A new integral inequality and its applications to robust control problems of uncertain nonlinear systems

In this paper, a new integral inequality is presented. By combining this integral inequality with adaptive approach, new design methods can be developed to synthesize some adaptive robust control schemes for a large class of uncertain nonlinear systems and to deal with well the unknown nonlinearities appearing in uncertain nonlinear control dynamical systems. As an application of the presented integral inequality to control theory, the robust stabilization problem is considered for a class of uncertain strict‐feedback nonlinear systems with both time‐delay and unknown dead‐zone input nonlinearities. It is shown that there are two main merits in the design method based on the integral inequality presented in this paper. The first one is that one need not estimate and know the unknown nonlinearities to synthesize some stabilizing control schemes. The second one is that the resulting feedback control schemes have rather simple structure.     

A unified framework for the study of anti-windup designs

We present a unified framework for the study of linear time-invariant (LTI) systems subject to control input nonlinearities. The framework is based on the following two-step design paradigm: ‘design the linear controller ignoring control input nonlinearities and then add anti-windup bumpless transfer (AWBT) compensation to minimize the adverse effects of any control input nonlinearities on closed loop performance’. The resulting AWBT compensation is applicable to multivariable controllers of arbitrary structure and order. All known LTI anti-windup and/or bumpless transfer compensation schemes are shown to be special cases of this framework. This unification of existing schemes for AWBT compensation under a general framework is the main result of the paper.     

Neural Network Based Adaptive Tracking Control for a Class of Pure Feedback Nonlinear Systems With Input Saturation

In this paper, an adaptive neural networks (NNs) tracking controller is proposed for a class of single-input/singleoutput (SISO) non-affine pure-feedback non-linear systems with input saturation. In the proposed approach, the original input saturated nonlinear system is augmented by a low pass filter. Then, new system states are introduced to implement states transformation of the augmented model. The resulting new model in affine Brunovsky form permits direct and simpler controller design by avoiding back-stepping technique and its complexity growing as done in existing methods in the literature. In controller design of the proposed approach, a state observer, based on the strictly positive real (SPR) theory, is introduced and designed to estimate the new system states, and only two neural networks are used to approximate the uncertain nonlinearities and compensate for the saturation nonlinearity of actuator. The proposed approach can not only provide a simple and effective way for construction of the controller in adaptive neural networks control of non-affine systems with input saturation, but also guarantee the tracking performance and the boundedness of all the signals in the closed-loop system. The stability of the control system is investigated by using the Lyapunov theory. Simulation examples are presented to show the effectiveness of the proposed controller.      

ROBUST ADAPTIVE CONTROL FOR STRICT‐FEEDBACK NONLINEAR SYSTEMS

In this paper, we propose a robust adaptive tracking control based on the backstepping strategy for strict‐feedback nonlinear systems with nonparametric uncertain nonlinearities. It is shown that one can design a stable adaptive control system provided that the uncertain nonlinearities can be decomposed by unknown bounded nonlinear functions and known nonlinear functions. The proposed method can deal with uncertain nonlinearities that appear at the control input term too. It is also shown that suitable choice of design parameters guarantees the convergence of tracking error to any desired bound.     

Adaptive Dynamic Inversion via Time-Scale Separation

This paper presents a full state feedback adaptive dynamic inversion method for uncertain systems that depend nonlinearly upon the control input. Using a specialized set of basis functions that respect the monotonic property of the system nonlinearities with respect to control input, a state predictor is defined for derivation of the adaptive laws. The adaptive dynamic inversion controller is defined as a solution of a fast dynamical equation, which achieves time-scale separation between the state predictor and the controller dynamics. Lyapunov-based adaptive laws ensure that the predictor tracks the state of the nonlinear system with bounded errors. As a result, the system state tracks the desired reference model with bounded errors. Benefits of the proposed design method are demonstrated using Van der Pol dynamics with nonlinear control input.     

Cooperative Adaptive Fuzzy Output Feedback Control for Synchronization of Nonlinear Multi‐Agent Systems in the Presence of Input Saturation

This paper considers the leader‐following synchronization problem of nonlinear multi‐agent systems with unmeasurable states in the presence of input saturation. Each follower is governed by a class of strict‐feedback systems with unknown nonlinearities and the information of the leader can be accessed by only a small fraction of followers. An auxiliary system is introduced and its states are used to design the cooperative controllers for counteracting the effect of input saturation. By using fuzzy logic systems to approximate the unknown nonlinearities, local adaptive fuzzy observers are designed to estimate the unmeasurable states. Dynamic surface control (DSC) is employed to design distributed adaptive fuzzy output feedback controllers. The developed controllers guarantee that the outputs of all followers synchronize to that of the leader under directed communication graphs. Based on Lyapunov stability theory, it is proved that all signals in the closed‐loop systems are semiglobally uniformly ultimately bounded (SGUUB), and the tracking error converges to a small neighborhood of the origin. An example is provided to show the effectiveness of the proposed control approach.     

Recursive design of discontinuous controllers for uncertain driftless systems in power chained form

Investigates the problem of almost asymptotic stabilization for a class of uncertain driftless systems in power chained form. The main obstacles for the control of this new type of driftless systems are: i) nonexistence of any time-invariant smooth (or even continuous) state feedback control law; ii) lack of affineness in the control input; and iii) high-order nonlinearities that make most of the nonlinear design methods inapplicable. To overcome these difficulties we propose a constructive approach that combines a discontinuous change of coordinates and the recent adding a power integrator technique. Sufficient conditions are given under which discontinuous robust and adaptive controllers can be explicitly constructed, achieving almost stabilization and adaptive regulation. Solutions to the problems of global robust regulation and adaptive regulation are also obtained by using switching control schemes.     

Adaptive output feedback quantised tracking control for stochastic nonstrict-feedback nonlinear systems with input saturation

This paper is concerned with the problem of adaptive output feedback quantised tracking control for a class of stochastic nonstrict-feedback nonlinear systems with asymmetric input saturation. Especially, both input and output signals are quantised by two sector-bounded quantisers. In order to solve the technical difficulties originating from asymmetric saturation nonlinearities and sector-bounded quantisation errors, some special technique, approximation-based methods and Gaussian error function-based continuous differentiable model are exploited. Meanwhile, an observer including the quantised input and output signals is designed to estimate the states. Then, a novel output feedback adaptive quantised control scheme is proposed to ensure that all signals in the closed-loop system are 4-moment (2-moment) semi-globally uniformly ultimately bounded while the output signal follows a desired reference signal. Finally, the effectiveness and applicability of the design methodology is illustrated with two simulation examples.     

Systematic design of adaptive controllers for feedback linearizablesystems

A systematic procedure for the design of adaptive regulation and tracking schemes for a class of feedback linearizable nonlinear systems is developed. The coordinate-free geometric conditions, which characterize this class of systems, do not constrain the growth of the nonlinearities. Instead, they require that the nonlinear system be transformable into the so-called parametric-pure feedback form. When this form is strict, the proposed scheme guarantees global regulation and tracking properties, and substantially enlarges the class of nonlinear systems with unknown parameters for which global stabilization can be achieved. The main results use simple analytical tools, familiar to most control engineers     

A globally stable saturated desired compensation adaptive robust control for linear motor systems with comparative experiments

The recently proposed saturated adaptive robust controller is integrated with desired trajectory compensation to achieve global stability with much improved tracking performance. The algorithm is tested on a linear motor drive system which has limited control effort and is subject to parametric uncertainties, unmodeled nonlinearities, and external disturbances. Global stability is achieved by employing back-stepping design with bounded (virtual) control input in each step. A guaranteed transient performance and final tracking accuracy is achieved by incorporating the well-developed adaptive robust controller with effective parameter identifier. Signal noise that affects the adaptation function is alleviated by replacing the noisy velocity signal with the cleaner position feedback. Furthermore, asymptotic output tracking can be achieved when only parametric uncertainties are present.     

Finite-time output feedback stabilisation of chained-form systems with inputs saturation

This paper investigates the problem of finite-time stabilisation by output feedback for a class of non-holonomic systems in chained form with input saturation. Rigorous design procedure for saturated output feedback control is presented by using the homogeneous domination approach and the nested saturation technique. Together with a novel switching control strategy, the designed controller renders that the states of closed-loop system are regulated to zero in a finite time. A simulation example is provided to illustrate the effectiveness of the proposed approach.     

Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems

In this paper, both full state and output feedback adaptive neural network (NN) controllers are presented for a class of strict-feedback discrete-time nonlinear systems. Firstly, Lyapunov-based full-state adaptive NN control is presented via backstepping, which avoids the possible controller singularity problem in adaptive nonlinear control and solves the noncausal problem in the discrete-time backstepping design procedure. After the strict-feedback form is transformed into a cascade form, another relatively simple Lyapunov-based direct output feedback control is developed. The closed-loop systems for both control schemes are proven to be semi-globally uniformly ultimately bounded.     

Adaptive neural control of uncertain MIMO nonlinear systems

In this paper, adaptive neural control schemes are proposed for two classes of uncertain multi-input/multi-output (MIMO) nonlinear systems in block-triangular forms. The MIMO systems consist of interconnected subsystems, with couplings in the forms of unknown nonlinearities and/or parametric uncertainties in the input matrices, as well as in the system interconnections without any bounding restrictions. Using the block-triangular structure properties, the stability analyses of the closed-loop MIMO systems are shown in a nested iterative manner for all the states. By exploiting the special properties of the affine terms of the two classes of MIMO systems, the developed neural control schemes avoid the controller singularity problem completely without using projection algorithms. Semiglobal uniform ultimate boundedness (SGUUB) of all the signals in the closed-loop of MIMO nonlinear systems is achieved. The outputs of the systems are proven to converge to a small neighborhood of the desired trajectories. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. The proposed schemes offer systematic design procedures for the control of the two classes of uncertain MIMO nonlinear systems. Simulation results are presented to show the effectiveness of the approach.     

Dynamic anti-windup scheme for feedback linearizable nonlinear control systems with saturating inputs

This paper proposes a dynamic compensation scheme for input-constrained feedback linearizable nonlinear systems to cope with the windup phenomenon. Given a dynamic feedback linearizing controller designed without considering its input constraint, an additional dynamic compensator is proposed to account for the constraint. This dynamic anti-windup is based on the minimization of a reasonable performance index. The proposed strategy is a nonlinear extended version of [Park, J.-K., & Choi, C.-H. (1995). Dynamic compensation method for multivariable control systems with saturating actuators. IEEE Transactions on Automatic Control, 40(9), 1635–1640] with simplified derivation of an optimization solution under relaxed assumptions. The parameter matrices and structure of the solution are explicitly decided by mathematical optimization for infinite horizon without tuning of design parameters unlike previous schemes. During input saturation, the role of the anti-windup scheme with the proposed dynamic feedback compensator is to maintain the controller states to be exactly the same as those without input saturation. The local asymptotic stability and the total stability of the resulting systems are proved. The usefulness of the proposed design method is illustrated by comparative simulations for a constrained control system.     

Adaptive actuator compensation control with feedback linearization

An adaptive inverse controller is developed for feedback linearizable nonlinear systems with nonsmooth actuator nonlinearities. The use of an actuator nonlinearity inverse and a feedback linearizing controller leads to an error equation suitable for deriving an adaptive update law for the inverse parameters. Closed-loop signal boundedness is proved analytically, and system performance improvement is shown by simulation results. Such adaptive control schemes are also developed for multivariable nonlinear systems with actuator nonlinearities. For nonlinear systems that do not possess a relative degree, dynamic extension is employed to realize adaptive inverse compensation designs for actuator nonlinearities. These adaptive designs ensure closed-loop stability in the presence of uncertain actuator nonlinearities     

MIMO纯反馈受限系统无模型非线性比例反演控制

针对模型未知的MIMO纯反馈系统,提出一种新的控制设计方案.该方案基于预设性能控制思想设计非线性比例控制器,并将其引入反演设计的每一步,以构建非线性比例反演控制器,并融合考虑了模型未知、状态受限、输入受限以及预设性能的需求,且无需引入任何逼近理论和自适应控制等技术即可保证系统具有良好的抗扰性和鲁棒自适应性,控制器结构极为简单.最后,基于Lyapunov稳定性定理证明了闭环系统所有信号一致有界,仿真结果验证了所提出设计方案的可行性和有效性.     

Adaptive Fuzzy Backstepping Tracking Control for Flexible Robotic Manipulator

In this paper, an adaptive fuzzy state feedback control method is proposed for the single-link robotic manipulator system. The considered system contains unknown nonlinear function and actuator saturation. Fuzzy logic systems (FLSs) and a smooth function are used to approximate the unknown nonlinearities and the actuator saturation, respectively. By combining the command-filter technique with the backstepping design algorithm, a novel adaptive fuzzy tracking backstepping control method is developed. It is proved that the adaptive fuzzy control scheme can guarantee that all the variables in the closed-loop system are bounded, and the system output can track the given reference signal as close as possible. Simulation results are provided to illustrate the effectiveness of the proposed approach.      

Observer-based adaptive fuzzy-neural control for unknown nonlineardynamical systems

In this paper, an observer-based adaptive fuzzy-neural controller for a class of unknown nonlinear dynamical systems is developed. The observer-based output feedback control law and update law to tune on-line the weighting factors of the adaptive fuzzy-neural controller are derived. The total states of the nonlinear system are not assumed to be available for measurement. Also, the unknown nonlinearities of the nonlinear dynamical systems are not restricted to the system output only. The overall adaptive scheme guarantees that all signals involved are bounded. Simulation results demonstrate the applicability of the proposed method in order to achieve desired performance.     

A new state observer for perspective systems

In this note, we consider the problem of estimating the state of a class of perspective systems. The problem can be converted into the observation of a dynamical system with nonlinearities. A new discontinuous state observer, which is motivated by the sliding mode control method and adaptive techniques, is proposed for the obtained dynamical system. The assumptions are reasonable, and the convergence conditions are intuitive and have apparently physical interpretations. The attraction of the new method is that the algorithm is very simple and easy to be implemented, and it is robust to measurement noises. Further, minor a priori knowledge of the system is required in the new formulation. Simulation results show the superiority of the new method to the traditional ones     

Stable indirect adaptive switching control for fuzzy dynamical systems based on T–S multiple models

A new indirect adaptive switching fuzzy control method for fuzzy dynamical systems, based on Takagi–Sugeno (T–S) multiple models is proposed in this article. Motivated by the fact that indirect adaptive control techniques suffer from poor transient response, especially when the initialisation of the estimation model is highly inaccurate and the region of uncertainty for the plant parameters is very large, we present a fuzzy control method that utilises the advantages of multiple models strategy. The dynamical system is expressed using the T–S method in order to cope with the nonlinearities. T–S adaptive multiple models of the system to be controlled are constructed using different initial estimations for the parameters while one feedback linearisation controller corresponds to each model according to a specified reference model. The controller to be applied is determined at every time instant by the model which best approximates the plant using a switching rule with a suitable performance index. Lyapunov stability theory is used in order to obtain the adaptive law for the multiple models parameters, ensuring the asymptotic stability of the system while a modification in this law keeps the control input away from singularities. Also, by introducing the next best controller logic, we avoid possible infeasibilities in the control signal. Simulation results are presented, indicating the effectiveness and the advantages of the proposed method.