Pattern-based NN control for uncertain pure-feedback nonlinear systems

Implementing human-like learning and control for nonlinear dynamical systems operating in different control situations is an important and challenging issue. This paper presents a pattern-based neural network (NN) control strategy for nonlinear pure-feedback systems via deterministic learning (DL). Firstly, an appropriately designed adaptive neural dynamic surface controller is proposed to achieve the finite time tracking control. By analyzing the recurrent property of NN input signals, a partial persistent excitation (PE) condition for radial basis function (RBF) network is established, the implicit desired control dynamics under different control situations are accurately identified via DL in the case that the dimension of NN input is reduced. And a set of pattern-based experienced actual and virtual controllers is constructed using the learned knowledge. Secondly, to classify different control situations, when the system is operating in different control situations but controlled by current normal experienced controller, the dynamics of each subsystem are accurately identified via DL, n sets of dynamical estimators are constructed using the learned knowledge. Thirdly, in the recognition phase, n sets of residuals are achieved by comparing each set of estimators with the monitored system, sudden change in the control situation is rapidly recognized based on the principle of the earliest occurrence of the minimum residual. Finally, in the control phase, according to the recognition result, the correct experienced actual and virtual controllers will be selected to control the plant, guaranteed stability and superior control performance are achieved without any further re-adaptation online. Simulation studies are given to verify the proposed scheme can not only acquire and memorize knowledge like humans, but also reuse the learned knowledge to achieve rapid recognition and control of current control situation.     

Adaptive fault-tolerant control with prescribed performance for switched nonlinear pure-feedback systems

In this paper, the problem of adaptive fuzzy fault-tolerant control is investigated for a class of switched uncertain pure-feedback nonlinear systems under arbitrary switching. The considered actuator failures are modeled as both lock-in-place and loss of effectiveness. By utilizing mean value theorem, the considered pure-feedback systems are transformed into a class of switched nonlinear strict-feedback systems. Under the framework of backstepping design technique and common Lyapunov function (CLF), an adaptive fuzzy fault-tolerant control (FTC) method with predefined performance bounds is developed. It is proved that under the proposed controller, all the signals of the close-loop systems are bounded and the state tracking error for each step remains within the prescribed performance bound (PPB) regardless of actuator faults and the system switchings. In addition, the tracking errors and magnitudes of control inputs can be reduced by adjusting the PPB parameters of errors in the first and last steps. The simulation results are provided to show the effectiveness of the proposed control scheme.     

Global sampled-data output feedback stabilization for a class of stochastic nonlinear systems with time-varying delay

This paper studies the global sampled-data output feedback stabilization problem for a class of stochastic nonlinear systems. The considered system is in non-strict feedback form with unknown time-varying delay. A state observer is introduced to estimate the unmeasured states. With the help of the backstepping method, a linear sampled-data output feedback controller is constructed. By choosing an appropriate Lyapunov–Krasoviskii functional and an allowable sampling period, it is shown that the stochastic system can be globally asymptotically stabilized in the mean square sense under the developed control scheme. Finally, two examples are presented to verify the effectiveness of the designed control scheme.     

Robust event-driven tracking control with preassigned performance for uncertain input-quantized nonlinear pure-feedback systems

This paper presents a simplified design methodology for robust event-driven tracking control of uncertain nonlinear pure-feedback systems with input quantization. All nonlinearities and quantization parameters are assumed to be completely unknown. Different from the existing event-driven control approaches for systems with completely unknown nonlinearities, the main contribution of this paper is to design a simple event-based tracking scheme with preassigned performance, without the use of adaptive function approximators and adaptive mirror models. It is shown in the Lyapunov sense that the proposed event-driven low-complexity tracker consisting of nonlinearly transformed error surfaces and a triggering condition can achieve the preselected transient and steady-state performance of control errors in the presence of the input quantization.     

Probability-constrained tracking control for a class of time-varying nonlinear stochastic systems

This paper is concerned with the probability-constrained tracking control problem for a class of time-varying systems with stochastic nonlinearities, stochastic noises and successively packet loss. The main purpose of this paper is to design a time-varying observer and tracking controller such that (1) the probabilities of both the estimation error and tracking error confined to given ellipsoidal sets are larger than prescribed constants, and (2) the ellipsoids are minimized in the sense of matrix norm at each time point. By using a stochastic analysis method, the probability constrained tracking control problem is solved and sufficient conditions are obtained in terms of recursive linear matrix inequalities. A recursive optimization algorithm is developed to design the observer and tracking controller such that not only the addressed probability constrained aim is satisfied, but also the ellipsoidal sets are minimized. At last, a simulation example is given to illustrate the effectiveness and applicability of the developed approach.     

Adaptive practical finite-time stabilization for switched nonlinear systems in pure-feedback form

This paper investigates adaptive practical finite-time stabilization for a class of switched nonlinear systems in pure-feedback form. Under some appropriate assumptions, a controller and adaptive laws are designed by using adding a power integrator technique, and neural networks are employed to approximate unknown nonlinear functions. It is proved that all states of the closed-loop system converge to a small neighborhood of the origin in finite time. Finally, two simulations are provided to show the feasibility and validity of the proposed control scheme.     

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.     

Sampled observer-based adaptive output feedback fault-tolerant control for a class of strict-feedback nonlinear systems

This paper studies the sampled outputs-based adaptive fault-tolerant control problem for a class of strict-feedback uncertain nonlinear systems, where the nonlinear functions are allowed to include the unmeasured system states. Within the framework, a sampled output observer is introduced to jointly estimate the system states and parameters. By combining the estimated states and the supervisory switching strategy, an adaptive fault-tolerant controller is designed to achieve the desirable tracking performance. By using Lyapunov stability theory, it is proved that all the signals of the closed-loop systems are bounded and the tracking error converges to an adjustable neighbourhood of the origin eventually both in the fault free and faulty cases. Especially, if the outputs are available all the time, the proposed output feedback fault-tolerant control method can ensure the tracking error satisfy the prescribed performance bounds regardless of the faults. Finally, two examples are used to illustrate the effectiveness of the proposed method.     

Event-triggered fault estimation and sliding mode fault-tolerant control for a class of nonlinear networked control systems

This paper is concerned with integrated event-triggered fault estimation (FE) and sliding mode fault-tolerant control (FTC) for a class of discrete-time Lipschtiz nonlinear networked control systems (NCSs) subject to actuator fault and disturbance. First, an event-triggered fault/state observer is designed to estimate the system state and actuator fault simultaneously. And then, a discrete-time sliding surface is constructed in state-estimation space. By the use of a reformulated Lipschitz property and delay system analysis method, the sliding mode dynamics and state/fault error dynamics are converted into a unified linear parameter varying (LPV) networked system model by taking into account the event-triggered scheme, actuator fault, external disturbance and network-induced delay. Based on this model and with the aid of Lyapunov–Krasovskii functional method, a delay-dependent sufficient condition is derived to guarantee the stability of the resulting closed-loop system with prescribed H_∞ performance. Furthermore, an observed-based sliding mode FTC law is synthesized to make sure the reachability of the sliding surface. Finally, simulation results are conducted to verify the effectiveness of the proposed method.     

Containment control of multi-agent systems via a disturbance observer-based approach

This paper deals with the containment control problem for multi-agent systems with exogenous disturbances. A disturbance observer-based control approach is employed to estimate the disturbances generated by an exogenous system. Consequently, distributed disturbance observer-based containment control protocols are proposed by using the state feedback control and the output feedback control, respectively. Furthermore, with the help of algebraic graph theory and Lyapunov stability theory, sufficient conditions are established to ensure that multi-agent systems with exogenous disturbances can achieve containment control via the disturbance observer-based approach. Finally, the effectiveness of our theoretical results is verified by providing numerical simulation examples.     

Sampled-data control of a class of switched nonlinear systems under asynchronous switching

This paper focuses on an output feedback stabilization problem for a class of switched nonlinear systems in non-strict feedback form under asynchronous switching via sampled-data control. Since the output of the considered systems is measurable only at the sampling instants, an observer is designed with a tunable scaling gain to estimate the state, and then a sampled-data controller is constructed with the sampled estimated state. As a distinctive feature, a merging virtual switching signal is introduced to describe the asynchronous switching generated by detecting the activation of the subsystem. By choosing an appropriate Lyapunov function, it is proved that the constructed controller with dwell time constraint can globally stabilize the considered systems under asynchronous switching. Finally, the effectiveness of the proposed method is illustrated by two examples.     

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.     

Adaptive neural design frame for uncertain stochastic nonlinear non-lower triangular pure-feedback systems with input constraint

This paper dedicates to dealing with the adaptive neural design problem for uncertain stochastic nonlinear systems with non-lower triangular pure-feedback form and input constraint. On the basis of the mean-value theorem, the pure-feedback structure is first transformed into the desired affine structure, and then the well-known backstepping technology is applied to construct the actual input signal of the controller. Although the considered system has a fairly complex structure, a new adaptive neural tracking controller design frame is established via the flexible application of radial basis function (RBF) neural networks’ (NNs’) structural characteristics. The proposed design frame guarantees the control objective of this paper can be achieved. Finally, a simulation example is given to further illustrate the availability of the proposed control scheme.     

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.     

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.     

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.     

Fuzzy adaptive control of nonlinear MIMO systems with unknown dead zone outputs

This paper addresses a novel fuzzy adaptive control method for a class of uncertain nonlinear multi-input multi-output (MIMO) systems with unknown dead-zone outputs and immeasurable states. The immeasurable states under consideration are estimated by designing a fuzzy state observer. Based on the properties of the Nussbaum-type function, the difficulty of fuzzy adaptive control caused by the unknown dead zone outputs of MIMO nonlinear uncertain systems is overcome. The presented design algorithm not only guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, but also ensures that the outputs of the MIMO system converge to a small neighborhood of the desired outputs. The main contributions of this research lie in that the developed MIMO systems are more general, and an efficient design method of output-feedback controller is investigated for the studied MIMO systems, which is more applicable in practical environment. Simulation results illustrate the effectiveness of the proposed scheme.     

Neural networks-based adaptive output feedback control for a class of uncertain nonlinear systems with input delay and disturbances

This paper focuses on the problem of adaptive output feedback control for a class of uncertain nonlinear systems with input delay and disturbances. Radial basis function neural networks (NNs) are employed to approximate the unknown functions and an NN observer is constructed to estimate the unmeasurable system states. Moreover, an auxiliary system is introduced to compensate for the effect of input delay. With the aid of the backstepping technique and Lyapunov stability theorem, an adaptive NN output feedback controller is designed which can guarantee the boundedness of all the signals in the closed-loop systems. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.     

Resilient sampled-data control design for singular networked systems with random missing data

This paper proposes an active resilient control strategy for singular networked control systems with external disturbances and missing data scenario based on sampled-data scheme. To characterize the missing data scenario, a stochastic variable satisfying Bernoulli distributed white sequence is introduced. Based on this scenario, in this paper, two different models are proposed. For both the models, by using Lyapunov–Krasovskii functional approach, which fully uses the available information about the actual sampling pattern, some sufficient conditions in terms of linear matrix inequalities (LMIs) are separately obtained to guarantee that the resulting closed-loop system is admissible and strictly dissipative with a prescribed performance index. In particular, Jensen’s and Wirtinger based integral inequalities are employed to simplify the integral terms which appeared in the derivation of stabilization results. Then, if the obtained LMIs are feasible, the corresponding parameters of the designed resilient sampled-data controller are determined. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed control design technique.     

On stability for sampled-data nonlinear ADRC-based control system with application to the ball-beam problem

This paper mainly concerns with the stability analysis of the sampled-data nonlinear active disturbance rejection control (ADRC)-based control system. Firstly, a class of single-input-single-output (SISO) continuous plant is discretized using zero-order-hold (ZOH), and several kinds of digital implementation methods for the nonlinear extended state observer (NLESO) are newly proposed. Then the sampled-data nonlinear ADRC (NLADRC) based closed-loop system is transformed into a discrete-time Lurie-like system, to which linear matrix inequality (LMI)-based sufficient conditions for absolute stability and robust absolute stability are obtained. The sufficient conditions provide convenient and effective methods for determining the stability and its relationship with the parameters of the controller, the plant and the sampling period. Using the ball-beam system as an example, the proposed results are verified in both simulations and experiments.