A PI controller configuration for robust control of a class of nonlinear systems

The PI control configuration for stabilization and signal tracking of nonlinear systems is investigated. Semiglobal asymptotic stability and semiglobal practical signal tracking of the controlled system are proven using results from the theory of nonlinear singularly perturbed systems.     

Probabilistic fuzzy logic controller for uncertain nonlinear systems

This paper proposes a probabilistic fuzzy proportional - integral (PFPI) controller for controlling uncertain nonlinear systems. Firstly, the probabilistic fuzzy logic system (PFLS) improves the capability of the ordinary fuzzy logic system (FLS) to overcome various uncertainties in the controlled dynamical systems by integrating the probability method into the fuzzy logic system. Moreover, the input/output relationship for the proposed PFPI controller is derived. The resulting structure is equivalent to nonlinear PI controller and the equivalent gains for the proposed PFPI controller are a nonlinear function of input variables. These gains are changed as the input variables changed. The sufficient conditions for the proposed PFPI controller, which achieve the bounded-input bounded-output (BIBO) stability are obtained based on the small gain theorem. Finally, the obtained results indicate that the PFPI controller is able to reduce the effect of the system uncertainties compared with the fuzzy PI (FPI) controller.     

Distributed robust event-triggered adaptive control for a class of uncertain nonlinear multi-agent systems with actuator saturation

This paper studies the event-triggered consensus control problem for high-order uncertain nonlinear multi-agent systems with actuator saturation. By using a smooth Lipschitz function to approximate the saturation nonlinearity, an augment system and the Nussbaum function are adopted to deal with the residual terms of saturation nonlinearity based on adaptive backstepping method. Since excessive energy and communication resources will be consumed during the procedure to handle actuator saturation, two event-triggered mechanisms are proposed to save the communication resources and reduce the controllers’ update frequency. Whenever the triggered conditions are satisfied, the control signals transmitted to the actuators are updated and broadcasted to the neighboring area. A ’disturbance-like’ term is integrated so that the event-triggered control problem with actuator saturation can be transformed into a robust problem while the unknown disturbances are tackled by adaptive update laws. Moreover, the requirement for global communication topology known by all the agents is relaxed by introducing new estimators. All the signals in the closed-loop system are uniformly bounded and the consensus tracking errors are exponentially converged to a bounded set. Meanwhile, the Zeno behavior is excluded. Simulation results are employed to validate the advantages of our proposed methods.     

Command filtered robust adaptive NN control for a class of uncertain strict-feedback nonlinear systems under input saturation

This paper develops a robust adaptive neural network (NN) tracking control scheme for a class of strict-feedback nonlinear systems with unknown nonlinearities and unknown external disturbances under input saturation. The radial basis function NNs with minimal learning parameter (MLP) are employed to online approximate the uncertain system dynamics. The adaptive laws are designed to online update the upper bound of the norm of ideal NN weight vectors, and the sum of the bounds of NN approximation errors and external disturbances, respectively. An auxiliary dynamic system is constructed to generate the augmented error signals which are used to modify the adaptive laws for preventing the destructive action due to the input saturation. Moreover, the command filtering backstepping control method is utilized to overcome the shortcoming of dynamic surface control method, the tracking-differentiator-based control method, etc. Our proposed scheme is qualified for simultaneously dealing with the input saturation effect, the heavy computational burden and the “explosion of complexity” problems. Theoretical analysis illuminates that our scheme ensures the boundedness of all signals in the closed-loop systems. Simulation results on two examples verify the effectiveness of our developed control scheme.     

Design of observers for a class of discrete-time uncertain nonlinear systems with time delay

This paper is concerned with the problem of observer design for a class of discrete-time Lipschitz nonlinear state delayed systems with, or without parameter uncertainty. The nonlinearities are assumed to appear in both the state and measured output equations. For both the cases with and without norm-bounded time-varying parameter uncertainties, a design method is proposed, which involves solving a linear matrix inequality (LMI). When a certain LMI is satisfied, the explicit expression of a desired nonlinear observer is also presented. An example is provided to demonstrate the applicability of the proposed approach.     

Optimal finite-time passive controller design for uncertain nonlinear Markovian jumping systems

This paper studies the optimal finite-time passive control problem for a class of uncertain nonlinear Markovian jumping systems (MJSs). The Takagi and Sugeno (T–S) fuzzy model is employed to represent the nonlinear system with Markovian jump parameters and norm-bounded uncertainties. By selecting an appropriate Lyapunov-Krasovskii functional, it gives a sufficient condition for the existence of finite-time passive controller such that the uncertain nonlinear MJSs is stochastically finite-time bounded for all admissible uncertainties and satisfies the given passive control index in a finite time-interval. The sufficient condition on the existence of optimal finite-time fuzzy passive controller is formulated in the form of linear matrix inequalities and the designed algorithm is described as an optimization one. A numerical example is given at last to illustrate the effectiveness of the proposed design approach.     

Finite-time adaptive control for a class of switched stochastic uncertain nonlinear systems

This paper addresses the problem of global finite-time adaptive control for a class of switched stochastic uncertain nonlinear systems under arbitrary switchings. By applying the delicate introduction of coordinate transformations and adding a power integrator technique, an adaptive controller is constructed to guarantee that the system state is regulated to the origin almost surely in a finite time while maintaining the boundedness of the resulting closed-loop systems in probability. Two examples are given to illustrate the effectiveness of the proposed control scheme.     

An adaptive actuator failure compensation scheme for a class of nonlinear MIMO systems

This paper develops an adaptive actuator failure compensation scheme for control of a class of nonlinear multi-input–multi-output systems with redundant actuators subject to uncertain failures. The design method is to estimate the failure pattern parameters and the failure signal parameters first, and then use the parameter estimates to construct the adaptive failure compensation controller, the control law calculation is done simultaneously with parameter estimation without explicit failure detection. Closed-loop signal boundedness and asymptotic output tracking, despite the actuator failure uncertainties, are ensured analytically and verified by simulation results from its application to attitude control of a near space vehicle dynamic model.     

Adaptive sliding mode control for a class of MIMO nonlinear systems with uncertainties

This paper proposes an adaptive scheme of designing sliding mode control (SMC) for affine class of multi-input multi-output (MIMO) nonlinear systems with uncertainty in the systems dynamics and control distribution gain. The proposed adaptive SMC does not require any a priori knowledge of the uncertainty bounds and therefore offers significant advantages over the non-adaptive schemes of SMC design. The closed loop stability conditions are derived based on Lyapunov theory. The effectiveness of the proposed approach is demonstrated via simulations considering an example of a two-link robot manipulator and has been found to be satisfactory.     

Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems

In this paper, the observer-based sliding mode control (SMC) problem is investigated for a class of uncertain nonlinear neutral delay systems. A new robust stability condition is proposed first for the sliding mode dynamics, then a sliding mode observer is designed, based on which an observer-based controller is synthesized by using the SMC theory combined with the reaching law technique. Then, a sufficient condition of the asymptotic stability is proposed in terms of linear matrix inequality (LMI) for the overall closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability problem is also discussed. It is shown that the proposed SMC scheme guarantees the reachability of the sliding surfaces defined in both the state estimate space and the state estimation error space, respectively. Finally, a numerical example is given to illustrate the feasibility of the proposed design scheme.     

Fault diagnosis for a class of nonlinear uncertain systems using deterministic learning approach

In this paper, we propose a fault diagnosis (FD) approach for a class of nonlinear uncertain systems based on the deterministic learning approach (DLA). Specifically, an adaptive learning observer is constructed, in which the adaptive neural networks (NNs) are constructed to approximate the unknown system dynamics under normal and fault modes. Based on the strictly positive real (SPR) condition, the convergence of the state estimation can be guaranteed. When the system is undergoing a periodic or periodic-like (recurrent) motion, the states of the observer will also become recurrent. Thus through DLA, the partial persistent excitation (PE) condition of the associated subvectors of NNs is satisfied. By utilizing the partial (PE) condition, the uniformly completely observable (UCO) property of the identification system is analyzed and the exponential convergence condition of the identification system is derived. Under this condition, the unknown dynamics under normal and fault modes can be accurately identified along the system trajectory. And by utilizing the knowledge obtained in the identification phase, the fault can be detected in the diagnosis phase. The main attraction of this paper lies in the analytical result, which shows that the exponential convergence condition of the learning observer not only depends on the observer gain matrix, but also depends on the PE level of the regressor subvector of NN. Simulation results are included to illustrate the effectiveness of the proposed scheme.     

Adaptive disturbance attenuation for a class of uncertain nonlinear systems: A double-gain nonlinear observer method

This paper is concerned with the problem of adaptive disturbance attenuation for a class of nonlinear systems. The traditional adaptive methods are almost impossible to compensate the time-varying unknown disturbance by designing parameter adaptive laws without a priori knowledge about the bounds of external disturbances. To solve the problem, a new strategy is proposed by constructing an augmented system where the external disturbance is considered as another component of the augmented state vector. Based on this, a double-gain nonlinear observer is employed to estimate the state of the augmented nonlinear system. Further, an output feedback control strategy is designed, and it is proved that the proposed strategy ensures that all the signals are bounded and the tracking error exponentially converges to an adjustable compact set. Finally, an example is performed to demonstrate the validity of the proposed scheme.     

一类非线性不确定多时滞中立型系统的鲁棒自适应控制（英文）

针对一类不确定多时滞中立型非线性系统，在其非线性不确定项的范数有界，但其上界未知的情况下，论证了自适应鲁棒控制器存在的条件，并给出了能适应未知参数变化且使得最终闭环系统一致最终有界的鲁棒控制律的设计方法。最后，具体算例的仿真结果说明了此法的有效性。     

Observer-based adaptive fuzzy control of a class of MIMO non-strict feedback nonlinear systems

This paper investigates the adaptive fuzzy control design problem of multi-input and multi-output (MIMO) non-strict feedback nonlinear systems. The considered control systems contain unknown control directions and dead zones. Fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear functions, and the state observers are designed to estimate immeasurable states. By constructing a dead zone compensator and introducing a Nussbaum gain function into the backstepping technique, an adaptive fuzzy output feedback control method is developed. The proposed adaptive fuzzy controller is proved to guarantee the semi-globally uniformly ultimately bounded (SGUUB) of the closed-loop system, and can solve the control design problems of unmeasured states, unknown control directions and dead zones. The simulation results are given to demonstrate the effectiveness of the proposed control method.     

Adaptive quantized tracking control for a class of uncertain nonlinear systems with guaranteed transient performance

In this paper, an adaptive quantized control method with guaranteed transient performance is presented for a class of uncertain nonlinear systems. By introducing the Nussbaum function technique, the difficulty caused by quantization is handled and a novel adaptive control scheme is designed. In comparing with the existing adaptive control scheme, the key advantages of the proposed control scheme are that the controller needs no information about the parameters of the quantizer and the stability of the closed-loop system and the transient performance are independent of the coarseness of the quantizer. Based on Lyapunov stability theory and Barbalat’s Lemma, it is proven that all the signals in the resulting closed-loop system are bounded and the tracking error converges to zero asymptotically with the prescribed performance bound at all times. Simulation results are presented to verify the effectiveness of the proposed control method.     

An improved design strategy for approximation-based adaptive event-triggered tracking of a class of uncertain nonlinear systems

This paper presents an improved adaptive design strategy for neural-network-based event-triggered tracking of uncertain strict-feedback nonlinear systems. An adaptive tracking scheme based on state variables transmitted from the sensor-to-controller channel is designed via only single neural network function approximator, regardless of unknown nonlinearities unmatched in the control input. Contrary to the existing multiple-function-approximators-based event-triggered backstepping control results with multiple triggering conditions dependent on all error surfaces, the proposed scheme only requires one triggering condition using a tracking error and thus can overcome the problem of the existing results that all virtual controllers with multiple function approximators should be computed in the sensor part. This leads to achieve the structural simplicity of the proposed event-triggered tracker in the presence of unmatched and unknown nonlinearities. Using the impulsive system approach and the error transformation technique, it is shown that all the signals of the closed-loop system are bounded and the tracking error is bounded within pre-designable time-varying bounds in the Lyapunov sense.     

Predictor-based optimal robust guaranteed cost control for uncertain nonlinear systems with completely tracking errors constraint

In this paper, a novel composite controller is proposed to achieve the prescribed performance of completely tracking errors for a class of uncertain nonlinear systems. The proposed controller contains a feedforward controller and a feedback controller. The feedforward controller is constructed by incorporating the prescribed performance function (PPF) and a state predictor into the neural dynamic surface approach to guarantee the transient and steady-state responses of completely tracking errors within prescribed boundaries. Different from the traditional adaptive laws which are commonly updated by the system tracking error, the state predictor uses the prediction error to update the neural network (NN) weights such that a smooth and fast approximation for the unknown nonlinearity can be obtained without incurring high-frequency oscillations. Since the uncertainties existing in the system may influence the prescribed performance of tracking error and the estimation accuracy of NN, an optimal robust guaranteed cost control (ORGCC) is designed as the feedback controller to make the closed-loop system robustly stable and further guarantee that the system cost function is not more than a specified upper bound. The stabilities of the whole closed-loop control system is certified by the Lyapunov theory. Simulation and experimental results based on a servomechanism are conducted to demonstrate the effectiveness of the proposed method.     

Finite-time robust control of a class of nonlinear time-delay systems via Lyapunov functional method

This paper investigates the finite-time robust control problem of a class of nonlinear time-delay systems with general form, and proposes some new delay-independent and delay-dependent conditions on the issue. First, by developing an equivalent form, the paper studies finite-time stabilization problem, and presents some delay-dependent stabilization results by constructing suitable Lyapunov functionals. Then, based on the stabilization results, we study the finite-time robust control problem for the systems, and give a robust control design procedure. Finally, the study of two illustrative examples shows that the results obtained of the paper work well in the finite-time stabilization and robust stabilization for the systems. It is shown that, by using the method in the paper, the obtained results do not contain delay terms, which can avoid solving nonlinear mixed matrix inequalities and reduce effectively computational burden. Moreover, different from existing finite-time results, the paper also presents delay-dependent sufficient conditions on the finite-time control problem for the systems.