Adaptive neural output feedback finite-time command filtered backstepping control for nonlinear systems with full-state constraints

In this paper, an adaptive neural finite-time control method via barrier Lyapunov function, command filtered backstepping, and output feedback is proposed to solve the tracking problem of uncertain high-order nonlinear systems with full-state constraints and input saturation. By utilizing the neural network (NN) to approximate unknown nonlinear functions, the finite-time command filters are used to filtering the virtual control signals and get the intermediate control signals in a finite time in the backstepping process. Because there are errors between the output of finite-time command filters and the virtual control signals, the error compensation signals are added to eliminate the influence of filtering errors. Based on the proposed control scheme, the states of the system can be constrained in the predetermined region, all signals in the system are bounded in finite time, and the tracking error can converge to the desired region in finite time. At last, a simulation example is given to show the effectiveness of the proposed control method.     

执行器有故障的多输入单输出系统的自适应输出反馈控制

对一类控制增益符号未知且执行器有故障的输出反馈多输入单输出非线性系统,提出了一种后推容错控制方案.该方案在系统状态不可量测的情况下,利用Nussbaum函数处理符号未知的常数增益,并通过构造K-滤波器来估计了系统不可量测的状态.在容错控制器设计过程中,引入变能量函数来处理利用虚拟控制律所无法抵消的部分.与现有研宄成果相比,放宽了未知增益需要上下界均为已知的假设条件.最后,通过选取合适的李雅普诺夫函数,证明了闭环系统所有信号半全局一致终结有界,且跟踪误差收敛到原点的一个小邻域内.仿真结果表明了所提控制方法的有效性.     

Adaptive backstepping output feedback control for SISO nonlinear system using fuzzy neural networks

In this paper, a new fuzzy-neural adaptive control approach is developed for a class of single-input and single-output （SISO） nonlinear systems with unmeasured states. Using fuzzy neural networks to approximate the unknown nonlinear functions, a fuzzy- neural adaptive observer is introduced for state estimation as well as system identification. Under the framework of the backstepping design, fuzzy-neural adaptive output feedback control is constructed recursively. It is proven that the proposed fuzzy adaptive control approach guarantees the global boundedness property for all the signals, driving the tracking error to a small neighbordhood of the origin. Simulation example is included to illustrate the effectiveness of the proposed approach.     

Adaptive output feedback control using fault compensation and fault estimation for linear system with actuator failure

The problem of linear systems subject to actuator faults（outage,loss of efectiveness and stuck）,parameter uncertainties and external disturbances is considered.An active fault compensation control law is designed which utilizes compensation in such a way that uncertainties,disturbances and the occurrence of actuator faults are account for.The main idea is designing a robust adaptive output feedback controller by automatically compensating the fault dynamics to render the close-loop stability.According to the information from the adaptive mechanism,the updating control law is derived such that all the parameters of the unknown input signal are bounded.Furthermore,a disturbance decoupled fault reconstruction scheme is presented to evaluate the severity of the fault and to indicate how fault accommodation should be implemented.The advantage of fault compensation is that the dynamics caused by faults can be accommodated online.The proposed design method is illustrated on a rocket fairing structural-acoustic model.     

带有海浪滤波器的船舶航向反步自适应输出反馈控制

针对复杂海况下船舶航向控制中的模型非线性、参数不确定和海浪扰动问题,提出了一种基于反步法的非线性自适应输出反馈控制算法.首先基于无源理论设计了一种状态观测器以实现海浪滤波和状态估计,这种观测器无需海浪扰动的方差信息从而减少了观测器参数数量.然后假定系统模型参数未知,基于反步法给出了非线性控制律和参数自适应律.利用Lyapunov理论证明了这种自适应输出反馈控制系统的稳定性.仿真结果表明本文所提控制器具有较好的控制性能,对不确定性模型参数具有良好的自适应性.     

Adaptive decentralized finite‐time output tracking control for MIMO interconnected nonlinear systems with output constraints and actuator faults

In this work, we present a novel adaptive decentralized finite‐time fault‐tolerant control algorithm for a class of multi‐input–multi‐output interconnected nonlinear systems with output constraint requirements for each vertex. The actuator for each system can be subject to unknown multiplicative and additive faults. Parametric system uncertainties that model the system dynamics for each vertex can be effectively dealt with by the proposed control scheme. The control input gain functions of the nonlinear systems can be not fully known and state dependent. Backstepping design with a tan‐type barrier Lyapunov function and a new structure of stabilizing function is presented. We show that under the proposed control scheme, with the use of graph theory, finite‐time convergence of the system output tracking error into a small set around zero is guaranteed for each vertex, while the time‐varying constraint requirement on the system output tracking error for each vertex will not be violated during operation. An illustrative example on 2 interacting 2‐degree‐of‐freedom robot manipulators is presented in the end to further demonstrate the effectiveness of the proposed control scheme.     

Robust output feedback control of polynomial growth nonlinear systems with measurement uncertainty

Even in the presence of uncertainty in both state and output equations, we prove that global asymptotic stabilization is still possible by output feedback for a family of uncertain nonlinear systems dominated by a triangular system with a polynomial output‐dependent growth rate. In contrast to the linear growth requirement in the recent work the nonlinear perturbations in this paper are allowed to satisfy a linear growth condition with a polynomial output‐dependent rate. To handle simultaneously the polynomial nonlinearities and unknown parameter in the system output, we propose a high‐gain estimator with a dynamic gain that is updated online through a Riccati‐type dynamic equation. Then, an estimator‐based controller is designed by a recursive algorithm that makes it possible to assign the controller gains step by step. The globally stabilizing output‐feedback controller developed in this paper is robust with respect to uncertainties in the system dynamics and output equations.     

Output‐feedback robust adaptive backstepping control for a class of multivariable nonlinear systems with guaranteed tracking performance

This paper is devoted to output‐feedback adaptive control for a class of multivariable nonlinear systems with both unknown parameters and unknown nonlinear functions. Under the Hurwitz condition for the high‐frequency gain matrix, a robust adaptive backstepping control scheme is proposed, which is able to guarantee the tracking performance and needs only one parameter to be updated online regardless of the system order and input–output dimension. To cope with the unknown nonlinear functions and improve the tracking performance, a kind of high‐gain K‐filters is introduced. It is proved that all signals of the closed‐loop system are globally uniformly bounded. Simulation results on coupled inverted double pendulums are presented to illustrate the effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

High-order sliding-mode observer based output feedback adaptive robust control of a launching platform with backstepping

A kind of launching platform driven by two permanent magnet synchronous motor (PMSM) motors which is used to launch kinetic load to hit the target, always faces strong parameter uncertainties and strong external disturbance such as the air current impulsion, which would degrade their tracking accuracy greatly. In this paper, an adaptive robust nonlinear controller is proposed for high-accuracy motion control of the launching platform, in which the adaption law is designed to estimate the unknown coupling coefficients of torque disturbance and feed-forward cancellation technique is used to compensate the coupling torque disturbance and some other constant disturbances. In addition, a nonlinear robust feedback term is designed to inhibit the influence of the parameter estimation error and the other model uncertainty to stabilise the closed-loop system. Considering that some system states are immeasurable due to cost-reduction, volume/weight limitations and structure restriction or heavy measurement noise is usually associated with the measurements, which may also deteriorate the achievable performance of full-state feedback controllers; a high-order sliding-mode observer is used to estimate the unmeasured system states, and it is synthesised with the adaptive robust controller via feed-forward cancellation method. The intermediary virtual control law and the final control law are derived by integrating the backstepping method. Furthermore, the controller theoretically guarantees a prescribed tracking transient performance and final tracking accuracy while achieving asymptotic tracking performance in the presence of parametric uncertainties only, which is very important for high-accuracy tracking control of launching platform. Extensive comparative experimental results are obtained to verify the high performance nature of the proposed control strategy.     

Observer‐based finite‐time output‐feedback controller for DC‐DC buck converters with unknown load variations

The output voltage regulation problem of a DC‐DC buck converter is investigated in this paper via an observer‐based finite‐time output‐feedback control approach. Considering the effects of unknown load variations and the case without current sensor, by using the technique of adding a power integrator and the idea of nonseparation principle, a finite‐time voltage regulation control algorithm via dynamic output feedback is designed. The main feature of the designed observer and controller does not need any load's information. Theoretically, it is proven that the output voltage can reach the desired voltage in a finite time under the proposed controller. The effectiveness of the proposed control method is illustrated by numerical simulations and experimental results.     

Adaptive finite‐time fault‐tolerant tracking control for a class of MIMO nonlinear systems with output constraints

In this work, we present a novel adaptive finite‐time fault‐tolerant control algorithm for a class of multi‐input multi‐output nonlinear systems with constraint requirement on the system output tracking error. Both parametric and nonparametric system uncertainties can be effectively dealt with by the proposed control scheme. The gain functions of the nonlinear systems under discussion, especially the control input gain function, can be not fully known and state‐dependent. Backstepping design with a tan‐type barrier Lyapunov function and a new structure of stabilizing function is presented. We show that under the proposed control scheme, finite‐time convergence of the output tracking error into a small set around zero is guaranteed, while the constraint requirement on the system output tracking error will not be violated during operation. An illustrative example on a robot manipulator model is presented in the end to further demonstrate the effectiveness of the proposed control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive output feedback tracking control of stochastic nonlinear systems with dynamic uncertainties

In this paper, adaptive output feedback tracking control is developed for a class of stochastic nonlinear systems with dynamic uncertainties and unmeasured states. Neural networks are used to approximate the unknown nonlinear functions. K‐filters are designed to estimate the unmeasured states. An available dynamic signal is introduced to dominate the unmodeled dynamics. By combining dynamic surface control technique with backstepping, the condition in which the approximation error is assumed to be bounded is avoided. Using It ô formula and Chebyshev's inequality, it is shown that all signals in the closed‐loop system are bounded in probability, and the error signals are semi‐globally uniformly ultimately bounded in mean square or the sense of four‐moment. Simulation results are provided to illustrate the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite‐time tracking control of uncertain nonholonomic systems by state and output feedback

This paper studies the finite‐time tracking control of nonholonomic systems in chained form with parameter uncertainties, unknown output gains, and mismatched uncertainties. To achieve the finite‐time tracking control of uncertain nonholonomic systems, we propose 2 types of controllers by state and output feedback, respectively. Both of the proposed 2 types of controllers can achieve the finite‐time output tracking control of the nonholonomic systems even in the presence of mismatched uncertainties and/or unknown gains. The effectiveness of our proposed controllers are illustrated with simulation examples.     

Adaptive output feedback stabilization for a class of nonlinear systems with inherent nonlinearities and uncertainties

This paper investigates the problem of adaptive stabilization by output feedback for a class of uncertain nonlinear systems. The distinguishing feature of such a class of systems is the presence of uncertain control coefficient and unmeasured states dependent growth with growth rate of polynomial‐of‐output multiplying an unknown constant. First, new high‐gain K‐filters with two dynamic gains are introduced, and an appropriate state observer is constructed based on the K‐filters. Then, motivated by the universal control idea, the backstepping scheme is successfully developed for the adaptive output feedback control design. By appropriate choice of the design parameters, the global stability of the closed‐loop system can be guaranteed. Finally, numerical simulations are provided to illustrate the correctness of the theoretical results. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive output feedback control for a class of nonlinear systems with quantised input and output

This paper aims at addressing the problem of global adaptive stabilisation by output feedback for a class of nonlinear systems, in which both the input and output are logarithmically quantised. The nonlinear functions of the systems are not necessary to be completely known and contain time-varying parameters that belong to an unknown bounded set. Based on dynamic high-gain technique, a linear-like quantised controller computed from quantised output is constructed and a guideline is derived to select the parameters of the quantisers. It is proved that, with the proposed scheme, all the states of the system can be globally steered to the origin while keeping the other signals of the closed-loop system bounded.     

Adaptive fuzzy backstepping output feedback control of nonlinear time-delay systems with unknown high-frequency gain sign

In this paper, an adaptive fuzzy robust feedback control approach is proposed for a class of single-input and single-output (SISO) strict-feedback nonlinear systems with unknown nonlinear functions, time delays, unknown high-frequency gain sign, and without the measurements of the states. In the backstepping recursive design, fuzzy logic systems are employed to approximate the unknown smooth nonlinear functions, K-filters is designed to estimate the unmeasured states, and Nussbaum gain functions are introduced to solve the problem of unknown sign of high-frequency gain. By combining adaptive fuzzy control theory and adaptive backstepping design, a stable adaptive fuzzy output feedback control scheme is developed. It has been proven that the proposed adaptive fuzzy robust control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin by appropriately choosing design parameters. Simulation results have shown the effectiveness of the proposed method.     

Adaptive output-feedback control for a class of nonlinear systems with actuator failures and input quantisation

In this paper, an adaptive output feedback control technique is proposed for a class of nonlinear systems with unknown parameters, unknown nonlinear functions, quantised input and possible actuator failures up to infinity. A modified backstepping approach is proposed by the use of high-gain K-filters, hyperbolic tangent function property and bound-estimation approach to compensate for the effect of possible number of actuator failures up to infinity, input quantisation and unknown nonlinear functions. It is proved both mathematically and by simulation that with the proposed controller, all the signals of the closed-loop system are globally bounded despite of input quantisation, unknown nonlinear functions and possible number of actuator failures up to infinity.     

Adaptive robust output tracking of uncertain strict-feedback nonlinear time-delay systems via control schemes with simple structure

The output tracking control problem is considered for a class of uncertain strict-feedback nonlinear systems with time-varying delays. In the paper, the time-varying delays are assumed to be any non-negative continuous and bounded functions, and it is not necessary for their derivatives to be less than one. It is also assumed that the upper bounds of nonlinear delayed state perturbations and external disturbances are unknown. On the basis of backstepping algorithm, a novel design method is proposed by which some simple adaptive robust output tracking control schemes are synthesised. The proposed design method can avoid the repeated differentiation problem which appears in using the conventional backstepping algorithm, and need not know all the nonlinear upper bound functions of uncertainties, which are repeatedly employed at each step of the backstepping algorithm. In particular, it is not necessary to know any information on the time-varying delays to construct our simple output tracking control schemes. It is also shown that the tracking error can converge uniformly exponentially towards a neighbourhood of the origin. Finally, a numerical example and its simulations are provided to demonstrate the design procedure of the simple method proposed in the paper.     

Nonstationary H∞ dynamic output feedback control for discrete‐time Markov jump linear systems with actuator and sensor saturations

This paper is concerned with the nonstationary dynamic output feedback control problem for a class of discrete‐time Markov jump linear systems (MJLSs) under simultaneous consideration of actuator and sensor saturations. The so‐called nonstationary controllers dominated by two other different piecewise‐stationary Markov chains are introduced, making the designed controllers not only mode‐dependent but also dependent on other variations associated with the mode transitions in the original MJLSs. The sufficient conditions formulated in terms of bilinear matrix inequalities for the H_∞ control problem are established such that the resulting closed‐loop system is stochastically stable and achieves a prescribed H_∞ noise attenuation level. A suboptimal algorithm with line search is exploited to solve for the associated controller gains. Effectiveness of the developed theoretical results is verified via a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.     

Modeling, simulation, and control of an electromechanical aerofin control system with a PWM-controlled DC motor

A nonlinear model of an electromechanical actuator (EMA) system for aerofin control is presented. The EMA is realized with a permanent magnet brush DC motor controlled by a constant current driver. In this paper we introduced a simulation model that includes nonlinearities of the motor driver. A PID position controller was designed using the simulation model, although it was impossible to develop a linear model. The simulation results have been of the great importance for understanding the system behavior and successful control system implementation. The proposed control system has experimentally been validated on a test bench. The EMA-AFC test bench is designed to provide real operating conditions. The text was submitted by the authors in English.