Observer-based adaptive fuzzy-neural control for a class of uncertain nonlinear systems with unknown dead-zone input

Based on the universal approximation property of the fuzzy-neural networks, an adaptive fuzzy-neural observer design algorithm is studied for a class of nonlinear SISO systems with both a completely unknown function and an unknown dead-zone input. The fuzzy-neural networks are used to approximate the unknown nonlinear function. Because it is assumed that the system states are unmeasured, an observer needs to be designed to estimate those unmeasured states. In the previous works with the observer design based on the universal approximator, when the dead-zone input appears it is ignored and the stability of the closed-loop system will be affected. In this paper, the proposed algorithm overcomes the affections of dead-zone input for the stability of the systems. Moreover, the dead-zone parameters are assumed to be unknown and will be adjusted adaptively as well as the sign function being introduced to compensate the dead-zone. With the aid of the Lyapunov analysis method, the stability of the closed-loop system is proven. A simulation example is provided to illustrate the feasibility of the control algorithm presented in this paper.     

Adaptive fuzzy prescribed performance control for MIMO nonlinear systems with unknown control direction and unknown dead-zone inputs

In this study, an adaptive fuzzy prescribed performance control approach is developed for a class of uncertain multi-input and multi-output (MIMO) nonlinear systems with unknown control direction and unknown dead-zone inputs. The properties of symmetric matrix are exploited to design adaptive fuzzy prescribed performance controller, and a Nussbaum-type function is incorporated in the controller to estimate the unknown control direction. This method has two prominent advantages: it does not require the priori knowledge of control direction and only three parameters need to be updated on-line for this MIMO systems. It is proved that all the signals in the resulting closed-loop system are bounded and that the tracking errors converge to a small residual set with the prescribed performance bounds. The effectiveness of the proposed approach is validated by simulation results.     

Adaptive output feedback tracking of nonlinear systems with uncertain nonsymmetric dead-zone input

In this paper, the problem of adaptive practical tracking is investigated by output feedback for a class of uncertain nonlinear systems subject to nonsymmetric dead-zone input nonlinearity with parameters of dead-zone being unknown. Instead of constructing the inverse of dead-zone nonlinearity, an adaptive robust control scheme is developed by designing an output compensator including two dynamic gains based respectively on identification and non-identification mechanism. With the aid of dynamic high-gain scaling approach and Backstepping method, stability analysis of the closed-loop system is proceeded using non-separation principle, which shows that the proposed controller guarantees that all closed-loop signal is bounded while the output of system tracks a broad class of bounded reference trajectories by arbitrarily small error prescribed previously. Finally, two examples are given to illustrate our controller effective.     

Memoryless disturbance-observer-based adaptive tracking of uncertain pure-feedback nonlinear time-delay systems with unmatched disturbances

This paper presents a delay-independent nonlinear disturbance observer (NDO) design methodology for adaptive tracking of uncertain pure-feedback nonlinear systems in the presence of unknown time delays and unmatched external disturbances. Compared with all existing NDO-based control results for uncertain lower-triangular nonlinear systems where unknown time delays have been not considered, the main contribution of this paper is to develop a delay-independent design strategy to construct an NDO-based adaptive tracking scheme in the presence of unknown time-delayed nonlinearities and non-affine nonlinearities unmatched in the control input. The proposed delay-independent scheme is constructed by employing the appropriate Lyapunov-Krasovskii functionals and the same function approximators for the NDO and the controller. It is shown that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to an adjustable neighborhood of the origin.     

Anti-disturbance control theory for systems with multiple disturbances: A survey

The problem of anti-disturbance control has been an eternal topic along with the development of the control theory. However, most methodologies can only deal with systems subject to a single equivalent disturbance which was merged by various types of uncertainties. In this paper, a review on anti-disturbance control is presented for systems with multiple disturbances. First, the classical control methods are briefly reviewed for disturbance attenuation or rejection problems. Then, recent advances in disturbance observer based control (DOBC) theory are introduced and especially, the composite hierarchical anti-disturbance control (CHADC) is firstly addressed. A comparison of different approaches is briefly carried out. Finally, focuses in the field on the current research are also addressed with emphasis on the practical application of the techniques.     

Adaptive iterative learning control of a class of nonlinear time-delay systems with unknown backlash-like hysteresis input and control direction

This paper presents an adaptive iterative learning control scheme for a class of nonlinear systems with unknown time-varying delays and control direction preceded by unknown nonlinear backlash-like hysteresis. Boundary layer function is introduced to construct an auxiliary error variable, which relaxes the identical initial condition assumption of iterative learning control. For the controller design, integral Lyapunov function candidate is used, which avoids the possible singularity problem by introducing hyperbolic tangent funciton. After compensating for uncertainties with time-varying delays by combining appropriate Lyapunov-Krasovskii function with Young's inequality, an adaptive iterative learning control scheme is designed through neural approximation technique and Nussbaum function method. On the basis of the hyperbolic tangent function's characteristics, 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 closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.     

Anti-disturbance backstepping control for air-breathing hypersonic vehicles based on extended state observer

In this paper, we propose an anti-disturbance backstepping control approach with extended state observer (ESO) for tracking control of air-breathing hypersonic vehicles. Considering the large uncertainties, the external disturbances, and especially the lack of aerodynamic knowledge, several ESOs are introduced in the backstepping controller. With the total disturbance estimation ability of ESOs, almost no aerodynamic knowledge is needed for the controller design. Meanwhile, ESOs are also used to estimate the derivatives of the virtual control signals. The problem of “explosion of terms” is avoided. A key strategy of the controller is that each step of backstepping is activated successively. Consequently, the closed-loop system has time-scale structure. Rigorous stability proof can be obtained. At last, compared simulation results verify the superior tracking performance of the proposed controller.     

Adaptive sensor fault-tolerant control for a class of multi-input multi-output nonlinear systems: Adaptive first-order filter-based dynamic surface control approach

This paper is concerned with the adaptive fault-tolerant control (FTC) problem for a class of multivariable nonlinear systems with external disturbances, modeling errors and time-varying sensor faults. The bias, drift, loss of accuracy and loss of effectiveness faults can be effectively accommodated by this scheme. The dynamic surface control (DSC) technique and adaptive first-order filters are brought together to design an adaptive FTC scheme which can reduce significantly the computational burden and improve further the control performance. The adaptation laws are constructed using novel low-pass filter based modification terms which enable under high learning or modification gains to achieve robust, fast and high-accuracy estimation without incurring undesired high-frequency oscillations. It is proved that all signals in the closed-loop system are uniformly ultimately bounded and the tracking-errors can be made arbitrary close to zero. Simulation results are provided to verify the effectiveness and superiority of the proposed FTC method.     

Decentralized adaptive control of interconnected nonlinear systems with unknown control directions

In this paper, we propose a decentralized adaptive control scheme for a class of interconnected strict-feedback nonlinear systems without a priori knowledge of subsystems' control directions. To address this problem, a novel Nussbaum-type function is proposed and a key theorem is drawn which involves quantifying the interconnections of multiple Nussbaum-type functions of the subsystems with different control directions in a single inequality. Global stability of the closed-loop system and asymptotic stabilization of subsystems' output are proved and a simulation example is given to illustrate the effectiveness of the proposed control scheme.     

On performance analysis of ADRC for a class of MIMO lower-triangular nonlinear uncertain systems

This paper designs the active disturbance rejection control (ADRC) to achieve desired performance for a class of MIMO lower-triangular nonlinear systems with large uncertainties under un-matched condition. We develop the ADRC with a set of extended state observers, and prove that the closed-loop system can achieve satisfied dynamic performance. The theoretical results illustrate the relationship between the bound of the concerned error and the bandwidth of extend state observers.     

Two-layer observer based control for a class of uncertain systems with multi-frequency disturbances

A novel disturbance estimation approach is presented for a class of uncertain systems subject to multiple-sinusoidal disturbances with unknown frequencies. Different from existing results on disturbance observer based control (DOBC), a new methodology with a two-layer observer structure is developed to effectively estimate and reject the disturbances. In the proposed control architecture, an auxiliary observer is derived to generate a disturbance representation in a parametric uncertainty form. Furthermore, the unknown parameters can be reduced to a constant vector with the dimension of the number of harmonic components in the disturbances. Then an augmented observer is designed to estimate the corresponding unknown parameters of the disturbances. As a result, the uncertain systems with disturbances constituting of multiple unknown-frequency sinusoidal components can be controlled within the DOBC framework, where asymptotic stability can be guaranteed. The proposed approach is successfully validated on a robotic manipulating example.     

Adaptive predictive functional control of a class of nonlinear systems

This paper describes the use of pseudo-partial derivative (PPD) to dynamically linearize a nonlinear system, and aggregation is applied to the predicted PPD, resulting in a model-free adaptive predictive control algorithm for a nonlinear system. The algorithm design is only based on the PPD derived online from the input/output data of the controlled process, however it does provide bounded input/output sequence and setpoint tracking without steady-state error. A detailed discussion on parameter selection is also provided. To show the capability of the algorithm, simulations of a time-delay plant and a pH neutralization process show that the proposed method is effective for system parameter perturbation and external disturbance rejection.     

Performance analysis of active disturbance rejection tracking control for a class of uncertain LTI systems

The paper considers the tracking problem for a class of uncertain linear time invariant (LTI) systems with both uncertain parameters and external disturbances. The active disturbance rejection tracking controller is designed and the resulting closed-loop system׳s characteristics are comprehensively studied. In the time-domain, it is proven that the output of closed-loop system can approach its ideal trajectory in the transient process against different kinds of uncertainties by tuning the bandwidth of extended state observer (ESO). In the frequency-domain, different kinds of parameters׳ influences on the phase margin and the crossover frequency of the resulting control system are illuminated. Finally, the effectiveness and robustness of the controller are verified through the actuator position control system with uncertain parameters and load disturbances in the simulations.     

非线性时滞系统自适应模糊动态面控制

针对含完全未知时滞的不确定非线性系统的控制问题,提出了一种自适应模糊动态面控制方案.首先采用模糊逻辑系统逼近系统的未知时滞函数,进而用参考信号代换逼近器输入中的未知时滞信号,取消了对未知时滞常作的假设,摆脱了控制器构造对时滞假设条件的依赖性.模糊逼近和时滞代换产生的误差则采用自适应边界技术处理.基于Lyapunov-Krasovskii泛函,证明了闭环系统所有信号半全局一致最终有界,通过调节设计参数可以实现任意的跟踪精度.仿真实例进一步说明了该方案的可行性.     

Disturbance observer-based backstepping sliding mode fault-tolerant control for the hydro-turbine governing system with dead-zone input

This paper investigates a backstepping sliding mode fault-tolerant tracking control problem for a hydro-turbine governing system with consideration of external disturbances, actuator faults and dead-zone input. To reduce the effects of the unknown random disturbances, the nonlinear disturbance observer is designed to identify and estimate the disturbance term. To drastically decrease the complexity of stability functions selection and controller design, the recursive processes of the backstepping technique are employed. Additionally, based on the nonlinear disturbance observer and the backstepping technique, the sliding mode fault-tolerant tracking control approach is developed for the hydro-turbine governing system (HTGS). The stability of HTGS is rigorously demonstrated through Lyapunov analysis which is capable to satisfy a tracking control performance. Finally, comprehensive simulation results are presented to illustrate the effectiveness and superiority of the proposed control scheme.     

Global adaptive output feedback control for a class of nonlinear time-delay systems

This paper addresses the problem of global output feedback control for a class of nonlinear time-delay systems. The nonlinearities are dominated by a triangular form satisfying linear growth condition in the unmeasurable states with an unknown growth rate. With a change of coordinates, a linear-like controller is constructed, which avoids the repeated derivatives of the nonlinearities depending on the observer states and the dynamic gain in backstepping approach and therefore, simplifies the design procedure. Using the idea of universal control, we explicitly construct a universal-type adaptive output feedback controller which globally regulates all the states of the nonlinear time-delay systems.     

Global adaptive control for uncertain nonaffine nonlinear hysteretic systems

In this paper, the global output tracking is investigated for a class of uncertain nonlinear hysteretic systems with nonaffine structures. By combining the solution properties of the hysteresis model with the novel backstepping approach, a robust adaptive control algorithm is developed without constructing a hysteresis inverse. The proposed control scheme is further modified to tackle the bounded disturbances by adaptively estimating their bounds. It is rigorously proven that the designed adaptive controllers can guarantee global stability of the closed-loop system. Two numerical examples are provided to show the effectiveness of the proposed control schemes.     

Model predictive control for a class of systems with isolated nonlinearity

The paper is concerned with an overall convergent nonlinear model predictive control design for a kind of nonlinear mechatronic drive systems. The proposed nonlinear model predictive control results in the improvement of regulatory capacity for reference tracking and load disturbance rejection. The design of the nonlinear model predictive controller consists of two steps: the first step is to design a linear model predictive controller based on the linear part of the system at each sample instant, then an overall convergent nonlinear part is added to the linear model predictive controller to combine a nonlinear controller using error driven. The structure of the proposed controller is similar to that of classical PI optimal regulator but it also bears a set-point feed forward control loop, thus tracking ability and disturbance rejection are improved. The proposed method is compared with the results from recent literature, where control performance under both model match and mismatch cases are enlightened.