoid the problem of singularity. According to the property of hyperbolic tangent function, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while keeping all the closedloop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.      

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.     

一类带死区输入的非线性不确定系统滑模自适应控制

研究一类参数不确定和带有未知死区的非线性系统滑模自适应控制问题。将死区分解为两部分,被控系统中有两类不确定性的系统参数,一类是常值的未知系统参数;另一类是时变的未知系统参数和部分未知的死区。采用滑模控制和自适应控制相结合的方式,第一类不确定性可以由自适应控制来处理,而第二类不确定性可以由滑模控制来处理,即滑模自适应控制器。为了消除滑模控制所带来的抖振,引入边界层。采用’Lyapunov函数证明了系统的稳定性。仿真实验表明方法的可行性。     

具有未知死区输入非线性系统的迭代学习控制

针对一类具有死区输入非线性系统,提出一种实现有限作业区间轨迹跟踪控制的神经网络迭代学习算法.基于Lyapunov-like方法设计学习控制器,回避了常规迭代学习控制中受控系统非线性特性需满足全局Lipschitz连续条件的要求.为处理输入死区,利用神经网络逼近这种强非线性特性;同时,通过对神经网络逼近误差界的估计并在控制器中设置补偿作用以消除其影响,从而提高系统的跟踪性能.     

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 neural practical fixed-time command filtered control for multi-input and multi-output nonlinear systems with dead zones input and unknown control direction

In this article, under the circumstance of dead zones input and unknown control direction, the adaptive practical fixed-time control strategy is presented for a general class of multi-input and multi-output (MIMO) nonlinear systems. The inherent explosion of computational complexity difficulty is eliminated by adopting a command filter technique and the universal approximation properties of radial basis function neural networks (RBFNNs) are applied to model the unknown nonlinear functions. The difficulties of the dynamic surface method and unknown directions can be handled by invoking error compensation mechanism and Nussbaum-type functions, respectively. The uniqueness of the presented control scheme is that the tracking system can achieve the fixed-time stability without relying on the boundedness of dead-zone parameters. The fixed-time convergence of the output tracking error and the semiglobally fixed-time stable of closed-loop system are assured via the developed adaptive fixed-time command filtered controller. Finally, a practical example is supplied to further validate the availability of the presented theoretic result.     

具有未知非线性死区的自适应模糊控制

基于滑模控制原理，利用模糊系统的逼近能力，提出一种自适应模糊控制方法．该方法提出一种简化非线性死区输入模型，取消了非线性死区输入模型的倾斜度相等以及死区边界对称的条件，还取消了非线性死区输入模型各种参数已知的条件．该方法通过引入逼近误差的自适应补偿项来消除建模误差和参数估计误差的影响．理论分析证明了闭环系统是半全局一致终结有界，跟踪误差收敛到零．仿真结果表明了该方案的有效性．     

Decentralized adaptive stabilization of interconnected nonlinear systems with unknown non-symmetric dead-zone inputs

The decentralized adaptive stabilization method is proposed for uncertain interconnected nonlinear systems with unknown non-symmetric dead-zone inputs. The class of systems considered in this paper consists of strict-feedback nonlinear subsystems with unknown non-symmetric dead-zone inputs which interact through their outputs. The unknown nonlinear interaction terms are assumed to be bounded by nonlinear functions with unknown parameters. For the simple controller design, the local controller for each subsystem is systematically derived based on the dynamic surface design technique, without constructing the dead-zone inverse and requiring the bound information of dead-zone parameters (slopes and break-points). All unknown parameters of interconnected nonlinear systems are compensated by the adaptive technique. From Lyapunov stability theorem, it is proved that all signals in the interconnected closed-loop system with decentralized adaptive controllers are semi-globally bounded. Simulation results for tripled inverted pendulums demonstrate the effectiveness of the proposed approach.     

Adaptive output control of uncertain nonlinear systems with non-symmetric dead-zone input

This paper deals with the adaptive output feedback control problem of a class of uncertain nonlinear systems with an unknown non-symmetric dead-zone nonlinearity. The nonlinear system considered here is dominated by a triangular system without zero dynamics satisfying polynomial growth in the unmeasurable states. An adaptive control scheme is developed without constructing the dead-zone inverse. The proposed adaptive control scheme requires only the information of bounds of the slopes and the breakpoint of dead-zone nonlinearity. The novelty of this paper is that a universal-type adaptive output feedback controller is numerically constructed by using a sum of squares (SOS) optimization algorithm, which ensures the boundedness of all the signals in the adaptive closed-loop without knowing the growth rate of the uncertainties. An example is presented to show the effectiveness of the proposed approach.     

带有死区输入和未建模动态的神经网络控制

针对一类具有死区非线性输入和未建模动态的非线性系统,提出一种自适应神经网络控制方法。该方法将后推技术和动态面技术结合,克服了计算复杂性问题,放宽了动态不确定性的假设,取消了神经网络逼近误差有界。借助中值定理和Young’s不等式,保证整个设计只需一个自适应参数,且控制增益只需存在一个上、下界。理论分析证明闭环系统所有信号半全局一致终结有界。仿真结果验证所提方案的有效性。     

Adaptive fuzzy control with smooth inverse for nonlinear systems preceded by non-symmetric dead-zone

In this study, the adaptive output feedback control problem of a class of nonlinear systems preceded by non-symmetric dead-zone is considered. To cope with the possible control signal chattering phenomenon which is caused by non-smooth dead-zone inverse, a new smooth inverse is proposed for non-symmetric dead-zone compensation. For the systematic design procedure of the adaptive fuzzy control algorithm, we combine the backstepping technique and small-gain approach. The Takagi–Sugeno fuzzy logic systems are used to approximate unknown system nonlinearities. The closed-loop stability is studied by using small gain theorem and the closed-loop system is proved to be semi-globally uniformly ultimately bounded. Simulation results indicate that, compared to the algorithm with the non-smooth inverse, the proposed control strategy can achieve better tracking performance and the chattering phenomenon can be avoided effectively.     

Adaptive neural control for pure-feedback nonlinear time-delay systems with unknown dead-zone: a Lyapunov-Razumikhin method

This paper addresses the problem of adaptive neural control for a class of uncertain pure-feedback nonlinear systems with multiple unknown state time-varying delays and unknown dead-zone. Based on a novel combination of the Razumikhin functional method, the backstepping technique and the neural network parameterization, an adaptive neural control scheme is developed for such systems. All closed-loop signals are shown to be semiglobally uniformly ultimately bounded, and the tracking error remains in a small neighborhood of the origin. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control schemes.     

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.     

Feedback-Linearization-Based Neural Adaptive Control for Unknown Nonaffine Nonlinear Discrete-Time Systems

A new feedback-linearization-based neural network (NN) adaptive control is proposed for unknown nonaffine nonlinear discrete-time systems. An equivalent model in affine-like form is first derived for the original nonaffine discrete-time systems as feedback linearization methods cannot be implemented for such systems. Then, feedback linearization adaptive control is implemented based on the affine-like equivalent model identified with neural networks. Pretraining is not required and the weights of the neural networks used in adaptive control are directly updated online based on the input–output measurement. The dead-zone technique is used to remove the requirement of persistence excitation during the adaptation. With the proposed neural network adaptive control, stability and performance of the closed-loop system are rigorously established. Illustrated examples are provided to validate the theoretical findings.      

Robust adaptive control of strict-feedback nonlinear systems with unmodelled dynamics and time-varying delays

This paper presents a novel robust adaptive neural control scheme which can be taken as a robustification of the adaptive backstepping design. The considered class of uncertainties contains unknown non-symmetric dead-zone inputs, time-varying delay uncertainties, unknown dynamic disturbances and unmodelled dynamics. The radial basis function neural networks (RBFNNs) are employed to approximate the unknown nonlinear functions obtained by Young’s inequality. By constructing exponential Lyapunov-Krasovskii functionals, the upper bound functions of the time-varying delay uncertainties are compensated for. Using Young’s inequality and RBFNNs, the assumptions with respect to unmodelled dynamics are relaxed. It is demonstrated that the proposed controller guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error eventually converges to a neighbourhood of zero.     

Adaptive fuzzy control for pure-feedback stochastic nonlinear systems with unknown dead-zone input

This paper is concerned with the problem of adaptive fuzzy output tracking control for a class of nonlinear pure-feedback stochastic systems with unknown dead-zone. Fuzzy logic systems in Mamdani type are used to approximate the unknown nonlinearities, then a novel adaptive fuzzy tracking controller is designed by using backstepping technique. The control scheme is systematically derived without requiring any information on the boundedness of dead-zone parameters (slopes and break-points) and the repeated differentiation of the virtual control signals. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded in probability and the system output eventually converges to a small neighbourhood of the desired reference signal in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the proposed control scheme.     

带有摄动死区输入的未知非线性系统自适应模糊控制

用自适应模糊控制来实现对带有摄动死区输入的一类未知非线性系统的控制. 文中给出了一种新的死区执行器模型, 该模型含有时变并且摄动的执行增益. 通过将死区非线性分解为一个线性类似项, 一个非线性项和一个扰动类似项降低了扰动类似项的上界, 从而可以用更小的控制力度来实现系统的鲁棒性. 利用反步后推技术与非线性参数化的模糊逼近器结合导出控制器, 该设计取消了模糊基函数须事先已知的限制. 本文不仅从理论上证明了所给控制器能够保证闭环系统的稳定性和预期的跟踪性能, 还用仿真实验验证了控制器的有效性.     

一类MIMO非线性时滞系统的鲁棒自适应控制

针对一类具有非线性输入的MIMO时变时滞系统,基于变结构控制原理,提出了一种稳定自适应控制器设计的新方案.该方案通过使用Lyapunov-Krasovskii(L-K)泛函抵消了因未知时变时滞带来的系统不确定性;进一步,利用Young's不等式和参数自适应估计取消了非线性死区输入模犁和不确定项假设中各种参数均为已知的要求.通过理论分析,证明了闭环控制系统半全局一致终结有界,跟踪误差收敛到零的一个邻域内.