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.     

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.     

Robust adaptive control of nonlinear systems with unknown time delays

In this paper, robust adaptive control is presented for a class of parametric-strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties of unknown time delays are compensated for. Controller singularity problems are solved by employing practical robust control and regrouping unknown parameters. By using differentiable approximation, backstepping design can be carried out for a class of nonlinear systems in strict-feedback form. It is proved that the proposed systematic backstepping design method is able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.     

Neural adaptive control for a class of nonlinear systems with unknown deadzone

This paper focuses on the adaptive control of a class of nonlinear systems with unknown deadzone using neural networks. By constructing a deadzone pre-compensator, a neural adaptive control scheme is developed using backstepping design techniques. Transient performance is guaranteed and semi-globally uniformly ultimately bounded stability is obtained. Another feature of this scheme is that the neural networks reconstruction error bound is assumed to be unknown and can be estimated online. Simulation results are given to demonstrate the effectiveness of the proposed controller.     

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

Robust tracking control of uncertain nonlinear systems with unknown control directions

A global robust tracking control design procedure is proposed for a class of uncertain nonlinear systems. The key point is that the signs of multiplicative uncertainties, the so-called control directions, are not assumed to be known a priori. The class of systems can be of arbitrary dynamic order and the unmatched additive uncertainties need not satisfy the global Lipschitz condition. It is proved that under the proposed control, all closed-loop states are bounded and the tracking error converges to any prescribed small neighborhood of the origin. The results of this paper enlarge the class of uncertain nonlinear systems for which global robust tracking control can be designed.     

Robust adaptive output-feedback control for a class of nonlinear systems with general uncertainties

This paper investigates the robust adaptive output-feedback control for a class of nonlinear systems with general uncertainties and unknown parameters. First, a stable state observer is constructed and the system state is observed, and then the adaptive output-feedback controller is constructively designed for tracking the given reference signal. It is proven that the constructed controller is robust to the uncertainties of both the unknown parameters and the system states. These results show that the global stability of the resulting closed-loop systems has been guaranteed and the ε-tracking problem has been solved. Meanwhile, it is also proven that the tracking error tends to a ‘steady state’ at the negative exponential attenuating rate. Simulation examples show that the tracking effects of the designed adaptive control systems are good, and the control quantities used in the simulation examples are always within the range of the admissible control.     

Robust adaptive control of a class of nonlinear systems including actuator hysteresis with Prandtl-Ishlinskii presentations

This paper deals with robust adaptive control of a class of nonlinear systems preceded by unknown hysteresis nonlinearities. By using a Prandtl-Ishlinskii model with play and stop operators, we attempt to fuse the model of hysteresis with the available control techniques without necessarily constructing a hysteresis inverse. A robust adaptive control scheme is therefore proposed. The global stability of the adaptive system and tracking a desired trajectory to a certain precision are achieved. Simulation results attained for a nonlinear system are presented to illustrate and further validate the effectiveness of the proposed approach.     

Fuzzy adaptive robust backstepping stabilization for SISO nonlinear systems with unknown virtual control direction

In this paper, a direct fuzzy adaptive robust control approach is proposed for a class of SISO nonlinear systems with completely unknown virtual control directions, unknown nonlinearities, unmodeled dynamics and dynamic disturbances. In the backstepping recursive design, fuzzy logic systems are employed to approximate the combined nonlinear uncertainties, a dynamic signal and Nussbaum gain technique are introduced into the control scheme to dominate the dynamic uncertainties and solve the unknown signs of virtual control directions, respectively. It is proved that the proposed robust fuzzy adaptive scheme can guarantee the all signals in the closed-loop system are semi-globally uniformly ultimately bounded. The effectiveness of the proposed approach is illustrated via three examples.     

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.     

一类不确定非线性系统的鲁棒自适应轨迹线性化控制

针对一类不确定非线性系统,研究了一种新的鲁棒自适应轨迹线性化控制方案.利用径向基神经网络的在线逼近能力以及被控对象分析模型的有用信息设计一种径向基神经网络干扰观测器来估计系统中存在的不确定性.观测器输出用于设计补偿控制律抵消不确定性对系统性能的影响,鲁棒自适应控制律用于克服逼近误差.采用Lyapunov方法严格证明了在自适应调节律作用下闭环系统所有误差信号最终有界.最后利用倒立摆系统验证了新方法的有效性.     

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．     

Robust adaptive control of nonlinear non-minimum phase systems with uncertainties

This paper, presents a robust adaptive control method for a class of nonlinear non-minimum phase systems with uncertainties. The development of the control method comprises two steps. First, stabilization of the system is considered based on the availability of the output and internal dynamics of the system. The reference signal is designed to stabilize the internal dynamics with respect to the output tracking error. Moreover, a combined neuro-adaptive controller is proposed to guarantee asymptotic stability of the tracking error. Then, the overall stability is achieved using the small gain theorem. Next, the availability of internal dynamics is relaxed by using a linear error observer. The unmatched uncertainty is compensated using a suitable reference signal. The ultimate boundedness of the reconstruction error signals is analytically shown using an extension of the Lyapunov theory. The theoretical results are applied to a translational oscillator/rotational actuator model to illustrate the effectiveness of the proposed scheme.     

Robust discrete-time set-based adaptive predictive control for nonlinear systems

The problem of robust adaptive predictive control for a class of discrete-time nonlinear systems is considered. First, a parameter estimation technique, based on an uncertainty set estimation, is formulated. This technique is able to provide robust performance for nonlinear systems subject to exogenous variables. Second, an adaptive MPC is developed to use the uncertainty estimation in a framework of min–max robust control. A Lipschitz-based approach, which provides a conservative approximation for the min–max problem, is used to solve the control problem, retaining the computational complexity of nominal MPC formulations and the robustness of the min–max approach. Finally, the set-based estimation algorithm and the robust predictive controller are successfully applied in two case studies. The first one is the control of anonisothermal CSTR governed by the van de Vusse reaction. Concentration and temperature regulation is considered with the simultaneous estimation of the frequency (or pre-exponential) factors of the Arrhenius equation. In the second example, a biomedical model for chemotherapy control is simulated using control actions provided by the proposed algorithm. The methods for estimation and control were tested using different disturbances scenarios.     

Observer-based synergetic adaptive neural network control for a class of discrete-time nonlinear systems with dead-zone

In this paper, the observer-based synergetic adaptive neural network control method is designed for a class of discrete-time systems with dead-zone. A macro-variable is introduced by a synergetic approach to control theory and neural networks are utilised to estimate unmeasured states and unknown functions in the system. Furthermore, by employing an adaptive design procedure and Lyapunov stability theory, the closed-loop system stability is guaranteed, and the desired system performance is achieved simultaneously. Finally, some simulation results are given to prove the validity of the developed control method.     

Robust integral control for a class of nonlinear systems with unknown control coefficients

The robust integral control problem is studied for a class of nonlinear systems with input-to-state stable (ISS)unmodeled dynamics in this paper.It does not require a priori knowledge of the control coefficients.Combining the Nussbaum-type gain technique and the backstepping design,we propose a state feedback controller,which could achieve the global asymptotic tracking for any constant reference signal,irrespective of the unmeasured dynamic disturbance.It is shown that the proposed methodology further extends the existing robust nonlinear integral control results.Simulation results verify the correctness of the theoretical analysis.     

一类不确定非线性系统的鲁棒自适应控制

针对一类MIMO不确定非线性系统的输出跟踪问题, 基于自适应反步法和滑模控制为其设计了鲁棒自适应控制器. 模型包含3种不确定性: 1) 参数不确定性; 2) 输入增益的不确定性; 3) 代表系统未建模动态和干扰的不确定函数, 该函数有界. 以非完整移动机械臂的输出跟踪控制为目标, 对其进行仿真实验, 实验结果表明所提出的控制算法是正确有效的.     

A set-theoretic model reference adaptive control architecture with dead-zone effect

A new set-theoretic model reference adaptive control architecture with dead-zone effect is presented. The key feature of our approach utilizes a new generalized restricted potential function, where it not only provides a user-defined uncertain dynamical system performance but also has the capability to stop the adaptation when system errors are small (i.e., inside dead-zone) — a practice adopted in adaptive control applications. The stability of the proposed technique is analyzed through showing the boundedness of an energy function in all possible variations and its experimental validation is also given through an aerospace testbed.