Predictive control

Artificial neural networks have also been proposed for predictive control. Ersü and others [69][109][101] have developed and applied, since 1982, a learning control structure, coined LERNAS, which is essentially a predictive control approach using CMAC networks.

Two CMAC networks (referred by Ersü as AMS) are used in their approach. The first one stores a predictive model of the process:

(2.42) where x_m[k] and v[k] denote the state of the process and the disturbance at time k, respectively. The second ANN stores the control strategy:

(2.43) where x_c[k] and w[k] denote the state of the controller and the value of the setpoint at time k, and u[k] is the control input to the plant.

At each time interval, the following sequence of operations is performed:

ANN

reference model

plant

+

-y_r[k]

y_p[k]

fixed gain controller

.

.

+ +

u[k]

u_n[k]

r[k]

x_m[k]

x_p[k]

x_m[ ] u kk , [ ] v k, [ ]

( )→y_m[k+1]

x_c[ ] w kk , [ ] v k, [ ]

( )→u k[ ]

i) the predictive model is updated by the prediction error ; ii) an optimization scheme is activated, if necessary, to calculate the optimal control value that minimizes a l-step ahead subgoal of the type:

(2.44) constrained in the trained region G_T of the input space of the predictive model of the plant. To speed up the optimization process, an approximation of , denoted as

, can be obtained from past decisions:

; (2.45)

iii) the control decision is stored in the controller ANN to be used, whether as a future initial guess for an optimization, or directly as the control input upon user decision;

iv) finally, before applying a control to the plant, a sub-optimal control input is sought, such that:

(2.46) for some specified . This process enlarges the trained region G_T and speeds up the learning.

More recently, Montague et al. [110] developed a nonlinear extension to Generalized Predictive Control (GPC) [111]. The following cost function is used in their approach:

(2.47)

where are obtained from a previously trained MLP, which emulates the forward model of the plant. At each time step, the output of the plant is sampled, and the difference between the output of the plant and the predicted value is used to compute a correction factor. The MLP is again employed to predict the outputs over the horizon . These values are later corrected and employed for the minimization of (2.47) with respect to the sequence . The first of these values, , is then applied to the plant and the sequence is repeated.

e k[ ] = y_p[ ] yk – _m[ ]k

The same cost function (2.47) is used by Sbarbaro et al. [112] who employs radial basis functions to implement an approach similar to the LERNAS concept. Hernandez and Arkun [113] have employed MLPs for nonlinear dynamic matrix control.

Artificial neural networks have been proposed for other adaptive control schemes. For instance, Chen [114] has introduced a neural self-tuner. Iiguni et al. [115] have employed MLPs to add nonlinear effects to a linear optimal regulator.

Conclusive results on the merit of neural controllers over traditional schemes are not currently available, due to the infancy of this new field. However, preliminary performance comparisons made by some researchers seems to indicate that ANN-based control delivers better results than traditional schemes when the plant is highly nonlinear [94][108][110] and also in the presence of noise [108]. For linear, noise free, plants no improvement over conventional techniques was obtained [94][108].

On the whole, ANN-based control offers definite promises. Several open questions exist, the biggest of all perhaps being stability issues. At present, there is no established methodology for determining the stability of ANN control schemes. However, this is not a unique situation in the area of control systems. The first self-tuners were used in industry before stability proofs were developed, and self-tuning is at present a consolidated field.

Whether the same thing will happen to neural control schemes, only time and a large research effort will tell.

2.4 Conclusions

In this Chapter artificial neural networks have been introduced. A chronological perspective of the research on ANN has been given and some of the reasons for the renewal of interest in this technology pointed out. From a brief discussion of the structure of the human brain, it can be concluded that the broad aspects of this complicated structure are also found in artificial neural networks models. However, since detailed knowledge of the brain is not currently available, a large number of ANN models has been proposed. A brief discussion on neuron models, patterns of connectivity and learning mechanism has been conducted. Finally the details of three neural models, Hopfield networks, CMAC networks and multilayer perceptrons have been given.

An overview of current applications of artificial neural networks to nonlinear identification and control of nonlinear dynamical systems has been conducted. It has been shown that ANNs are emerging as a cost effective tool for nonlinear systems identification.

Neural networks, during the past three years, have been integrated in several different control

schemes. Promising results have been obtained that, when compared with conventional techniques, seem to indicate that neural networks have an important role to play in nonlinear adaptive control.

From this overview, it is clear that MLPs are the most commonly employed ANN in control systems. For this field, the most exploited feature of MLPs is the ability to perform arbitrary nonlinear mappings. In the next Chapter this capacity of MLPs will again be exploited in a problem of great practical importance: the autotuning of PID controllers.

Chapter 3