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This study proposes a low-computational composite adaptive neural control scheme for the longitudinal dynamics of a swept-back wing aircraft subject to parameter uncertainties. To efficiently release the constraint often existing in conventional neural designs, whose closed-loop stability analysis always necessitates that neural networks (NNs) be confined in the active regions, a smooth switching function is presented to conquer this issue. By integrating minimal learning parameter (MLP) technique, prescribed performance control, and a kind of smooth switching strategy into back-stepping design, a new composite switching adaptive neural prescribed performance control scheme is proposed and a new type of adaptive laws is constructed for the altitude subsystem. Compared with previous neural control scheme for flight vehicle, the remarkable feature is that the proposed controller not only achieves the prescribed performance including transient and steady property but also addresses the constraint on NN. Two comparative simulations are presented to verify the effectiveness of the proposed controller.

Morphing aircraft has received considerable interest, since it possesses distinct advantages, which is capable of altering autonomously its aerodynamic configuration to obtain optimal flight performance, adapting different flight environments and high efficiency executing multiple types of missions [

Adaptive back-stepping method has been widely studied in tracking control designs for nonlinear systems in strict-feedback or pure-feedback form, because it owns capability of systematically manipulating mismatched uncertainties [

Despite the recent progress in the neural networks control of unknown nonlinear systems, certain issues still remain open. In practice, even though the stability analysis of aforementioned adaptive neural control schemes is proven, it relies on the condition that the approximation ability of NN must be effective all the time (i.e., the NN should be permanently working in the neural active region). Therefore, the deterioration of the tracking performance or even instability may happen provided that the transient states overstep the neural active region. Additionally, such a condition is also difficult to verify beforehand in real applications [

Motivated by the aforementioned discussion, a switching strategy based composite adaptive neural control scheme is proposed for a swept-wing morphing aircraft. NNs are employed to approximate unknown functions; thus a priori knowledge of the aerodynamic parameters is not necessary. It is proven that all the signals in the closed-loop systems are bounded. The main contributions of this work are shown as follows:

Different from the works [

In contrast to traditional neural control schemes [

The longitudinal dynamics of a morphing aircraft considered in this study are derived from [

Thrust

Define

Velocity subsystem is transformed into the following formulation:

In order to transform the altitude system into pure-feedback system,

the altitude and velocity can track the desired trajectory

the corresponding altitude and velocity tracking errors achieve prescribed transient and steady-state performance.

To achieve the control objective, the tracking error

To transform the constrained tracking error condition (

Using (

The boundaries of the compact subsets

The following inequality holds for any

The “first-order sliding mode differentiator (FOSD)” is designed as

In order to process the derivation, motived by [

In this paper, we assume that all of the system states are measurable.

The functions

Obviously, there exist ideal weight vectors

Define velocity tracking error as

By employing MLP technique, the controller

Consider the following adaptive laws for

Suppose that the velocity subsystem (

The velocity design is partially derived from [

The following coordinate change is constructed to facilitate the control design:

The time derivative of

By using (

The virtual controller

Invoking (

In order to avoid the tedious computation of

Then, we have

The differentiation of

The virtual controller

The structure of adaptive control laws is expressed as follows:

Substituting (

The following FOSD is adopted to estimate

From (

The differentiation of

The virtual control law

Substituting (

As done previously, the following FOSD is employed to estimate

Thus, we have

In this step, the actual controller

The controller

Thus, (

Consider the altitude subsystem (

The altitude controller, composed of a normal adaptive neural controller working in the neural active region, a robust controller being in charge outside the neural approximation region, and a switching strategy supervising the exchange of the former two controllers, is constructed.

In this paper, in order to estimate the derivative of virtual controllers

In this section, two comparative cases are presented to illustrate the effectiveness of the switching functions based adaptive neural control for longitudinal model of the morphing aircraft. The aerodynamic coefficients and model parameters are the same as [

In this simulation, we assume that the aircraft is cruising at trim states, and only the morphing process is considered. The initial tracking errors are assumed to be

Sweep reference and switch signal.

Altitude and velocity tracking errors.

System states and NN weights.

Control inputs.

In this simulation, the control gains are kept the same as Case

Altitude and velocity tracking.

System states and NN weights.

Control inputs.

Switching functions.

Partial response of PPC scheme.

A composite switching neural prescribed performance control scheme has been proposed for the longitudinal dynamic model of the morphing aircraft. In the control design, by using neural networks to approximate the unknown functions, the prior information of the aerodynamic parameters is unnecessary. By introducing the performance function, the proposed controller is able to permit attributes such as a lower bound on the convergence rate and maximum allowable steady error to be specified. A switching mechanism supervising the exchange of control authorities between the normal neural controller and a robust controller is used to relax the constraint that NN should be kept in the active regions all the time. Two comparative simulations have revealed the superiority of this control scheme.

Invoking (

Consider the following candidate Lyapunov function:

Based on (

Note that the following inequalities hold:

By considering (

If

It is obvious that

Select the candidate Lyapunov function as follows:

On the basis of (

Differentiating

Employing (

Using (

Define the following compact sets:

If

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work is partially supported by the National Natural Science Foundation of China (Grant nos. 61374032 and 61573286).