In this paper, an adaptive sliding mode control method based on neural networks is presented for a class of manipulator systems. The main characteristic of the discussed system is that the output variable is required to keep within a constraint set. In order to ensure that the system output meets the time-varying constraint condition, the asymmetric barrier Lyapunov function is selected in the design process. According to Lyapunov stability theory, the stability of the closed-loop system is analyzed. It is demonstrated that all signals in the resulted system are bounded, the tracking error converges to a small compact set, and the system output limits in its constrained set. Finally, the simulation example is used to show the effectiveness of the presented control strategy.

The application of manipulator is of great significance to the development of human society. So far, many effective control strategies have been produced for manipulator control, such as the PID control [

In recent years, with the rapid development of science and technique, the adaptive control technology has become particularly important. Especially, the fuzzy logic system-based and neural network-based adaptive control is one of the current research hot topics. These two methods are more suitable for nonlinear systems with unknown dynamics. In this aspect, a large number of research results have been obtained [

In addition, under the influence of environment and other factors, variables in the controlled system are often limited [

According to the above analysis, an adaptive sliding mode controller with time-varying output constraint is designed. In order to ensure that the system output is with the specified time-varying constraint range, the asymmetric logarithmic Lyapunov function is selected. The unknown nonlinear function existed in the considered system is approximated by the radial basis function neural networks (RNFNNs). Then, an adaptive sliding mode controller is constructed by combining the backstepping technique and the sliding mode control approach.

Compared with the existing results, the innovations of this paper mainly include the following two aspects:

Compared with the existing results in [

A new adaptive sliding mode control approach for manipulator systems is proposed by combining the barrier Lyapunov function method and the backstepping technique. A sufficient condition for the adaptive constrained control problem is derived. Moreover, the uncertainties are considered in this paper, which increase the design complexity.

The rest of this paper is organized as follows: Section

Consider the manipulator system in [

(see [

The control target of this paper is to design an adaptive NN controller such that the closed-loop system is stable, and the system output can track the desired reference signal

In this paper, the backstepping method is used to design the adaptive NN controller, and the following coordinate transformation is defined:

From (

Consider the following asymmetric obstacle Lyapunov function:

For convenience of expression, define the following error coordinate transformation:

Similarly, if

Combining (

Then, the time derivative of

Design the following virtual controller:

Substituting (

From (

In this paper, we consider the case that the load mass is uncertain, and then according to the definitions of the system parameter in [

(see [

Substituting (

Select the following Lyapunov function:

Then, combining (

Based on Young’s inequality, it has

Select the following virtual controller and adaptive law

Substituting (

In order to ensure that the tracking error of the system tends to zero in finite time, improve the convergence accuracy, and avoid singular problems; an integral end face sliding surface is designed as

According to

The function

Therefore,

Consider the Lyapunov function

Taking the derivative of

Substituting (

Using Young’s inequality, we have

Design the following actual controller and adaptive law:

On the basis of (

Let

Furthermore, consider the inequality

Based on the above analysis, the following theorem is obtained.

Consider the manipulator system (

. Select the Lyapunov function as follows:

According to the above analysis, it is easily known that

The above inequality is integrated on both sides over

According to the definition of

In addition, from (

Furthermore, when

Similarly, when

Therefore, when

Furthermore, from

This completes the proof of Theorem

It is worth noting that equation (

In this section, the manipulator system (

In this simulation, the desired signal is chosen as

Figures

Trajectories of

The trajectory of

The trajectory of

Trajectories of the update laws.

The trajectory of control input

A sliding mode-based adaptive neural network control strategy is proposed for a manipulator system with output constraint. Combining the sliding mode control method with backstepping technique, an adaptive controller is designed, which not only solves the output constraint issue of the considered system, but also makes the error between system output and the reference signal to converge to a small compact set. Moreover, the output satisfies the constraint condition. Finally, the effectiveness of the proposed approach is illustrated by the simulation example.

The data used to support the findings of this study are included within the article.

The author declares no conflicts of interest.