Adaptive backstepping dead-zone control for a class of nonlinear time-delay systems ussing fuzzy approximators

This paper addresses the problem of adaptive tracking control for a class of stochastic nonlinear systems with time-varying input delays, and the nonlinear functions of the systems are with not only the unknown parameters but also the unknown state time-varying delays, which is different from the previous work. In this paper, through a state transformation, the system can be easily transformed into a system without the time-varying input delay; the appropriate Lyapunov–Krasovskii functionals are used to compensate the unknown time-varying delay terms, and the quadratic functions instead of the quartic functions often utilized in the existing results are used as Lyapunov functions to analyze the stability of systems and the hyperbolic tangent functions are introduced to deal with the Hessian terms. Fuzzy logic systems (FLSs) in Mamdani type are used to approximate the unknown nonlinear functions. Then, based on the backstepping technique, the adaptive fuzzy controller is designed. The three main advantages of the developed scheme are that (i) unlike the existing results which deal with the nonlinearly parameterized functions by using the separation principle, the nonlinearly parameterized functions are lumped into the continuous functions which can be approximated by using the FLS; (ii) the number of the adjusted parameters only depend on the order of the investigated systems, which can reduce the computational burden greatly; and (iii) the existence of the time-varying input delay such that the controller design becomes much more difficult, and in this paper, it can be dealt with by using an appropriate state transformation. It is proven that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded in probability, whereas the tracking error converges to a small neighborhood of the origin. Finally, simulation results are provided to show the effectiveness of the proposed approach.

Adaptive iterative learning control of a class of nonlinear time-delay systems with unknown backlash-like hysteresis input and control direction

An observer-based adaptive neural-network robust control for a class of nonlinear time-delay systems with unmodeled dynamics. It is presented for a class of nonaffine nonlinear time-delay systems with external disturbance and unavailable states. By the implicit function theorem, Taylor’s formula and mean theorem, the form of the non-affine nonlinear systems is transformed into the form of affine nonlinear systems. The controller designed to attenuate the effect of external disturbance and approximation errors of the neural networks on tracking. The unknown time-delay is compensated by using appropriate Young inequality, the weight update laws based on Lyapunov stability theory can guarantee the system stability and asymptotic convergence of the tracking error to zero. Theoretical analysis and simulation results demonstrate the effectiveness of the approach.

In this paper, a hybrid fuzzy adaptive output feedback control design approach is proposed for a class of multiinput and multioutput strict-feedback nonlinear systems with unknown time-varying delays, unmeasured states, and input saturation. First, fuzzy logic systems are employed to approximate unknown nonlinear functions in the system. Next, a smooth function is used to approximate the input saturation and an adaptive fuzzy state observer is constructed to solve the problem of unmeasured states. Based on the designed adaptive fuzzy state observer, a serial-parallel estimation model is established. By applying adaptive fuzzy dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial-parallel estimation model, a new fuzzy controller with the composite parameters adaptive laws is developed based on Lyapunov-Krasovskii functional. It is proved that all variables of the closed-loop system are bounded and the system outputs can follow the given bounded reference signals as close as possible. A simulation example is provided to further show the effectiveness of this novel control scheme.

Robust adaptive fuzzy filters output feedback control of strict-feedback nonlinear systemsIn this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of single input single output (SISO) strict-feedback nonlinear systems without measurements of states. The nonlinear systems addressed in this paper are assumed to possess unstructured uncertainties, unmodeled dynamics and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds is available. In recursive design, fuzzy logic systems are used to approximate unstructured uncertainties, and K-filters are designed to estimate unmeasured states. By combining backstepping design and a small-gain theorem, a stable adaptive fuzzy output feedback control scheme is developed. It is proven that the proposed adaptive fuzzy control approach can guarantee the all the signals in the closed-loop system are uniformly ultimately bounded, and the output of the controlled system converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by a simulation example and some comparisons.

This article discusses the adaptive fuzzy asymptotic tracking control for high-order nonlinear time-delay systems with full-state constraints. Fuzzy-logic systems and a separation principle are utilized to relax growth assumptions imposed on unknown nonlinearities. The adverse effect caused by unknown time delays is eliminated by choosing appropriate Lyapunov-Krasovskii functionals. By integrating nonlinear-transformed functions with a key coordinate transformation into the control design and constructing a specific compact set on the initial values of system states, the desired trajectory and parameter estimates, it is rigorously proved that all closed-loop signals are semiglobally bounded, the fuzzy approximation is valid, the full-state constraints are not violated without feasibility conditions on virtual controllers, and asymptotic tracking is achieved. The effectiveness and advantages of this control scheme are confirmed by two examples including a single-link robotic system.

This paper proposes a bioinspired reference model based fuzzy adaptive tracking control for active suspension systems. A general bioinspired nonlinear structure, which can present ideal nonlinear quasi-zero stiffness for vibration isolation, is adopted as tracking reference model. Fuzzy logic systems are used to approximate unknown nonlinear terms in nonlinear suspension systems. Particularly, a nonlinear damping is designed to improve damping characteristics of the bioinspired reference model. With beneficial nonlinear stiffness and improved nonlinear damping of the bioinspired reference model, the proposed fuzzy adaptive controller can effectively suppress vibration of suspension systems with less actuator force and much improved ride comfort, thus energy saving performance can be achieved. Finally, a quarter-vehicle active suspension system with considering payload uncertainties, general disturbance, and actuator saturation is provided for evaluating the validity and superiority of the bioinspired nonlinear dynamics based fuzzy adaptive control approach proposed in this paper.

A new adaptive fuzzy sliding-mode control (FSMC) scheme was proposed, which incorporated the fuzzy logic into sliding-mode control using fuzzy logic to approximate the equivalent control and the upper bound of uncertainty which involved the disturbance and approximation error, thus the influence of modeling error was reduced and the gain of sliding-mode control part was more fitting, such that the chattering effects could be alleviated . Besides, inspired by the thought of fully tuned RBF neural networks, a fully tuned fuzzy logic was proposed which enhanced the approximating ability of fuzzy logic system. Lyapunov stability theorem was used to prove the stability of the system and the adaptive laws were deduced. Finally, simulation results of some BTT missile were included to illustrate the effectiveness of the adaptive fuzzy sliding-mode control scheme.

Variable structure adaptive fuzzy control for a class of nonlinear time-delay systems

This paper investigates the adaptive fuzzy control problem of strict-feedback nonlinear systems with unknown dead-zone. Fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear systems. The control input signal is nonlinear and experienced both dead-zone nonlinearity and actuator faults. By combining the effects of both dead-zone and actuator faults, the actual control input signal is expressed as a nonlinear function with bounded disturbance. The stability of the closed-loop nonlinear system is obtained via Lyapunov function and under the effects of unknown dead-zone, actuator fault, and unknown external disturbances. Finally, a numerical simulation example is given to verify the effectiveness of the proposed adaptive fuzzy control strategy.

Adaptive fuzzy tracking control for a class of pure-feedback stochastic nonlinear systems with non-lower triangular structure

This paper investigates the adaptive fuzzy output feedback event-triggered control problem for a class of switched nonlinear systems with sensor faults. Due to that the unknown nonlinearities of the systems are more general and the sensor undergoes faults, the considered problem is difficult to be addressed by existing schemes. Therefore, fuzzy logic systems are employed to approximate unknown nonlinear terms and a fault compensation coefficient is introduced to compensate for the effect of sensor failures. Then, a state observer is established for estimating unmeasured states. By choosing a suitable common Lyapunov function, an adaptive fuzzy output feedback fault-tolerant event-triggered controller is derived. It is proven that the proposed scheme can guarantee that the system output tracks the desired trajectory effectively, all states of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the Zeno phenomenon is excluded. Finally, two simulation examples, which include a switched RLC circuit system and a numerical example, are presented to show the the effectiveness of the proposed strategy.

This paper presents a theoretical study on a model-reference adaptive fuzzy logic controller for vector-controlled permanent magnet AC servomotor drives. In the proposed system, fuzzy logic is used to implement the direct controller as well as the adaptation mechanism. The operation of the direct fuzzy controller and the fuzzy logic based adaptation mechanism is studied. The control performance of the adaptive fuzzy controller is evaluated by simulation for various operating conditions. The results are compared with that provided by a nonadaptive fuzzy controller. The implementation of proposed adaptive fuzzy controller is also discussed.

In this paper, temperature monitoring of sterilizing equipment system was established with the help of fuzzy and self tuning Adaptive fuzzy logic controller designed in Lab VIEW software. It combines the advantages of both fuzzy logic and self tuning Adaptive fuzzy logic controller. The implementation attempts to rectify the errors between the measured value and the set point which helps to achieve efficient temperature control. The Adaptive fuzzy controller uses defined rules to control the system based on the current values of input variables and temperature errors. The simulation results presented in order to evaluate the proposed method. The result shows that self tuning Adaptive fuzzy logic controller was tolerant to disturbance and the temperature control is most accurate.

Adaptive fuzzy control for full states constrained systems with nonstrict-feedback form and unknown nonlinear dead zone