Finite‐time robust simultaneous stabilization of a set of nonlinear time‐delay systems

This paper investigates the finite‐time robust simultaneous stabilization problem of a set of nonlinear time‐delay systems with general forms and proposes some new simultaneous stabilization results. First, by developing an equivalent form and applying augmented technique, this paper obtains an augmented equivalent form of the original systems. Secondly, based on the equivalent form, we study finite‐time simultaneous stabilization problem and present some new stabilization results by constructing some suitable Lyapunov functionals. Thirdly, using the simultaneous stabilization results obtained, this paper investigates the finite‐time robust simultaneous stabilization problem for the set systems and proposes a delay‐dependent robust simultaneous stabilization result. Finally, the study of an illustrative example shows that the results obtained by this paper work well in the finite‐time robust simultaneous stabilization the set systems. It is shown that, by using the method in this paper, the developed conditions do not contain delay terms, which can avoid solving nonlinear mixed matrix inequalities and reduce effectively computational burden in studying nonlinear time‐delay systems.     

Finite‐time stability of switched nonlinear time‐delay systems

This article addresses the problem of finite‐time stability (FTS) and finite‐time contractive stability (FTCS) for switched nonlinear time‐delay systems (SNTDSs). By virtues of the Lyapunov‐Razumikhin method, Lyapunov functionals approach, and the comparison principle technique, we obtain some improved Razumikhin‐type theorems that verify FTS and FTCS property for SNTDSs. Moreover, our results allow the estimate of the upper bound of the derivatives for Lyapunov functions to be mode dependent functions which can be positive and negative. Meanwhile, the proposed results also improve the related existing results on the same topic by removing some restrictive conditions. Finally, two examples are presented to verify the effectiveness of our methods.     

Finite‐time stabilization for a class of nonlinear systems with time‐varying delay

This paper investigates the finite‐time stabilization problem for a class of nonlinear systems with time‐varying delay. Under suitable assumptions, a new state feedback control law is designed by using the adding a power integrator technique. By constructing an appropriate Lyapunov‐Krasovskii functional, it is shown that the corresponding closed‐loop system is finite‐time stable. Two simulation examples are given to verify the effectiveness of the proposed scheme.     

Observer‐based Adaptive fuzzy control of time‐delay uncertain nonlinear systems

An observer‐based adaptive fuzzy model following controller is proposed for a class of MIMO nonlinear uncertain systems to cope with time‐delay, uncertainty in plant structure and disturbances. Based on universal approximation theorem the unknown nonlinear functions are approximated by fuzzy systems, where the premise and the consequent parts of the fuzzy rules are tuned with adaptive schemes. To have more robustness, and at the same time to alleviate chattering, an adaptive discontinuous structure is suggested. Moreover, the availability of the states measurement is not required and an adaptive observer is used to estimate the states. Asymptoic stability of the overall system is ensured using suitable a Lyapunov‐Krasovskii functional candidate. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Indirect adaptive robust control of nonlinear systems with time‐varying parameters in a strict feedback form

Without any prior knowledge of the physical bounds of unknown parameters and uncertain nonlinearities, an indirect adaptive robust controller is constructed for uncertain nonlinear time‐varying systems in a strict‐feedback form. Firstly, an adaptive strong robust controller is derived based on the command filtered adaptive backstepping approach. This controller not only can guarantee the boundedness of the closed‐loop system signals in the presence of time‐varying (TV) parameters and uncertain nonlinearities but also obviate the need to compute analytic derivatives of virtual control functions. Thus, the problem of “explosion of terms” in the standard adaptive backstepping technique is avoided. Through introduction of a simple adaptation law on the upper bound of uncertainties, a smooth robust control term is used to realize the disturbance attenuation. Afterwards, based on the nonlinear X‐swapping techniques, a modular approach in which the controller and the identifier can be designed separately is exploited. A novel algorithm is proposed to estimate the TV parameters accurately. By adopting the variation trend of the covariance matrix as an indicator of the driving signals' persistent excitation level, this online parameter estimation law is switched between a modified least‐squares algorithm and a gradient algorithm based on fixed σ‐modification. Finally, a series of properties on the asymptotic stability and the global uniform ultimate boundedness of the closed‐loop system is established. Simulation results verify the effectiveness of the suggested method.     

A novel adaptive robust control architecture for bilateral teleoperation systems under time‐varying delays

Bilateral teleoperation technology has caused wide attentions due to its applications in various remote operation systems. The communication delay becomes one of the main challenging issues in the teleoperation control design. Meanwhile, various nonlinearities, parameter variations, and modeling uncertainties existing in manipulator and environment dynamics need to be considered carefully in order to achieve good control performance. In this paper, a globally stable nonlinear adaptive robust control algorithm is developed for bilateral teleoperation systems to deal with these control issues. Namely, the unknown dynamical parameters of the environmental force are estimated online by the improved least square adaptation law. A novel communication structure is proposed where only the master position signal is transmitted to the slave side for the tracking design, and the online estimators of the environmental parameters are transmitted from the slave to the master to replace the traditional environmental force measurement. Because the estimated environmental parameters are not power signals, the passivity problem of the communication channel and the trade‐off limitation between the transparency performance and robust stability in traditional teleoperation control are essentially avoided. The nonlinear adaptive robust control is subsequently developed to deal with nonlinearities, unknown parameters, and modeling uncertainties of the master, slave, and environmental dynamics, so that the guaranteed transient and steady‐state transparency performance can be achieved. The experiments on two voice‐coil motor‐driven manipulators are carried out, and the comparative results verify that the proposed control algorithm achieves the excellent control performance and the guaranteed robust stability simultaneously under time delays. Copyright © 2014 John Wiley & Sons, Ltd.     

Constrained robust sampled‐data control for nonlinear uncertain systems

In industrial process control, computer control, which makes the closed‐loop system a sampled‐data one containing both continuous‐ and discrete‐time signals, is widely used. In contrast with traditional approximation methods, sampled‐data synthesis, a direct digital controller design procedure without approximation, has received increasing attention during the past few years. However, many of the existing results cannot be applied to sampled‐data control design for the uncertain systems. In this paper, a result of robust asymptotic stability of sampled‐data systems with constraints on the state is presented based on a result on practical stability for these systems. Then the robust sampled‐data control for a class of uncertain nonlinear systems with constraints on the output is developed. The problem is formulated from vehicle steering control with constraint on the side slip angle of body. The result is described by some matrix inequalities which could be solved by an iterative algorithm based on the linear matrix inequality technique. Finally, a numerical example is presented to demonstrate the result. Copyright © 2002 John Wiley & Sons, Ltd.     

Robust stabilization and H∞ control of uncertain stochastic time‐delay systems with nonlinear perturbation

This paper investigates the problem of delay‐dependent robust stochastic stabilization and H_∞ control for uncertain stochastic nonlinear systems with time‐varying delay. System uncertainties are assumed to be norm bounded. Firstly, by using novel method to deal with the integral terms, robustly stochastic stabilization results are obtained for stochastic uncertain systems with nonlinear perturbation, and an appropriate memoryless state feedback controller can be chosen. Compared with previous results, the new technique can sufficiently utilize more negative items information. Then, robust H_∞ control for uncertain stochastic system with time‐varying delay and nonlinear perturbation is considered, and the controller is designed, which will guarantee that closed‐loop system is robustly stochastically stable with disturbance attenuation level. Finally, two numerical examples are listed to illustrate that our results are effective and less conservative than other reports in previous literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust adaptive fault-tolerant control for time delay uncertain nonlinear systems with time-varying performance bounds

In this paper, a robust adaptive fault tolerant controller guaranteeing with time-varying performance bounds is designed for a class of time delay uncertain nonlinear systems subject to actuator failures and external disturbance. The influence of time delay on the system is mitigated and the system performance can be guaranteed by introducing a positive nonlinear control gain function and the generalised restricted potential function. A new method with more design degrees of freedom is developed to ensure the norm of the system state within a-priori, user-defined time varying performance bounds. Using the online estimation information provided by adaptive mechanism, a robust adaptive fault-tolerant control method guaranteeing time varying performance bounds is proposed. It is shown that all the signals of the resulting closed-loop system are bounded and the system state less than a-priori, user-defined performance bounds. Finally, simulation results are given to demonstrate the efficacy of the proposed fault-tolerant control method.     

Robust adaptive control for a class of uncertain strict‐feedback nonlinear systems

In this paper, robust adaptive control is presented for a class of perturbed strict‐feedback nonlinear systems with both completely unknown control coefficients and parametric uncertainties. The proposed design method does not require the a priori knowledge of the signs of the unknown control coefficients. For the first time, the key technical Lemma is proven when the Nussbaum function is chosen by N(ζ)=ζ²cos(ζ), based on which the proposed robust adaptive scheme can guarantee the global uniform ultimate boundedness of the closed‐loop system signals. Simulation results show the validity of the proposed scheme. Copyright © 2008 John Wiley & Sons, Ltd.     

Discrete‐time robust H∞control of a class of nonlinear uncertain systems

This paper presents an approach to discrete‐time robust H^∞ control for a class of nonlinear uncertain systems on the basis of the use of Sum Quadratic Constraints. The approach involves controllers, which include copies of the system nonlinearities in the controller. The nonlinearities being considered are those that satisfy a certain global Lipschitz condition. The linear part of the controller is synthesized using linear robust H^∞ control theory, and this leads to a nonlinear controller, which gives an upper bound on the attainable disturbance attenuation level. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive event‐triggered global fast finite‐time control for a class of uncertain nonlinear systems

This article designs an adaptive event‐triggered controller to solve the problem of global finite‐time stabilization for a class of uncertain nonlinear systems. By using the symbol function technique, the event‐triggered error is completely compensated, the adaptive technique and the back‐stepping method are simultaneously applied to the controller design, and the new way of designing controller is completed on the basis of fast finite‐time stability theory. Subsequently, taking Lyapunov stability theorem into account, the system stability is proved, and the system is demonstrated by contradiction to be non‐zeno. Finally, giving a simulation example to display the feasibility of this method.     

A robust discrete‐time adaptive control approach for systems with almost periodic time‐varying parameters

A periodic adaptive control approach is proposed for a class of nonlinear discrete‐time systems with time‐varying parametric uncertainties which are almost periodic, and the only prior knowledge is the periodicity. The new adaptive controller updates the parameters and the control signal periodically in a pointwise manner over one entire period, in the sequel that achieves a bounded tracking convergence. The result is further extended to scenarios with unknown input gain, higher order dynamics, and tracking. Copyright © 2012 John Wiley & Sons, Ltd.     

一类非线性激励器系统的鲁棒自适应跟踪

考虑一类具有非线性激励器不确定系统的鲁棒跟踪问题，其不确定性是部分已知的。所构造的鲁棒自适应控制方案能确保系统的跟踪误差终极一致有界．与已有文献结果相比．未知参数估计的自适应律和控制器是连续的，从而使得所提出的设计方案在实际控制问题中易实现。且与具有线性激励器的系统一样具有较强的鲁棒性．最后通过数值算例进一步说明了该设计方案是有效的。     

A robust continuous‐time fixed‐lag smoother for nonlinear uncertain systems

This paper presents a scheme for the design of a robust fixed‐lag smoother for a class of nonlinear uncertain systems. The proposed approach combines a nonlinear robust estimator with a stable fixed‐lag smoother, to improve the estimation error covariance. The robust fixed‐lag smoother is based on the use of integral quadratic constraints and minimax linear quadratic regulator estimation and control theory. The state estimator uses a copy of the system nonlinearity in the estimator and combines an approximate model of the delayed states to produce a smoother signal. Also in this work, a characterization of the delay approximation error is presented, and the corresponding integral quadratic constraint is included in the design, which gives a guaranteed bound on the performance cost function. In order to see the effectiveness of the method, it is applied to a quantum optical phase estimation problem. Results show a significant improvement in the error covariance of the estimator when compared with a robust nonlinear filter. Copyright © 2015 John Wiley & Sons, Ltd.     

Integrated adaptive robust control for multilateral teleoperation systems under arbitrary time delays

With the increasing industrial requirements such as bigger size object, stable operation, and complex task, multilateral teleoperation systems extended from traditional bilateral teleoperation are widely developed. In this paper, the integrated control design is developed for multilateral teleoperation systems, where n master manipulators are operated by human to remotely control n slave manipulators cooperatively handling a target object. For the first time, the control objectives of multilateral teleoperation including stability, synchronization, transparency, and internal force distribution are clarified systematically. A novel communication architecture is proposed to cope with communication delays, where the estimated environmental parameters are transmitted from the slave side to the master, to replace the traditional environmental force measurement in the communication channel. A kind of nonlinear adaptive robust control technique is used to deal with nonlinearities, unknown parameters, and modeling uncertainties existing in the master, slave, and environmental dynamics, so that the excellent tracking performance is achieved in both master and slave sides. The coordinated motion/force control is designed in the slave side by the optimal internal force distribution among n slave manipulators, and the impedance control is designed in the master side to realize the target transparency behavior. In summary, the proposed control algorithm can achieve the guaranteed robust stability, the excellent synchronization and transparency performance, and the optimal internal force distribution simultaneously for multilateral teleoperation systems under arbitrary time delays and various modeling uncertainties. The simulation is carried out on a 2‐master/2‐slave teleoperation system, and the results show the effectiveness of the proposed control design. Copyright © 2015 John Wiley & Sons, Ltd.     

Multidimensional Taylor network adaptive control for MIMO time‐varying uncertain nonlinear systems with noises

In this paper, an adaptive control approach based on the multidimensional Taylor network (MTN) is proposed here for the real‐time tracking control of multiple‐input–multiple‐output (MIMO) time‐varying uncertain nonlinear systems with noises. Two MTNs are used to formulate the optimum control and adaptive filtering approaches. The feed‐forward MTN controller (MTNC) is developed to realize the precise tracking control. The closed‐loop errors between the filtered outputs and expected values are directly chosen as the MTNC's inputs. A valid initial value selection scheme for the weights of the MTNC, which can ensure the initial stability of adaptive process, is introduced. The proposed MTNC can update its weights online according to errors caused by system's uncertain factors, based on stable learning rate. The resilient backpropagation algorithm and the adaptive variable step size algorithm via linear reinforcement are utilized to update the MTNC's weights. The MTN filter (MTNF) is developed to eliminate measurement noises and other stochastic factors. The proposed adaptive MTN filtering system possesses the distinctive properties of the Lyapunov theory–based adaptive filtering system and MTN. Lyapunov function of the filtering errors between the measured values and MTNF's outputs is defined. By properly choosing the weights update law in the Lyapunov sense, the MTNF's outputs can asymptotically converge to the desired signals. The design is independent of the stochastic properties of the input disturbances. Simulation of the MTN‐based control is conducted to test the effectiveness of the presented results.     

Finite‐time stability of linear fractional‐order time‐delay systems

In this paper, a finite‐time stability results of linear delay fractional‐order systems is investigated based on the generalized Gronwall inequality and the Caputo fractional derivative. Sufficient conditions are proposed to the finite‐time stability of the system with the fractional order. Numerical results are given and compared with other published data in the literature to demonstrate the validity of the proposed theoretical results.     

Tuning functions‐based robust adaptive tracking control of a class of nonlinear systems with time delays

In this paper, an adaptive backstepping tracking control scheme is proposed for a class of nonlinear state time‐varying delay systems, which are subject to parametric uncertainties and external disturbances. The bounds of the time delays and their derivatives are assumed to be unknown. Tuning functions method is exploited to construct the control law and adaptive laws. Unknown time‐varying delays are compensated by using appropriate Lyapunov–Krasovskii functional. It is shown that the proposed controller can guarantee the boundedness of all the closed‐loop signals. The tracking performance can be adjusted by choosing suitable design parameters. At the end, a simulation example is provided to illustrate the effectiveness of the design procedure. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive Finite‐Time Robust Control of Nonlinear Delay Hamiltonian Systems Via Lyapunov‐Krasovskii Method

This paper investigates the adaptive finite‐time robust control problem of a class of nonlinear time‐delay Hamiltonian systems via the Lyapunov‐Krasovskii (L‐K) method, and proposes some delay‐dependent results on the issue. Different from existing works, this paper first presents a time‐varying finite‐time stability (FTS) criterion via an L‐K functional approach, and obtains two FTS conditions by constructing specific L‐K functionals. Then, the adaptive finite‐time robust control problem is investigated for nonlinear time‐delay port‐controlled Hamiltonian (PCH) systems, and a control design procedure is presented. Finally, the effectiveness of the results is demonstrated by an illustrative example.