We propose a new type of neural adaptive control via dynamic neural networks. For a class of unknown nonlinear systems, a neural identifier-based feedback linearization controller is first used. Dead-zone and projection techniques are applied to assure the stability of neural identification. Then four types of compensator are addressed. The stability of closed-loop system is also proven.

Feedback control of the nonlinear systems is a big challenge for engineer, especially when we have no complete model information. A reasonable solution is to identify the nonlinear, then a adaptive feedback controller can be designed based on the identifier. Neural network technique seems to be a very effective tool to identify complex nonlinear systems when we have no complete model information or, even, consider controlled plants as “black box”.

Neuroidentifier could be classified as static (feed forward) or as dynamic (recurrent) ones [

Neurocontrol seems to be a very useful tool for unknown systems, because it is model-free control, that is, this controller does not depend on the plant. Many kinds of neurocontrol were proposed in recent years, for example, supervised neuro control [

In this paper we extend our previous results in [

The controlled nonlinear plant is given as

The dynamic neural network (

Let us define identification error as

the unmodeled dynamic

If we define

the pair (

local frequency condition [

There exist a stable matrix

This condition is easily fulfilled if we select

Subject to assumptions

Select a Lyapunov function as

if

if

if

If

From (I) and (II),

The weight update law (

Projection algorithm.

Figure

Start from any initial value for

Do identification until training time arrives

If the

If the

Since the updating rate is

Let us notice that the upper bound (

From (

Equation (

The object of adaptive control is to force the nonlinear system (

From (

If

If

If

Approaches (A) and (C) are exactly compensations of

Finally, we give following design steps for the robust neurocontrollers proposed in this paper.

According to the dimension of the plant (

Do online identification. The learning algorithm is (

Use robust control (

In this section, a two-link robot manipulator is used to illustrate the proposed approach. Its dynamics of can be expressed as follows [

Now we check the neurocontrol. We assume the robot is changed at

The neurocontrol is (

(B)

Tracking control of

Tracking control of

(C)

Tracking control of

Tracking control of

(D)

Tracking control of

Tracking control of

We may find that the neurocontrol is robust and effective when the robot is changed.

By means of Lyapunov analysis, we establish bounds for both the identifier and adaptive controller. The main contributions of our paper is that we give four different compensation methods and prove the stability of the neural controllers.