Nonstrict-feedback Nonlinear Systems Research Articles

Global adaptive practical tracking control for high‐order uncertain nonstrict feedback nonlinear systems with unknown control coefficients

SummaryIn this article, the problem of global adaptive practical tracking for high‐order uncertain nonstrict feedback nonlinear systems with unknown control coefficients is studied. To avoid the algebraic loop problem associated with the nonstrict feedback condition and guarantee the controllability of the tracking error, a novel dual dynamic gain scaling method is introduced to compensate nonlinearities and the tracking error simultaneously. Besides, by incorporating the sign functions into the design of adding a power integrator, a general approach for the handing of unknown control coefficients and the direction design of the controller is developed. The presented control scheme can ensure that all system states are globally bounded without constraints on state variables while the reference signal is tracked with expected precision. Three simulation examples, including a practical application, are provided to illustrate the validity of the control scheme.

Practical fixed-time neural control for MIMO non-strict feedback nonlinear systems: an adaptive neural network approach

ABSTRACT This paper studies the non-singular practical fixed-time neural adaptive control issues for multi-input and multi-output (MIMO) nonlinear systems with non-strict feedback form. Neural networks (NN) are used to estimate the unknown nonlinearities and deal with the problem of an algebraic loop. Under the framework of the backstepping control design, a practical fixed-time adaptive NN control method is developed by using the adding power integration technology. According to the Lyapunov function theory, it is proved that the closed-loop system is practical fixed-time stable, and the system can track the desired reference signal within a fixed time. Finally, the proposed practical fixed-time control method is applied to a multi-motor control platform, which proves the effectiveness of the control method.

Adaptive fuzzy finite-time output feedback fault-tolerant control for MIMO stochastic nonlinear systems with non-affine nonlinear faults

This paper investigates adaptive fuzzy finite-time output feedback fault-tolerant tracking control problem for multiple-input multiple-output (MIMO) stochastic non-strict feedback nonlinear systems with non-affine nonlinear faults and states unmeasured. Firstly, high-gain fuzzy state observers are constructed to overcome the state unmeasured problem in the system. Secondly, the mean-value theorem and input compensation techniques are employed to decouple non-affine nonlinear faults, and the resulting unknown control coefficients problem is handled using Nussbaum functions. In addition, dynamic surface control techniques and error compensation mechanisms are considered in the controller design, which effectively decreases the computational complexity of the control scheme. By combining the adaptive backstepping technique with finite-time control, a novel adaptive fuzzy dynamic surface finite-time output feedback fault-tolerant tracking control algorithm is proposed. The designed controller guarantees that all signals in the stochastic systems are semi-global finite-time stable in probability (SGFSP) as well as the tracking errors can converge to a small neighborhood within the origin in finite-time. Finally, two simulation examples are introduced to verify the effectiveness of the suggested control strategy.

Fixed-Time Fault-Tolerant Consensus Control for High-Order Nonlinear Multiagent Systems Under Directed Topology

This paper addresses the fixed-time fault-tolerant consensus control problem for high-order nonstrict-feedback nonlinear multi-agent systems under directed topology. A distributed high-order fixed-time observer is proposed to obtain the accurate estimations of the full states of the leader. Different from the fixed-time observer design methods, a much more concise estimate for the upper bound of the convergence time is provided. Based on the fixed-time observer and adding a power technique, a fixed-time tracking protocol is designed for a group of followers subject to unknown nonidentical dynamics and unpredictable actuation faults. It is shown that there is no need to know the information of the nonstrict-feedback nonlinear dynamics, the control gains, and the actuation faults in the control design and implementation completely, which is deemed favorable in practice. Simulation results are provided to validate the effectiveness of the developed control scheme.

Safe tracking control based on a secure boundary protection method for nonlinear systems with unknown initial tracking condition

Aiming to the sudden change of the system actual output constraint, a novel safe tracking control strategy is investigated for a class of non-strict feedback nonlinear systems with unknown initial tracking condition in this paper. A secure boundary protection method (SBPM) based on prescribed performance and a new prescribed finite-time performance function (PFTPF) are proposed. The SBPM can automatically construct two adjustable secure boundaries, so that the system output meets both the control performance prescribed by the PFTPF and the secure boundary constraint. In order to solve the problem of the excessive control input jitter caused by the sudden change of output constraint, a bidirectional filtering smoothing mechanism (BFSM) is proposed. The proposed SBPM can effectively ensure the safe tracking control of the system with unknown initial tracking condition when the actual output constraint changes suddenly, and ensure that the system has the prescribed finite-time control performance given by the PFTPF. Differently from the existing works, the system output will be strictly constrained into the actual output constraint without the prediction for the system output value. Finally, the effectiveness of this proposed method is verified by simulations.

Event-triggered fixed-time tracking control for nonstrict feedback nonlinear systems with unknown coexistence uncertainties

In fixed time interval, event-triggered tracking control for nonlinear systems with unknown coexistence uncertainties has been investigated in this paper. The control scheme can handle unknown virtual control gains, external disturbances and nonsymmetric input dead zone. The unknown nonlinearities are identified by using neural networks. In the traditional backstepping design process, a bound estimation strategy is developed to design the adaptive parameters. Based on the adaptive estimation tactic, the severe coexistence uncertainties caused by the unknown virtual control gains, external disturbances, nonsymmetric input dead zone and identify errors can be estimated online, such that the robust performance of the system can be effectively elevated. Note that, the priori knowledge of the boundary are not required for the proposed bound estimation mechanism, and the control gains and the slope of dead zone have been relaxed to be completely unknown. In view of fixed time stability design scheme, the singularity phenomenon for the differential of virtual control signal has been conquered by employing the piecewise functions method. Furthermore, to decrease the resource consumption, a dynamic event triggered rule is used to cut down the data sampling and communication. And two practical examples are used to verify the effectiveness.

Fixed-time fuzzy tracking control for high-order nonstrict feedback nonlinear systems with unknown virtual control gains and actuator faults

In this paper, fuzzy fault-tolerant tracking control is investigated for high-order nonstrict feedback nonlinear systems in fixed time interval. The gain fault and bias fault in actuator are considered for high-order nonstrict feedback nonlinear systems. Contrary to the existing results, an adaptive estimation tactic is proposed to estimate the coexisting uncertainties such that no priori knowledge is needed for the adaptive parameters, in spite of unknown virtual control gains, nonlinear uncertainties, time-varying disturbances and actuator faults. Based on this tactic, the unknown virtual control gains are slackened to completely unknown, which is more practical. Unlike the general fixed time control tactics, the singularity problem has been overthrew by using the inequality transformation strategy without destroying the control performance. The growth assumptions are removed and the complex nonstrict feedback structure is overcome with the support of fuzzy logic systems (FLS). Finally, two examples demonstrate the validity of the formulated method.

Adaptive Fault-Tolerant Tracking Control for Discrete-Time Nonstrict-Feedback Nonlinear Systems With Stochastic Noises

This paper discusses the problem of fault-tolerant tracking control for discrete-time nonstrict-feedback nonlinear systems in the presence of stochastic noises and actuator faults. The system is characterized by a discrete-time nonstrict-feedback structure and multiplicative stochastic noise related to the states, which poses a challenge for the design and analysis of the fault-tolerant controller. Moreover, the considered actuator faults include multiplicative and additive faults without prior information. By integrating the properties of the backstepping framework and neural networks, and by introducing an adaptive fault compensation term, a novel fault-tolerant tracking control strategy is proposed. The effects of faults are compensated and the difficulties caused by the system structure are overcome, avoiding the algebraic loop problem and overcoming the causal contradiction. Given specific parameters, the designed fault-tolerant controller can ensure that the tracking error converges to an adjustable region regarding the origin and that all system signals are uniformly bounded concerning the mean-square sense. The simulation examples illustrate the effectiveness of the designed fault-tolerant control method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —As system complexity has been increasing, practical systems are often affected by faults when performing tracking control. Fault-tolerant control can provide acceptable robustness and improve system safety. On the one hand, many practical systems are nonlinear, difficult to model mathematically and accurately, and affected by stochastic noises. On the other hand, with digital control, the object is a discrete-time system. In practical applications, the upper bounds of the faults and the noises are often unknown. In this paper, a novel adaptive fault-tolerant control method is proposed for the more general uncertain discrete-time nonlinear systems, i.e., nonstrict-feedback nonlinear systems, with stochastic noises and actuator faults. Neural networks and an adaptive fault compensation term are integrated into the fault-tolerant controller. By adjusting the controller parameters properly, it is ensured that the tracking error converges to a small neighborhood of zero in the event of a fault occurring. In future research, sensor faults, input constraints, optimal control design, and applications in multi-agent systems will be considered.

Neural networks-based adaptive fault-tolerant control for a class of nonstrict-feedback nonlinear systems with actuator faults and input delay

&lt;abstract&gt;&lt;p&gt;This paper addresses the challenge of adaptive control for nonstrict-feedback nonlinear systems that involve input delay, actuator faults, and external disturbance. To deal with the complexities arising from input delay and unknown functions, we have incorporated Pade approximation and radial basis function neural networks, respectively. An adaptive controller has been developed by utilizing the Lyapunov stability theorem and the backstepping approach. The suggested method guarantees that the tracking error converges to a compact neighborhood that contains the origin and that every signal in the closed-loop system is semi-globally uniformly ultimately bounded. To demonstrate the efficacy of the proposed method, an electromechanical system application example, and a numerical example are provided. Additionally, comparative analysis was conducted between the Pade approximation proposed in this paper and the auxiliary systems in the existing method. Furthermore, error assessment criteria have been employed to substantiate the effectiveness of the proposed method by comparing it with existing results.&lt;/p&gt;&lt;/abstract&gt;

Adaptive Neural Finite-Time Control of Non-Strict Feedback Nonlinear Systems With Non-Symmetrical Dead-Zone.

The control design method for a class of non-strict feedback nonlinear systems is studied in this brief considering uncertain nonlinearities and unknown non-symmetrical input dead-zone. Combining with the finite-time command filtered backstepping (FCFB) technique, a novel finite-time adaptive control approach is proposed in which a neural network-based methodology is adopted to cope with the uncertain nonlinearities in the non-strict feedback form. The input dead-zone model is transformed into a simple linear system with unknown gain and bounded disturbance which is estimated by an adaptive factor. Using the finite-time Lyapunov theory, the system convergence is proved. And the effectiveness of the proposed control scheme is verified through comparative numerical simulations.

Neural networks-based adaptive command filter control for nonlinear systems with unknown backlash-like hysteresis and its application to single link robot manipulator

&lt;abstract&gt;&lt;p&gt;In this paper, an adaptive neural network control problem for nonstrict-feedback nonlinear systems with an unknown backlash-like hysteresis and bounded disturbance was presented. Radial basis function neural networks (RBFNN) were used to approximate the unknown functions and the problem of the explosion of complexity problem was handled by utilizing the command filter method. Furthermore, the influence of an unknown backlash-like hysteresis input was addressed by approximating an intermediate variable. Based on the backstepping method and the command filter technique, an adaptive neural network controller was designed via the approximation abilities of RBFNN. With the help of the Lyapunov stability theory, the proposed controller ensures that all of the signals in closed-loop systems are bounded and that the tracking error fluctuates close to the origin within a bounded area. Finally, a real-world example based on the single-link manipulator was shown to demonstrate the viability of the presented approach.&lt;/p&gt;&lt;/abstract&gt;

Adaptive Iterative Learning Control for Nonlinearly Parameterized Non-Strict Feedback Nonlinear Systems with Full-State Constraints

Adaptive Iterative Learning Control for Nonlinearly Parameterized Non-Strict Feedback Nonlinear Systems with Full-State Constraints

Optimized Adaptive Fuzzy Security Control of Nonlinear Systems With Prescribed Tracking Performance.

This article studies the optimized fuzzy prescribed performance control problem for nonlinear nonstrict-feedback systems under denial-of-service (DoS) attacks. A fuzzy estimator is delicately designed to model the immeasurable system states in the presence of DoS attacks. To achieve the preset tracking performance, a simper prescribed performance error transformation is constructed considering the characteristics of DoS attacks, which helps obtain a novel Hamilton-Jacobi-Bellman equation to derive the optimized prescribed performance controller. Furthermore, the fuzzy-logic system, combined with the reinforcement learning (RL) technique, is employed to approximate the unknown nonlinearity existing in the prescribed performance controller design process. An optimized adaptive fuzzy security control law is then proposed for the considered nonlinear nonstrict-feedback systems subject to DoS attacks. Through the Lyapunov stability analysis, the tracking error is proved to approach the predefined region by the preset finite time, even in the presence of DoS attacks. Meanwhile, the consumed control resources are minimized due to the RL-based optimized algorithm. Finally, an actual example with comparisons verifies the effectiveness of the proposed control algorithm.

Finite-Time Stability Control of Uncertain Nonlinear Systems With Self-Limiting Control Terms.

In this brief, we define a self-limiting control term, which has the function of guaranteeing the boundedness of variables. Then, we apply it to a finite-time stability control problem. For nonstrict feedback nonlinear systems, a finite-time adaptive control scheme, which contains a piecewise differentiable function, is proposed. This scheme can eliminate the singularity of derivative of a fractional exponential function. By adding a self-limiting term to the controller and the virtual control law of each subsystem, the boundedness of the overall system state is guaranteed. Then the unknown continuous functions are estimated by neural networks (NNs). The output of the closed-loop system tracks the desired trajectory, and the tracking error converges to a small neighborhood of the equilibrium point in finite time. The theoretical results are illustrated by a simulation example.

Predefined-Time Adaptive Fault-Tolerant Control for Switched Odd-Rational-Power Multi-Agent Systems

This paper studies the distributed adaptive neural network (NN) predefined-time (PT) fault-tolerant consensus tracking control for unknown non-strict feedback nonlinear multi-agent systems (MASs) with time-varying full state constraints (TVFSCs), arbitrary switching behavior functions (possibly asynchronous), actuator faults and high powers. Compared with existing results, the convergence time estimation bound in this paper is less conservative due to the upper bound of convergence time presents as a tuning parameter. This paper avoids the control gain of each virtual controller to appear in the next virtual controller by using separable function technique, so it can reduce the control action complexity. Besides, this paper does not use any filters or piecewise continuous function in the controller design process, which can effectively avoid the potential singularity problem. An adaptive NN fault-tolerant consensus tracking controller is designed via backstepping technique and tangent barrier Lyapunov functions (BLF-Tans), which can ensure that all the closed-loop signals are bounded within a PT and the TVFSC bounds are not violated. Finally, numerical simulation and practical example further verify the effectiveness of the presented control algorithm. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Many practical (underactuated, weakly coupled and unstable mechanical systems) control systems can be modeled as uncertain high-order MAS with high powers. Due to the influence of environment and other factors, the values of some variables in the practical systems are limited and cannot be arbitrarily selected. In addition, the actual systems may fail due to human factors and in most of the relevant literatures, it is often assumed that the powers are equal to 1 and only achieve the controlled systems asymptotic stability as time approaches infinity. Therefore, in this paper, an adaptive PT fault-tolerant control scheme is developed for MASs with high powers, time-varying full state constraints and actuator faults. The effectiveness of the control scheme is illustrated based on simulation study.

Finite-Time Adaptive Quantized Motion Control for Hysteretic Systems With Application to Piezoelectric-Driven Micropositioning Stage

This study addresses the finite-time adaptive output feedback quantized control problem for nonstrict-feedback nonlinear systems subject to unknown hysteresis and time delays. An estimated inverse compensator (EIC) is constructed to mitigate hysteresis by resorting to a generalized Duhem model. A Lyapunov–Krasovskii functional is employed to deal with the uncertainties of time delays. However, the system performance deteriorates when the quantized signal is directly applied to the hysteretic system. To overcome this obstacle, this study proposes a new composite quantizer consisting of an adaptive state-estimation filter and a modified hysteretic quantizer, in which the former facilitates the state approximation by incorporating the feedback information of the system and the latter regulates the communication rate. With the proposed finite-time prescribed adaptive quantized control with an estimated inverse compensator (EIC–FPAQC) scheme, all solutions of the closed-loop systems are semiglobal practical finite-time stable and the tracking error can be ensured in a predefined accuracy. Finally, experiments are conducted on a piezoelectric-driven micropositioning stage to demonstrate the effectiveness of the proposed method.

Adaptive neural optimal tracking control of stochastic nonstrict-feedback nonlinear systems with output constraints

In this article, a novel adaptive optimal control method is proposed for constrained stochastic nonlinear systems in the form of nonstrict-feedback. The output constraints are handled by employing nonlinear mapping, and the controller is composed of feedforward and optimal parts. The feedforward controller is designed based on dynamic surface control technology with Gaussian properties, where a dynamic signal and linearly parametrized neural networks are employed to approximate the unknown dynamics and unavailable nonlinear functions, respectively. Using the mean value theorem and Young’s inequality, only one parameter must be online tweaked at each step. In the optimal part, the cost function is approximately obtained using adaptive dynamic programming for the optimal control law. All signals in the closed-loop systems are analytically proved to be semi-globally uniformly ultimately bounded in the probabilistic space. Numerical simulations are provided to verify the effectiveness of the proposed approach.

Event-trigger-based composite adaptive fuzzy control for nonlinear time-varying state constraint systems with asymmetric input saturation

In this paper, a novel composite adaptive fuzzy control (AFC) based on the command filtered backstepping and event-triggered mechanism is proposed for nonstrict-feedback nonlinear systems with input saturation and time-varying full-state constraints. A fuzzy observer is designed to estimate the unmeasured states. Simultaneously, by introducing a serial-parallel estimation model, a fuzzy control tactic with the composite adaptive law of parameters is established which greatly increases the precision of unknown term estimation. In addition, the command filtering technique is employed to solve the issue of “explosion of complexity” and compensate for the errors caused by the command filters. The event-triggered mechanism is utilized to effectively decrease the data redundancy. By using the time-varying barrier Lyapunov functions (BLFs), all the states can remain within a prescribed time-varying interval. The designed controller can guarantee the convergence of the tracking error at the origin and the boundedness of all closed-loop signals. Finally, two simulation examples are carried out to validate the effectiveness of the proposed control scheme.

Observer-Based Adaptive Fuzzy Control of Nonstrict Feedback Nonlinear Systems With Function Constraints

In this paper, an adaptive fuzzy tracking control scheme based on fuzzy state observer is proposed for a class of uncertain non-strict feedback nonlinear systems with function constraints. In the first place, based on the approximation characteristic of fuzzy logic systems (FLSs), a fuzzy state observer is designed to estimate the immeasurable state variables in the controlled system. Next, under the framework of adaptive backstepping control technology, FLSs are selected not only to approximate unknown nonlinear functions, but also to avoid algebraic loop problem caused by non-strict feedback structure. At the same time, asymmetric Barrier Lyapunov functions (BLFs) are selected to solve the problem that system states are subject to function constraints, which are related to states and time. Then, Lyapunov stability theory is utilized to prove the stability of the controlled system, the realizability of function constraints and the convergence of output tracking errors. Finally, a simulation is given to check the effectiveness of the proposed control scheme.

Observer-Based Finite-Time Fault-Tolerant Control for Nonstrict-Feedback Nonlinear Systems With Multiple Uncertainties

In the fault-tolerant control (FTC) tasks of nonstrict-feedback nonlinear systems, unmeasurable states, disturbance, and actuator faults are recognized as the main factors that obstacle the effective controller design and, thus, the tracking performance improvement. To tackle these obstructions, a fuzzy observer is introduced to address the difficulties of the unmeasurable states involving nonstrict-feedback nonlinear systems by benefiting from the approximation property of fuzzy logic systems. Owing to the newly employed damping term in the intermediate control law being utilized to compensate for the possibly unlimited number of faults, the proposed FTC strategy is able to deal with actuator faults properly without imposing tighter requirements on the fault mechanism. To reach fast transient performance, stability of finite time is reached by exploiting the backstepping method. The investigated strategy ensures that all the responses of the systems are semiglobal practical finite-time stable. Meanwhile, the tracking error converges to a small neighborhood of the origin within finite time. In addition, to demonstrate its effectiveness, the provided approach is applied to the position tracking of a robotic system, which shows anticipated control performances in spite of various uncertainties.