Nonstrict-feedback Systems Research Articles

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.

Adaptive Neural Tracking Control for Nonstrict-Feedback Nonlinear Systems with Unknown Control Gains via Dynamic Surface Control Method

This paper addresses the tracking control problem of nonstrict-feedback systems with unknown control gains. The dynamic surface control method, Nussbaum gain function control technique, and radial basis function neural network are applied for the design of virtual control laws, and adaptive control laws. Then, an adaptive neural tracking control law is proposed in the last step. By using the dynamic surface control method, the “explosion of complexity” problem of conventional backstepping is avoided. Based on the application of the Nussbaum gain function control technique, the unknown control gain problem is well solved. With the help of the radial basis function neural network, the unknown nonlinear dynamics are approximated. Furthermore, through Lyapunov stability analysis, it is proved that the proposed control law can guarantee that all signals in the closed-loop system are bounded and the tracking error can converge to an arbitrarily small domain of zero by adjusting the design parameters. Finally, two examples are provided to illustrate the effectiveness of the proposed control law.

Adaptive Fuzzy Asymptotic Tracking for Nonlinear Nonstrict-feedback Systems With Input Quantization

This article investigates an adaptive fuzzy tracking control problem for the nonlinear nonstrict-feedback systems with quantized input. The control signal has a new transformation since a time varying auxiliary signal and a hyperbolic tangent function are introduced to the controller. Moreover, a novel adaptive fuzzy control scheme is proposed such that input quantization can be solved by applying hysteresis quantizer in the case of unknown quantization parameters. For traditional adaptive quantization control schemes with nonstrict-feedback form, current studies have shown that the tracking error can only converge to a small neighborhood of the origin. Based on the proposed control method, all the signals in the closed-loop system are bounded, and the tracking error can converge to zero asymptotically. Finally, the effectiveness of the presented method is shown via the numerical simulation results.

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.

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.

NN adaptive optimal tracking control for a class of uncertain nonstrict feedback nonlinear systems

A novel reinforcement learning-based adaptive optimal controller is proposed to obtain the desired tracking performance for a class of nonlinear nonstrict feedback systems with uncertain dynamics in this paper. The main feature is that the proposed control scheme can handle the control problem that traditional reinforcement learning-based algorithm cannot deal with. To achieve the optimal control of the high-order system, the virtual and the actual control of the system are optimized by using reinforcement learning method. Radial basis function neural networks are employed to approximate the uncertain system dynamics, the optimal cost function and the optimal control law, respectively. According to Lyapunov stability theorem, it is proved that all the error signals in the closed-loop systems are semi-globally uniformly ultimately bounded (SGUUB) while the desired tracking control performance can be obtained. Simulation results are given to illustrate the effectiveness of the proposed algorithm.

Adaptive neural tracking control for high angle of attack maneuver with average dwell time

SummaryThis article attempts to study the high angle of attack maneuver from the perspective of switched system control. In view of the complex aerodynamic characteristics, an improved longitudinal attitude motion model is presented, which is a switched stochastic nonstrict feedback nonlinear system with distributed delays. The significant design difficulty is the completely unknown diffusion and drift terms and distributed delays with all state variables. Based on a technical lemma and neural networks, an improved smooth state feedback control law for nonstrict feedback systems is proposed without any growth assumptions. To eliminate the influence of distributed delays, an improved Lyapunov–Krasovskii function is constructed, which skillfully removes the constraint of the upper bound of the delay change rate. Then, by combining the average dwell‐time scheme and stochastic backstepping technique, an adaptive neural network tracking control law is designed, which extends a newly proposed switched system stability condition to the stochastic switched system. Theoretical analysis and flight control simulation experiments are provided to illustrate the effectiveness of the proposed control method.

Finite-time dynamic surface control for multi-agent systems with prescribed performance and unknown control directions

In this paper, the finite-time adaptive fuzzy control method is proposed for nonlinear nonstrict-feedback multi-agent systems (MASs) with unknown control directions. The Nussbaum function is introduced to compensate the influence of unknown control directions. By combining the finite-time stability criterion, an adaptive fuzzy controller is constructed to ensure that systems reach a steady state in a finite time, and the tracking errors of all output signals converge to a small neighbourhood of the origin. By using the Lyapunov finite-time stability theorem, all signals are proved to be semi-global practically finite-time stable. Finally, the effectiveness of the proposed control method is proved through some results of simulation experiments.

Adaptive Fuzzy Consensus Tracking Control for Nonlinear Multiagent Systems with Time-Varying Delays and Constraints

This paper proposes an adaptive fuzzy distributed consensus tracking control scheme for a class of uncertain nonlinear dynamic multiagent systems (MASs) with state time-varying delays and state time-varying constraints. The existing controllers with Lyapunov–Krasovskii functions (LKFs) were not suitable to address time-varying delays and time-varying constraints in nonlinear MASs simultaneously. State constraints further increase the difficulty of controller design and stability analysis, especially for nonstrict feedback systems. Fuzzy logic systems (FLSs) tackle the approximation of unknown dynamics functions and parameters. Especially when the distributed consensus tracking error is infinitely close to the origin, although there is no singular value, it would lead to the rapid growth of control rate or uncontrollability. Constructing appropriate piecewise functions can effectively avoid the above occurrence and accelerate convergence. Based on Lyapunov stability theory and algebraic graph theory, the constructed tracking control can ensure states within defined time-varying constraint bounds and eliminate the influence of time delays. All signals in closed-loop systems can be guaranteed semiglobally uniformly ultimately bounded (SUUB). Finally, the validity of the theoretical method is verified by the simulation.

Neural adaptive fault-tolerant finite-time control for nonstrict feedback systems: An event-triggered mechanism

The problem of event-triggered neural adaptive fault-tolerant finite-time control is investigated for a class of nonstrict feedback nonlinear systems in the presence of nonaffine nonlinear faults. The event-triggered signal is designed by using a relative-threshold to reduce communication burden. The dynamic surface control method is used to relax the assumption of the reference signal and deal with the computational complexity issue. Based on the finite-time stability, a new neural adaptive backstepping design method is developed. The event-triggered neural adaptive fault-tolerant control law is developed for the closed-loop system so that not only the semi-global practical finite-time stability is ensured, but also the tracking performance with a small residual set is guaranteed. Finally, the effectiveness of the proposed control law is verified via simulation results.

Adaptive fuzzy tracking for flexible-joint robots with random noises via command filter control

This study investigates the issue of adaptive tracking control for flexible-joint robots with random disturbances that can be correlated to all system states.The system considered under this case is a typical multi-input and multi-output (MIMO) nonstrict-feedback system, which cannot be controlled by the traditional backstepping design. For this reason, fuzzy logic systems play a vital role in solving this difficulty. Moreover, a finite-time adaptive control scheme is proposed by combining command filtered control and backstepping design, in which the “explosion of complexity” problem is successfully avoided and the tracking error can be kept within a very small range of the origin in a limited time. Finally, the effectiveness of the proposed control scheme is further demonstrated by the simulation results. It can be seen from the simulation comparison that under the proposed method, the maximum value of ‖q1-qr‖ at the steady-state phase is only 0.0055, which is smaller than 0.0199 in the existing method.

Finite-Time Adaptive Fuzzy Prescribed Performance Control for High-Order Stochastic Nonlinear Systems

In this article, the high-order nonlinear system is commonly studied in an underactuated weakly coupled mechanical system, the control design is difficult from the tractional control design for nonlinear systems. Thus, we study the finite-time fuzzy adaptive error constraint control problem for stochastic high-order nonlinear nonstrict feedback systems. Fuzzy logic systems are utilized to identify the unknown nonlinear dynamics, a new error transfer variable is used to achieve the prescribed performance. Based on adding a power integrator technique and adaptive backstepping recursive control, a novel adaptive fuzzy finite-time prescribed performance control scheme is developed. By utilizing stochastically finite-time stable theory, the proposed control method can guarantee that the high-order system is semi-global finite-time stable in probability. Finally, both numerical and practical simulations are provided to verify the feasibility and effectiveness of the developed control method.

Fuzzy adaptive event-triggered output feedback control for nonlinear systems with tracking error constrained and unknown dead-zone

ABSTRACT In this paper, an adaptive fuzzy event-triggered output feedback control scheme is studied for a class of non-strict feedback systems with tracking error constrained and unknown dead-zone. Fuzzy logical systems (FLSs) are employed to solve the uncertainties of the controlled plant, and the immeasurable states are estimated by employing the fuzzy observer. In the designed observer, to compensate for the effect of unknown dead-zone by invoking the known designed event-triggered input signal, an adaptive parameter is designed. Furthermore, due to event-triggered control (ETC) places a great burden on the computing space, the dynamic surface control (DSC) technique is used to solve the problem of ‘explosion of complexity’ in each step, and the simplified barrier Lyapunov function (SBLF) is utilised to restrict the tracking error within the prescribed boundaries. Consequently, the designed parameter adaptive laws and event-triggered controller can ensure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB). Ultimately, two numerical simulation examples are provided to illustrate the effectiveness of the proposed event-triggered control theory.

Disturbance observer–based neural flight control for aircraft with switched time-varying distributed delays

In this article, the high angle of attack (AOA) maneuver control problem is studied under multiple disturbances and uncertainties. For the first time, the switched distributed delay is constructed to characterize the unsteady aerodynamics. Based on neural networks (NNs) and hyperbolic tangent function, the disturbance observer technique is extended to the nonstrict-feedback system control. To handle the switching problem, time-delay problem, and nonstrict-feedback problem caused by switched distributed delay terms, the Lyapunov–Krasovskii (LK) functional method and a variable separation method are cleverly combined. The proposed LK function can relax the constraints on time-varying delay. Finally, a disturbance observer–based neural finite-time prescribed performance flight control law is developed to improve the flight performance at high AOA, and its effectiveness has been verified through rigorous theoretical analysis and simulation experiments.

Fuzzy Adaptive Decentralized Control for Nonstrict-Feedback Large-Scale Switched Fractional-Order Nonlinear Systems.

This article investigates the adaptive fuzzy control algorithm for a class of large-scale switched fractional-order nonlinear nonstrict feedback systems. In this algorithm, we utilize fuzzy-logic systems (FLSs) to approximate the complicated unknown nonlinear functions. Based on the fractional Lyapunov stability rules, a virtual control law is presented. A fuzzy adaptive decentralized control method is developed under the technique of the Lyapunov function. Under the operation of the proposed algorithm, the stability of the proposed systems and the control performance can be guaranteed. Finally, simulation results are presented to illustrate the feasibility and effectiveness of the proposed method.

Observer-Based Adaptive Event-Triggered Control for Nonstrict-Feedback Nonlinear Systems With Output Constraint and Actuator Failures

An observer-based adaptive dynamic surface control (DSC) strategy is proposed for nonlinear nonstrict-feedback systems with time-varying disturbance, event-triggered mechanism, and actuator failures in this paper. Fuzzy logic systems are implemented to construct an observer to estimate the unmeasured states. The DSC method is exploited to solve the issue of “explosion of complexity” with the backstepping control technique. The constructed event-triggered mechanism can avoid the waste of communication resources. The barrier Lyapunov functions are utilized to address the problem of output constraint. It is demonstrated that the reference signals can be well tracked by the system output and all closed-loop signals remain semi-globally uniformly ultimately bounded. Two examples illustrate the effectiveness of the constructed controller.

Fixed-Time Adaptive Fuzzy Control for Uncertain Nonstrict-Feedback Systems With Time-Varying Constraints and Input Saturations

This article investigates the adaptive fuzzy tracking control design for uncertain nonstrict-feedback nonlinear systems with time-varying constraints and asymmetric input saturations. It is known that time-varying output constraint, time-varying error constraints, and input saturations are commonly seen issues in many practical engineering systems due to inherent physical limitations and performance requirements. To deal with these problems and improve the convergence rate of the control system, a novel fixed-time convergent adaptive fuzzy control scheme is proposed for the considered uncertain nonlinear systems via the time-varying barrier Lyapunov function (BLF) technique. First, to deal with the unknown nonlinearities and uncertainties in the system dynamic model, fuzzy logic systems are utilized to approximate the unknown functions of the considered model. Then, the problem of asymmetric input amplitude and rate saturations is handled by constructing a unified smooth characterizing function and an innovative auxiliary design signal system. Subsequently, considering physical limitations and performance requirements, a novel time-varying BLF-based adaptive fuzzy backstepping control scheme is designed for the uncertain nonstrict-feedback nonlinear systems to realize superior tracking performances and keep the states staying in predefined time-varying compact regions during operations. Further, rigorous theoretical analyses have been conducted to show that the proposed control scheme achieves fixed-time convergence of all signals in the closed-loop control system. Finally, representative simulation results verify the effectiveness of the proposed control scheme.

Adaptive Fuzzy Asymptotic Tracking for Nonlinear Systems With Nonstrict-Feedback Structure.

In this article, the tracking control problems of the nonlinear nonstrict-feedback systems are considered. By combining the backstepping technique and bound estimation method, a novel nonlinear adaptive asymptotical control law is proposed, which offsets the effect of the unknown virtual control parameters and the uncertain nonlinearities. Correspondingly, an improved Lyapunov function by introducing the lower bounds of control parameters has been devised in this article. Compared with the existing adaptive tracking control schemes, the controller designed in this article can guarantee that the tracking control error converges to zero asymptotically and all the signals which contain the state variables and the adaptive laws are bounded. Moreover, the asymptotic stability of the system is realized for the first time. Finally, simulation examples are applied to test and prove the availability of the presented methods and the performance of the controlled system.

Adaptive fuzzy output feedback FTC for nonstrict-feedback systems with sensor faults and dead zone input

This paper solves the fault-tolerant control (FTC) problem of uncertain nonlinear systems in nonstrict-feedback form. The controlled plants considered in this paper are more complicated than existing ones, which is composed of the unknown nonlinearities, unmeasured states, and sensor faults and unknown dead zone input nonlinearity. Fuzzy logic systems and a fault-estimation-based state observer are used for identifying the unknown nonlinearities and obtaining the unmeasured states, respectively. By designing the sensor faults compensation and the dead zone inverse compensation methods, an observer-based fault-tolerant compensation control scheme is developed under backstepping recursive design frame. And it is testified that the closed-loop signals are bounded, and the tracking performance is satisfied even when the controlled systems are not free of sensor faults and unknown dead zone input nonlinearity. An electromechanical system is used to test the effectiveness of the developed control strategy.

Global neuro-adaptive control of nonstrict-feedback systems with unknown control directions and multiple time delays

Issues of control of nonstrict-feedback systems with unknown control directions and multiple time delays are investigated. The proposed design consists of three major parts, a nominal minimal-learning-parameter (MLP) based adaptive neural controller, a supervisory robust controller for pulling back the escaped transients, and the dynamic surface control (DSC) for solving the explosion of complexity and algebraic-loop problems simultaneously. Meanwhile, the Nussbaum gain function (NGF) and the Lyapunov–Krasovskii functional (LKF) are included for handling the unknown control directions and the time delays, respectively. In particular, global instead of the semi-global tracking stability is achieved. Simulation results are provided to show the effectiveness of the proposed approach.