Control For Strict-feedback Nonlinear Systems Research Articles

A signal smoothness-based approach to prescribed performance control of strict-feedback nonlinear systems with quantization

This paper investigates the prescribed performance control problems of strict-feedback nonlinear systems with state quantization, input quantization, unknown disturbances and unknown nonlinear functions. Since the quantized states are discontinuous, the differentiability of the stabilizing functions in the backstepping technique cannot be guaranteed. To this end, a smooth approximation of the quantized states is first obtained by introducing a class of functions. Based on this smooth approximation, a quantized control scheme is presented such that all the closed-loop signals are bounded with the prescribed performance bounds. It is shown that the unknown nonlinearities and the unknown disturbances are not estimated and the derivatives of the stabilizing functions are eliminated. Lastly, two examples are provided to illustrate the effectiveness of the presented method.

A signal smoothness-based approach to prescribed performance control of strict-feedback nonlinear systems with quantization

This paper investigates the prescribed performance control problems of strict-feedback nonlinear systems with state quantization, input quantization, unknown disturbances and unknown nonlinear functions. Since the quantized states are discontinuous, the differentiability of the stabilizing functions in the backstepping technique cannot be guaranteed. To this end, a smooth approximation of the quantized states is first obtained by introducing a class of functions. Based on this smooth approximation, a quantized control scheme is presented such that all the closed-loop signals are bounded with the prescribed performance bounds. It is shown that the unknown nonlinearities and the unknown disturbances are not estimated and the derivatives of the stabilizing functions are eliminated. Lastly, two examples are provided to illustrate the effectiveness of the presented method.

Predefined Time and Accuracy Adaptive Fault-Tolerant Control for Nonlinear Systems with Multiple Faults

This work mainly studies the issue of predefined time and accuracy adaptive fault-tolerant control for strict-feedback nonlinear systems with multiple faults. The faults in the controlled system include actuator faults and external system faults. The unknown functions for nonlinear systems are approximated by fuzzy logic systems (FLSs). And then, according to the backstepping technique and the predefined time stability theory, an adaptive fuzzy control algorithm is presented, which can make sure that all closed-loop system signals remain predefined time bound and the tracking error converges to a predefined accuracy within the predefined time. Ultimately, the effectiveness of the presented control algorithm is proved through two simulation examples.

Estimator-based neural adaptive event-triggered control for strict-feedback nonlinear systems with incomplete measurements

This article addresses a neural adaptive event-triggered tracking control for a class of strict-feedback nonlinear dynamics with incomplete measurements, which is novel on the research of Cyber-physical Systems. The incomplete measurement problem caused by packet loss, saturation, and other issues during data transmission can lead to the unavailability of system state variables, which can degrade system performance and even lead to instability. To solve these problems, a state estimator for data-losing case and two controllers for normal and data-losing cases are designed utilising event-triggered strategies which can reduce the burden of calculation and data transmission. Radial basis function neural networks are adopted to approximate the unknown nonlinear system functions. A strict stability analysis in probability shows that the control laws for the considered strict-feedback nonlinear system can guarantee all the closed-loop to be uniformly ultimately bounded in mean square. Two examples are performed to demonstrate the effectiveness of the provided control method.

Neural-network-based adaptive control of strict-feedback nonlinear systems with actuator faults: Event-triggered communications strategy

This article considers the neural network-based event-triggered adaptive control problem for a class of strict-feedback nonlinear impulsive systems with actuator faults and external disturbances. It is well known that reducing computational resources and carrier loads is a long-standing task in the field of adaptive control. However, the event-triggered scheme used in traditional research still consumes relatively more resources. To solve the problem, the control scheme in this paper only updates the controller and weight parameters at the event-triggered moments. Dedicated efforts are made to certificate the stability of the system through a new Lyapunov theory, in such a way that the system maintains its stability well even under uncertainties. Finally, two emulation examples are exploited to demonstrate the efficacy and applicability of the proposed approach.

Adaptive Control of Strict-Feedback Nonlinear Systems Under Denial-of-Service: A Synthetic Analysis

Adaptive Control of Strict-Feedback Nonlinear Systems Under Denial-of-Service: A Synthetic Analysis

Adaptive optimal backstepping control for strict-feedback nonlinear systems with time-varying partial output constraints

This paper investigates the optimal backstepping control strategy for strict-feedback nonlinear systems subject to input saturation and time-varying partial output constraints. Compared with the existing results on output constraints, the time-varying partial output constraint is a more general constraint that can start and end at any time during the system operation, or remain unconstrained, which can be called as output constraints occurring in a limited time interval (OCOLT). A special barrier function is embedded into the optimal performance index function to satisfy the OCOLT condition under the optimal control framework, and a shift function is introduced to address the function discontinuity caused by the OCOLT problem. Then, an auxiliary system and a disturbance observer are respectively constructed to handle the influence of the input saturation and compounded disturbances. Meanwhile, the simplified reinforcement learning algorithm, employing the identifier-critic-actor architecture, is developed to achieve the optimal control objective within the framework of the backstepping technology. Moreover, the proposed optimal control method ensures the semi-globally uniformly ultimately bounded of all signals within the closed-loop system. Finally, two simulation examples are given to further prove the effectiveness of the presented optimal control approach.

Prescribed performance event-triggered fuzzy optimal tracking control for strict-feedback nonlinear systems

The prescribed performance event-triggered optimal tracking control problem is considered for a class of uncertain strict-feedback nonlinear systems with external disturbances. First, the disturbance observers are constructed to estimate external disturbances. Then, the controller contains an adaptive fuzzy controller and an optimal compensation term, in which the unknown nonlinearities and cost function are approximated by the fuzzy logic systems. An adaptive fuzzy controller is established by the dynamic surface control (DSC) technique, which is addressed to handle “computation complexity” issue occurred in conventional backstepping approach. Based on adaptive dynamic programming (ADP) method, an optimal compensation term is developed by minimizing the cost function. Furthermore, communication load is reduced via embedding event-triggered mechanism. In addition, the tracking error can be restricted in the prescribed region with the aid of the prescribed performance control. Thus, the whole control scheme can not only ensure that the tracking error converges to a boundary but also achieve optimization, reduce the communication burden and avoid “computation complexity” issue. The boundedness of all signals in the closed-loop is proved. Finally, the simulation examples illustrate the validity of the designed control scheme.

Fixed-time command-filtered composite adaptive neural fault-tolerant control for strict-feedback nonlinear systems

The research investigates the fixed-time command-filtered composite adaptive neural fault-tolerant (FCCANF) control issue of strict-feedback nonlinear systems (SFNSs). There exist unknown functions and bounded disturbances in the considered systems. Radial basis function neural networks (RBFNNs) will be used in the estimate of the unknown functions. By the serial–parallel estimation models (SPEMs), the forecast biases and the track biases can change the weights of RBFNNs and the approximate characteristics of RBFNNs will be improved. Then, utilizing the novel fixed-time command filter and adaptive disturbance observers, the issue of complex explosion will be effectively solved and the external disturbance is effectively compensated. Subsequently, by utilizing the adaptive control technique, a novel FCCANF controller is developed. Additionally, we have that the system internal variables are bounded and the output variable inclines to a little interval around zero in fixed time which is not determined by the system initial variables. Eventually, numerical and practical examples are shown to prove the availability of the obtained control technique.

Predefined-time event-triggered adaptive tracking control for strict-feedback nonlinear systems with full-state constraints

This paper investigates the problem of predefined-time event-triggered adaptive tracking control for strict-feedback nonlinear systems (SFNSs) with full-state constraints. To handle asymmetric full-state constraints, a nonlinear state-dependent function (NSDF) that purely depends on the constraint state is introduced. Then, a switching threshold event-triggered mechanism (ETM) is designed to enhance usage efficiency of communication resources. Moreover, a predefined-time event-triggered adaptive tracking controller is constructed by incorporating a smooth tuning function into each step of the backstepping design based on dynamic surface technology. Under such a control scheme, the output tracking error can be steered to the small neighborhood of the origin within the user setting time. Compared to various previous control schemes developed for full-state constrained systems, our proposed method can circumvent the demanding feasibility conditions in controller designs. Finally, a simulation result is given to illustrate the effectiveness of the control scheme.

Event-Triggered Neural-Network Adaptive Control for Strict-Feedback Nonlinear Systems: Selections on Valid Compact Sets.

This article studies neural-network (NN) adaptive control for strict-feedback nonlinear systems with matched uncertainties and event-triggered communication. Radial basis function NNs (RBFNNs) are used in the backstepping design approach to compensate for nonlinear uncertain functions. The concept of valid compact sets for RBFNN adaptive controllers is proposed, where a local RBFNN approximator is defined and the closed-loop state can remain. To guarantee the existence of such valid compact sets, a new property on RBFNNs is presented, which shows that, in some properly designed RBFNNs, the norm of their ideal weight vectors can always become arbitrarily small. By utilizing this property, the selections on valid compact sets are investigated, resulting in rigorous proof on RBFNN adaptive controllers to solve a local tracking problem with a given smooth enough reference signal. Subsequently, to save limited communication resources, a Zeno-free event-triggering mechanism in controller-to-actuator channels is proposed. Under this event-triggered adaptive controller, the corresponding tradeoff among the tracking performance, computational burden, and communication consumption is analyzed. Furthermore, two extensions are made to the general local function approximator, which is in the form of a weight vector multiplying a group of basis functions, and to the communication in sensor-to-controller channels. Finally, several simulation results are provided to illustrate the efficiency and feasibility of the obtained results.

Command filter-based adaptive fuzzy fixed-time tracking control for strict-feedback nonlinear systems with nonaffine nonlinear faults

Command filter-based adaptive fuzzy fixed-time tracking control for strict-feedback nonlinear systems with nonaffine nonlinear faults

Adaptive Uniform Performance Control of Strict-Feedback Nonlinear Systems With Time-Varying Control Gain

In this paper, we present a novel adaptive performance control approach for strict-feedback nonparametric systems with unknown time-varying control coefficients, which mainly includes the following steps. Firstly, by introducing several key transformation functions and selecting the initial value of the time-varying scaling function, the symmetric prescribed performance with global and semi-global properties can be handled uniformly, without the need for control re-design. Secondly, to handle the problem of unknown time-varying control coefficient with an unknown sign, we propose an enhanced Nussbaum function (ENF) bearing some unique properties and characteristics, with which the complex stability analysis based on specific Nussbaum functions as commonly used is no longer required. Thirdly, by utilizing the core-function information technique, the non-parametric uncertainties in the system are gracefully handled so that no approximator is required. Furthermore, simulation results verify the effectiveness and benefits of the approach.

Adaptive reinforcement learning optimal tracking control for strict-feedback nonlinear systems with prescribed performance

The reinforcement learning-based prescribed performance optimal tracking control problem is considered for a class of strict-feedback nonlinear systems in this paper. The unknown nonlinearities and cost function are approximated by radial-basis-function (RBF) neural network (NN). The overall controller consists of an adaptive controller and an optimal compensation term. Firstly, the adaptive controller is designed by backstepping control method. Subsequently, the optimal compensation term is derived via policy iteration by minimizing cost function. In addition, depending on the prescribed performance control, the tracking error can be limited in the prescribed area. Therefore, the whole control scheme can effectively guarantee that the tracking error converges to a bound with prescribed performance while the cost function is minimized. The stability analysis shows that all signals in the closed-loop system are bounded. Finally, the effectiveness and advantages of the designed control strategy are illustrated by the simulation examples.

Finite-time performance guaranteed event-triggered adaptive control for nonlinear systems with unknown control direction

This paper studies the issue of finite-time performance guaranteed event-triggered (ET) adaptive neural tracking control for strict-feedback nonlinear systems with unknown control direction. A novel finite-time performance function is first constructed to describe the prescribed tracking performance, and then a new lemma is given to show the differentiability and boundedness of the performance function, which is important for the verification of the closed-loop system stability. Furthermore, with the help of the error transformation technique, the origin constrained tracking error is transformed into an equivalent unconstrained one. By utilizing the first-order sliding mode differentiator, the issue of “explosion of complexity” caused by the backstepping design is adequately addressed. Subsequently, an ingenious adaptive updated law is given to co-design the controller and the ET mechanism by the combination of the Nussbaum-type function, thus effectively handling the influences of the measurement error resulted from the ET mechanism and the challenge of the controller design caused by the unknown control direction. The presented event-triggered control scheme can not only guarantee the prescribed tracking performance, but also alleviate the communication burden simultaneously. Finally, numerical and practical examples are provided to demonstrate the validity of the proposed control strategy.

Event-Triggered Communication-Based Control for Strict-Feedback Nonlinear Systems.

In this article, we shall investigate the event-triggered communication control problem for strict-feedback nonlinear systems with measurement outputs. First, two event-triggered communication schemes are designed. Based on both event-triggered schemes, the measurement output and control input signals are only transmitted at triggering time instants, which saves communication costs from the sensor to the controller and from the controller to the actuator. Meanwhile, Zeno behavior can be excluded under the proposed triggering schemes. Second, since the full-state information is not available to the controller, by developing an observer, the system state is estimated and a controller based on estimated state information is designed. Due to the irregular sampling of information communication and state estimation error affects each other, the parameters of the state observer, the controller, and the event-triggering mechanism should be jointly designed. It is proved that the closed-loop system state converges to the origin. Finally, a simulation example verifies the validity of the obtained theoretical result.

Command-filtered backstepping robust adaptive emotional control of strict-feedback nonlinear systems with mismatched uncertainties

Emotional models have recently gained increasing attention in the design of intelligent control systems because of their desirable properties, such as universal approximation and fast response. However, stable emotional controllers have generally been for full-state feedback linearizable systems with only matched uncertainties. They also require knowing the reference signal and its higher derivatives. In contrast, we propose here a command-filtered backstepping H∞ robust adaptive emotional controller (CFBRAEC) for strict-feedback nonlinear systems with mismatched uncertainties. Our approach applies command filters to address the “explosion of complexity” in backstepping control and introduces a compensating filter consistent with the H∞-based design to deal with the approximation errors of command filters. The command-filtered backstepping approach handles matched/mismatched uncertainties and disturbances while requiring only the reference signal and its first derivative to be known and continuous. Accordingly, CFBRAEC is more suitable for practical applications and applicable to a broader group of dynamic systems. The boundedness of the tracking error and other closed-loop signals are established based on Lyapunov theory. The effectiveness of CFBRAEC is shown through simulations in the presence of measurement noise and matched/mismatched disturbances with unknown bounds on two different uncertain nonlinear systems: an inverted pendulum and an electromechanical motor.

Observer-based Adaptive Fuzzy Control for Strict-feedback Nonlinear Systems with Prescribed Performance and Dead Zone

This paper proposes an observer-based fuzzy controller for strict-feedback nonlinear systems. A fuzzy state observer is designed to estimate unmeasurable system states via a fuzzy logic system to approximate the unknown nonlinear functions of the system. A tangent prescribed performance function is utilized to gather the tracking error in a small neighborhood of the origin. The control input is designed to deal with the dead-zone property of the system. The proposed controller can guarantee that all the signals in the closed-loop system are semi-globally, uniformly, and ultimately bounded. Simulation results demonstrate the effectiveness of the proposed controller.

Adaptive neural tracking control of strict-feedback nonlinear systems with event-triggered state measurement

This paper investigates the adaptive neural tracking control of the strict-feedback nonlinear systems, where the states are measured in an event-triggered manner so as to save the communication resources. As the neural networks (NNs) account for the unknown dynamics of the system, the minimum learning parameters (MLPs) are extracted from the weights of the NNs and the upper bounds of the disturbances. The estimates of the MLPs are updated in an event-triggered manner to ensure the approximation ability of the NNs and the stability of the closed-loop system. An adaptive neural model is established to substitute for the original strict-feedback system and direct the design of the backstepping-based control laws. The states of this adaptive model are reset to the measured states of the original system when the triggering condition is violated. The triggering condition is constructed in the compound form and with the adaptive threshold. The dead-zone operator is involved to avoid the accumulation of triggering instants. In this paper, we notice the problem of “jumps of virtual control laws” for the event-triggered control (ETC) in the backstepping frame, and a detailed formulaic definition is given in section 2.2. To solve this problem, the first-order filters are fabricated to provide the continuous substitutes for virtual control laws. In addition, the “complexity explosion” generated by direct differentiating of virtual control laws can be averted. Through the proposed scheme, the closed-loop system can be viewed as an impulsive dynamic system, and the semi-globally uniformly ultimate boundedness (SGUUB) of all the errors is proved. Finally, two examples validate the feasibility of the proposed control scheme.

Observer-Based Neuro-Adaptive Optimized Control of Strict-Feedback Nonlinear Systems With State Constraints.

This article proposes an adaptive neural network (NN) output feedback optimized control design for a class of strict-feedback nonlinear systems that contain unknown internal dynamics and the states that are immeasurable and constrained within some predefined compact sets. NNs are used to approximate the unknown internal dynamics, and an adaptive NN state observer is developed to estimate the immeasurable states. By constructing a barrier type of optimal cost functions for subsystems and employing an observer and the actor-critic architecture, the virtual and actual optimal controllers are developed under the framework of backstepping technique. In addition to ensuring the boundedness of all closed-loop signals, the proposed strategy can also guarantee that system states are confined within some preselected compact sets all the time. This is achieved by means of barrier Lyapunov functions which have been successfully applied to various kinds of nonlinear systems such as strict-feedback and pure-feedback dynamics. Besides, our developed optimal controller requires less conditions on system dynamics than some existing approaches concerning optimal control. The effectiveness of the proposed optimal control approach is eventually validated by numerical as well as practical examples.