Nonstrict Feedback Research Articles

Barrier Lyapunov functions-based adaptive neural tracking control for non-strict feedback stochastic nonlinear systems with full-state constraints: A command filter approach

<p style='text-indent:20px;'>In this paper, an adaptive neural network command filter controller is investigated for a class of non-strict feedback stochastic nonlinear systems with full-state constraints. By using the command filter approach and error compensation mechanism, the "explosion of complexity" problem caused by the backstepping method and the filtering errors are eliminated. In order to avoid excessive and burdensome computations and to ensure that the backstepping method works normally for non-strict feedback structures, neural networks are employed to approximate the unknown nonlinear functions that contain all the state variables of the system. Meanwhile, the barrier Lyapunov functions are constructed to ensure the constraints are not transgressed. Finally, based on the Lyapunov stability theorem, an adaptive neural tracking controller is presented to guarantee that all the signals of the closed-loop system are semi-global uniformly ultimately bounded (SGUUB) in probability, and the tracking error converges to a small neighborhood around the origin, besides the full-state constraints are not violated. The simulation results are given to confirm the effectiveness of the proposed control method.</p>

Adaptive Fuzzy Event-Triggered Control for Non-Strict Feedback Nonlinear Systems With Input Delay and Full State Constraints

Adaptive Fuzzy Event-Triggered Control for Non-Strict Feedback Nonlinear Systems With Input Delay and Full State Constraints

Fast Finite-Time Fuzzy Control for a Class of Nonstrict Feedback Systems with Input Quantization

Fast Finite-Time Fuzzy Control for a Class of Nonstrict Feedback Systems with Input Quantization

Adaptive neural quantized control for fractional-order full-state constrained non-strict feedback systems subject to input fault and nonlinearity

In this work, an adaptive neural network (NN)-based quantized fault-tolerant controller (FTC) has been designed for incommensurate fractional-order (FO) nonlinear systems (NSs) in the non-strict feedback form subject to independent asymmetric time-varying full-state constraints, input quantization, unknown dynamics, infinite number of actuator faults and unknown input nonlinearities. It is assumed that the controller communicates with the actuator via a network with limited bandwidth. To avoid network congestion, the control signal is first quantized by an asymmetric hysteresis quantizer (HQ), then transmitted to the actuator via the network. By incorporating the backstepping algorithm, barrier Lyapunov functions (BLFs) and fractional direct Lyapunov stability (FDLS) theorem, a novel method has been proposed to design a control scheme for FO state constrained NSs and establish the closed-loop stability. In this method, the Lyapunov function of each step of the backstepping algorithm is chosen based on the BLF and parameter estimation error of the considered step and their boundedness is shown from the last step to the first one. Under the proposed control approach, the full-state constraints are met, the tracking error can be made small by selecting proper design parameters and all closed-loop signals remain bounded. Finally, three simulation examples have been provided to demonstrate the designed controller effectiveness.

Event-triggered adaptive neural control for state-constrained switched nonlinear systems based on nonlinear shifting function technique

This paper addresses the event-triggered tracking control design for state-constrained switched nonstrict feedback nonlinear systems. With the help of a time-varying nonlinear shifting function (TVNSF) introduced into the switched nonlinear system, the proposed solution is seen as a unified tool regardless of whether the constraint conditions are state constraints, output constraint, or even no constraint. Also, by allowing the triggering error to vary with the switching signal in time, the negative effects of the mismatch between the individual controller and the subsystem on system performance are trumped. Moreover, by using constructed individual Lyapunov function that depends on the lower bound of the control gain function of individual subsystem, a novel switching signal satisfying the average dwell time (ADT) is provided to ensure the boundedness of all variables in the closed-loop system. Finally, the proposed theory is carried over into a mass-spring-damper system to verify its effectiveness.

Adaptive Backstepping Control of Uncertain Sandwich-Like Nonlinear Systems With Deadzone Nonlinearity

A systematic differentiator-based adaptive backstepping control methodology is proposed for a class of sandwich-like nonlinear system with unknown state-dependent deadzone nonlinearity and parametric uncertainties. The novelty of our approach is that a high-order sliding mode differentiator is utilized to estimate the nonstrict feedback coupling term resulting from the sandwiched deadzone, and all the outputs of the differentiator are integrated into the backstepping procedure based on Lyapunov functions with flat zone recursively. By this approach, all the unknown parameters are estimated online, the discontinuity of the virtual input caused by bound estimations is avoided. It is shown that the ultimate boundedness of all the closed-loop signals is achieved and the output tracking error converges to a preset set. Simulation is performed to verify the theoretical findings.

Observer-based adaptive fuzzy finite time control for non-strict feedback nonlinear systems with unmodeled dynamics and input delay

Observer-based adaptive fuzzy finite time control for non-strict feedback nonlinear systems with unmodeled dynamics and input delay

Command filter-based adaptive fault-tolerant tracking control for uncertain non-strict feedback multi-agent systems with or without state constraints

This paper considers the topic of adaptive leader-following fault-tolerant tracking control for a class of non-strict feedback nonlinear multi-agent systems with or without state constraints in a unified solution. Through the use of certain transformation techniques, the original constraint system is recast as a new completely unconstrained system. Compared with the existing results, the limitation that the constraint functions need upper bound is relaxed. By employing radial basis function neural networks (RBFNNs) to approximate the unknown functions. A novel adaptive fault-tolerant consensus tracking control (CTC) manner is raised with command filtered backstepping design. Then, through the Lyapunov stability analysis, the proposed scheme can ensure all signals in the closed-loop system are cooperative semi-globally uniformly ultimately bounded (SGUUB). Finally, simulation example confirms the efficiency of the proposed method.

Event-triggered adaptive neural finite-time tracking control for non-strict feedback stochastic nonlinear systems with unknown time-varying control directions and input nonlinearities

This paper focuses on dynamic-surface-based event-triggered adaptive neural finite-time tracking control for a category of non-strict feedback stochastic nonlinear system subject to unknown time-varying control directions, and input nonlinearities. Firstly, an improved event-triggered mechanism is presented, which simultaneously considers tracking error variables and compensating for event errors in threshold value. Secondly, a novel Lemma is provided to address concurrently the issues of Nussbaum terms in stability analysis and stochastic system finite-time stability. Thirdly, neural networks are utilized to cope with unknown functions. In addition, the Nussbaum functions are applied to identify time-varying unknown control directions and input nonlinearities. Moreover, the errors of the dynamic surface technique are compensated successfully by error compensation signals. By combining the proposed Lemma 1 and event-triggered adaptive neural finite-time control scheme, finite-time stability of considered systems in probability can be guaranteed, the tracking error can drive to a small neighborhood of the origin in finite time, and the Zeno behavior can be excluded. Finally, the effectiveness of the designed control scheme has been demonstrated through a second-order numerical system and a mass-spring-damper example.

Adaptive Fuzzy Fixed-Time Tracking Control for Switched High-Order Multi-Agent Systems With Input Delay

This paper investigates the adaptive fuzzy fixed-time-based distributed consensus tracking control for non-strict feedback nonlinear switched high-order multi-agent systems (MASs) with completely unknown function, input delay, switched behavior dynamics (possibly asynchronous) and high powers (possibly different). In this work, the “explosive of complexity” issue is overcome by designing an improved fixed-time-based nonlinear filter. Unlike traditional linear filters, this paper skillfully introduces auxiliary terms (tanh function and cubic function) into each filter, which can completely compensate the effects resulted by filter errors and ensure the closed-loop system fixed-time convergence. Meanwhile, input delay is deal with a robust compensation signal constructed via a finite integral of the past control values. Besides, this paper adopts separable function technique to avoid the control gain of each virtual controller appearing in the next virtual controller, thus reducing the complexity of control actions. In the backstepping framework, a distributed fixed-time-based control scheme was presented, which can ensure that all the closed-loop signals are bounded within a fixed-time. Numerical simulation and practical example further verify the effectiveness of the developed control scheme.

Prescribed Performance Fuzzy Adaptive Output Feedback Control for Nonlinear MIMO Systems in a Finite Time

This article studies the fuzzy adaptive output feedback control design problem for nonstrict feedback multi-input–multi-output nonlinear systems with full-states prescribed performance in finite time. Fuzzy logic systems are introduced to solve the problem of unknown nonlinear dynamics. And on this basis, a fuzzy-based state observer is designed to observe the unmeasurable state. Further, by combining the adaptive back-stepping control algorithm and the nonlinear filters, a novel dynamic surface control (DSC) method is proposed, which not only solves the computational complexity explosion problem inherent in the back-stepping control algorithm, but also improves the control performance, in contrast to the traditional DSC methods with linear filters. Besides, to further improve the tracking performance under the structure of full-states prescribed performance, a new Lyapunov function is designed considering the transform error constraint. Based on the Lyapunov theory, the stability of the closed-loop system is analyzed to ensure that all signals of the closed-loop system are semiglobal practical finite-time stability. Finally, to elaborate on the feasibility and effectiveness of the proposed control method, a simulation example is provided.

Real‐time implementation of adaptive neural backstepping controller for battery‐less solar‐powered PMDC motor

A low-cost battery-less solar-powered PMDC motor using an adaptive backstepping Chebyshev neural network controller to track the desired speed for any change in irradiance and load torque is proposed in this paper. The neural network is used for approximating the variable load torque because of its approximation property. The computational burden of the control law is reduced because of the orthogonal property of Chebyshev polynomials. The asymptotically stable system is obtained by tuning the weights of neurons in accordance with the Lyapunov stability analysis. From the Lyapunov control function of backstepping control design procedure, the control law is obtained by an innovative way of elucidating the cubic equation, in place of resolving the derivative of the control law in the control function. This approach eliminates the constraints caused by the non-strict feedback system for the backstepping control approach and also this reduces ripples in the duty cycle which makes its appropriateness in real-time. To ensure its robustness in tracking the desired speed at a faster time and minimum overshoot, simulations are done for an extensive range of variations in irradiance and load torque, and the obtained results are assessed by comparing it with the PID controller and conventional backstepping controller. Because of the use of neural network the robustness of the proposed controller is ensured with enhanced transient and steady state responses. A prototype is developed in the laboratory and the obtained results are assessed by comparing it with the backstepping controller and PID controller.

Improved Adaptive Fuzzy Control for Non-Strict Feedback Nonlinear Systems: a Dynamic Compensation System Approach

This paper investigates the tracking control problem for uncertain nonlinear non-strict feedback systems (NSFSs) in the presence of full-state constraints and unmeasured disturbances. It is of great practical significance to realize the full-state constraint under disturbed conditions. In view of the non-strict feedback problem, a novel design framework of the state feedback control is given based on the newly proposed dynamic compensation system (DCS). Different from the traditional backstepping, the estimated signal based on the adaptive fuzzy system is indirectly introduced into the virtual and actual control laws through the DCS, which has the advantage of avoiding the algebraic-loop problem in NSFSs. Accordingly, the disturbance observer (DO) design method is improved based on this framework. Integrating the DCS into the DO design avoids the coupling problem between the disturbance and the unknown nonlinear function. An improved barrier Lyapunov function (BLF) is designed by introducing the concept of the inducible factor, and full-state constraints can be guaranteed after a transitional period for any initial state. By combining the DCS, the DO and the improved BLF, a novel adaptive fuzzy tracking control law is constructed, and all the signals in the closed-loop system are semiglobally uniformly ultimately bounded. Finally, the theoretical analysis and simulation results show that all states meet the corresponding constraints while meeting the stability.

Dual-Condition event-Triggered distributed adaptive neural control for multi-Agent systems with nonlinear fault

This paper studies the cooperative adaptive dual-condition event-triggered tracking control problem for the uncertain nonlinear nonstrict feedback multi-agent systems with nonlinear faults and unknown disturbances. Under the framework of backstepping technology, a new threshold update method is designed for the state event-triggered mechanism. At the same time, we develop a novel distributed dual-condition event-triggered strategy that combined the fixed threshold triggered mechanism acted on the controller with the new event-triggered mechanism, which can better reduce the waste of communication bandwidth. To deal with the algebraic loop problem caused by the non-affine nonlinear fault, the Butterworth low-pass filter is introduced. At the same time, the unknown function problems are solved by the neural network technology. All signals of the system are semiglobally uniformly ultimately bounded and the tracking performance is achieved, which proved by the Lyapunov stability theorem. Finally, the results of the simulation test the efficiency of the proposed control scheme.

Full-state time-varying asymmetric constraint control for non-strict feedback nonlinear systems based on dynamic surface method

We investigate the tracking control problem for a non-strict feedback nonlinear system with external disturbance and time-varying asymmetric full state constraints. Firstly, the unknown nonlinear term with external disturbance in the system are estimated by fuzzy logic system. The backstepping method is applied to the design of adaptive fuzzy controller. However, to prevent that the constraints are overstepped by introducing an improved log-type time-varying asymmetric barrier Lyapunov function (TABLF) in each step of backstepping design. Secondly, the dynamic surface control (DSC) is introduced in the designed algorithm to solve the computational explosion problem of controller caused by the derivative of control law. The proposed control scheme can speed up the tracking speed of the system. Compared with the previous work, it is verified that the combination of DSC and TABLF can obtain good performance within the constraint range, and can ensure fast and stable tracking convergence under external disturbance. Finally, two simulation examples verify the performance of the adaptive controller.

Distributed adaptive bipartite consensus tracking of high-order nonstrict-feedback nonlinear multi-agent systems

This paper is concerned with the problem of adaptive bipartite tracking problem for multi-agent systems (MASs) over signed directed graphs with unknown nonlinear functions. Each following agent is modelled by a higher-order nonlinear system in nonstrict-feedback form. The virtual and the actual control items of the considered system are the power functions with positive odd integers rather than linear items. A distributed neural-based adaptive backstepping scheme is proposed, where the unknown nonlinear dynamics are approximated by Neural networks. Under the proposed protocol, the bipartite output tracking errors converge to a small neighbourhood of the origin and all the signals of the closed-loop system remain semiglobally uniformly ultimately bounded. Since the considered high-order non-strict feedback nonlinear MASs in our paper include some existing nonlinear MASs as the special case, our result can be extended to control more general nonlinear MASs. Finally, the simulation results illustrate the validity of the proposed schemes by a numerical example and a practical example about a group of forced damped pendulums.

Observer‐based controller for nonaffine time‐delayed systems subject to input nonlinearities, state constraints, and unknown control direction

SUMMARYIn this work, an adaptive observer‐based control scheme has been designed for uncertain nonaffine nonstrict feedback systems subject to state time delay, various types of input nonlinearities, time‐varying asymmetric state constraints, and unknown control direction. Compared to the existing controllers for systems with state constraints, the designed control scheme in this work can be applied to state‐constrained systems with nonaffine structure subject to state delays, unknown control direction, and different types of input nonlinearities, while full‐states measurement is not required. Moreover, by introducing a novel saturated Nussbaum function in the present work, not only has the problem of unknown control direction been handled, but also the probability of a control shock due to applying the conventional Nussbaum functions has been eliminated. The system unknown dynamics has been approximated by using neural networks (NNs), and by updating the maximum norm of NNs weight vectors, only one adaptive law is required for the controller implementation. By employing appropriate Lyapunov functions, it has been shown that all signals in the closed‐loop system are bounded, state constraints are satisfied, and the output tracking error can be made small by selecting appropriate design parameters. The effectiveness of the designed control scheme has been shown through two simulation studies. Moreover, the superiority of the proposed saturated Nussbaum function in comparison with conventional Nussbaum functions has been shown via simulation.

Event-triggered funnel control for network systems with unknown dynamic leader based on BP neural networks

This paper studies the cooperative adaptive funnel tracking control problem for a class of uncertain nonlinear nonstrict feedback multi-agent systems with nonlinear faults, and the dynamic leader has nonlinear unknown function. By designing two value functions and combining with the back propagation neural networks, an event-triggered strategy that can be adjusted automatically is designed to reduce the waste of communication bandwidth. The Butterworth low-pass filter signal is introduced to solve the non-smooth function problems. In addition, the radial basis function neural networks are used to approximate unknown functions in the system. Then, an event-triggered control protocol is constructed, which can achieve the tracking performance and all signals of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, some simulation results confirm the effectiveness of the proposed control scheme.

Command-Filter-Based Fixed-Time Bipartite Containment Control for a Class of Stochastic Multiagent Systems

This article studies the command-filter-based fixed-time bipartite containment control problem for a class of nonlinear stochastic multiagent systems (MASs). The considered stochastic MASs in nonstrict feedback form is subject to unknown nonlinear functions and stochastic disturbances, which can be solved by exploiting the universal approximation property of radial basis function neural networks. In addition, the event-triggered mechanism is used to improve the utilization of communication resources while avoiding Zeno behavior. The control protocol based on the command-filtered backstepping technique is proposed to ensure that the followers can converge to the convex hull formed by the leaders. Moreover, the closed-loop stability of stochastic MASs is proved to be semiglobal practical fixed-time stability. Finally, a numerical example simulation and an actual system simulation about a group of five single-link manipulator systems are presented to verify the effectiveness of the proposed method.

Adaptive command-filtered finite-time control of non-strict feedback stochastic non-linear systems

In this paper, an adaptive neural network (NN) finite-time command filter controller for a class of non-strict feedback stochastic non-linear systems has been investigated. Using error compensation signals and NNs, a command filter controller is presented which guarantees that all the signals of the closed-loop system are practical finite-time stable and the output signal tracks the given reference signal under the bounded error. In the design procedure, NNs are employed to approximate unknown non-linear functions, which contain all the state variables of the whole system, in order to avoid excessive and burdensome computations and ensure that the backstepping method works normally for non-strict feedback systems. Meanwhile, the “explosion of complexity” problem caused by the backstepping method is avoided using the command filter approach. The control scheme not only resolves the “explosion of complexity” problem but also eliminates the filtering error in finite-time. Finally, the simulation results are given to prove the effectiveness of the proposed control method.