An adaptive fuzzy control approach is proposed for nonaffine pure-feedback systems with nonaffine functions being semibounded and possibly indifferentiable. A semibounded and continuous condition for nonaffine function is presented to guarantee the controllability of system. To overcome the difficulty from this mild condition, a compact set is introduced, and the nonaffine nonlinear functions are modeled in a new way based on this compact set, which is proved to be invariant set eventually. By using the dynamic surface control (DSC) technique, the problem of explosion of complexity inherent in backstepping method is avoided in the proposed adaptive fuzzy control scheme. Robust compensators are used to minify the influence of uncertainties and disturbances. Furthermore, it is proved that all the closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.

Adaptive Fuzzy Control for Pure-Feedback Nonlinear Systems With Nonaffine Functions Being Semibounded and Indifferentiable

This paper is concerned with finite-time stabilization of a class of pure-feedback systems with dead-zone input. A systematic design procedure is established to derive the finite-time controller. Firstly, to circumvent the difficulties arising from the nonaffine properties, through a change of coordinates and incorporating mean value theorem, a system transformation technique is introduced to convert the original nonaffine system into an affine one. Then, based on the strengthened finite-time Lyapunov stability theorem as well as utilizing the bounds of dead-zone parameters, the finite-time stabilizer is explicitly constructed via backstepping design approach. It is proven that the designed controller can ensure all the states of the closed-loop system converge to zero in a finite time and maintain at zero afterwards. The proposed design framework is also extended to finite-time stabilization of uncertain pure-feedback systems and finite-time tracking control of pure-feedback systems. The effectiveness of the theoretical results are finally demonstrated by a numerical example and a realistic example.

Global finite time stabilization of pure-feedback systems with input dead-zone nonlinearity

A novel adaptive fuzzy dynamic surface control (DSC) scheme is for the first time constructed for a larger class of (multi-input multi-output) MIMO non-affine pure-feedback systems in the presence of input saturation nonlinearity. First of all, the restrictive differentiability assumption on non-affine functions has been canceled after using the piecewise functions to reconstruct the model for non-affine nonlinear functions. Then, a novel auxiliary system with bounded compensation term is firstly introduced to deal with input saturation, and the dynamic system employed in this work designs a bounded compensation term of tangent function. Thus, we successfully relax the strictly bounded assumption of the dynamic system. Additionally, the fuzzy logic systems (FLSs) are used to approximate unknown continuous systems functions, and the minimal learning parameter (MLP) technique is exploited to simplify control design and reduce the number of adaptive parameters. Finally, two simulation examples with input saturation are given to validate the effectiveness of the developed method.

/pdf/fuzzy-adaptive-dsc-design-for-an-extended-class-of-mimo-pure-4ok8h7zxv2.pdf

Fuzzy adaptive DSC design for an extended class of MIMO pure-feedback non-affine nonlinear systems in the presence of input constraints

In this study, the fault-tolerant control problem is investigated for a class of non-affine output-constrained multi-input multiple-output non-linear systems with actuator faults. The controlled systems contain unknown non-linear functions, unknown external disturbance and immeasurable states. The fuzzy logic systems and a robust compensation function are employed to deal with the unknown non-linear functions and non-affine non-linear actuator fault problems. Then, the state observer and the non-linear disturbance observer are developed for estimating the immeasurable states and unknown compounded disturbance, respectively. By using the barrier Lyapunov function method and in the unified framework of adaptive backstepping output feedback control design, a novel adaptive fuzzy fault-tolerant controller design scheme is developed. It is shown that all the variables of the closed-loop system are semi-globally uniformly bounded. Moreover, the system outputs cannot violate their predefined bounds in the presence of the non-affine non-linear faults. A simulation is given to validate the effectiveness of the proposed approach.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-cta.2016.0612

Adaptive output feedback fault-tolerant control for MIMO non-affine non-linear systems based on disturbance observer

A neural-network based variable universe fuzzy control method for power and axial power distribution control of large pressurized water reactors

In this study, the authors present a novel adaptive non-back-stepping alleviating computation tracking control algorithm for a class of MIMO pure-feedback systems with unknown dead-zone inputs. Based on the introduced new state variables and coordinate transforms, the pure-feedback form is converted into a normal form where back-stepping scheme is not necessary. Owing to the unavailability of the new states, the tracking control problem is changed from a state-feedback one to an output-feedback one. Therefore, observers need to be designed to estimate the indirect un-measurable states. In the controller and observer design procedure, the control method is based on non-back-stepping scheme and for each subsystem only three adaptive adjusted parameters are needed to be updated on-line. Thus, different from the back-stepping-based ones, this new algorithm can not only alleviate on-line computation burden but also can considerably simplify the control procedure. According to Lyapunov stable analysis methods, the bounded of all the signals in the closed-loop system can be guaranteed and the tracking error is proven to converge to a small neighbourhood of the origin. Simulation results are presented to illustrate the effectiveness of this proposed approach.

Adaptive non-backstepping fuzzy tracking control for a class of multiple-input–multiple-output pure-feedback systems with unknown dead-zones

A novel adaptive non-backstepping VUFC algorithm for a class of MIMO nonlinear systems with unknown dead-zones in pure-feedback form

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Adaptive non-backstepping fuzzy tracking control for a class of multiple-input–multiple-output pure-feedback systems with unknown dead-zones

A novel adaptive non-backstepping VUFC algorithm for a class of MIMO nonlinear systems with unknown dead-zones in pure-feedback form