**1. Introduction**

We are interested, in this chapter, in adaptive system control of a class of singleinput single-output (SISO) non-linear systems using neural network. In fact, this system control is a very general approach to adaptive control since one can combine in principle any parameter estimation scheme with any control strategy. In addition, its architecture is based on two neural network blocks corresponding to the system controller and the model identification of the dynamic behavior of the system [1, 2].

The use of artificial neural network (ANN) for identification, diagnosis, modeling and control has generated a lot of interest for quite some time now, because they have proved to be excellent function approximators, mapping any function to an arbitrary degree of accuracy, coupled with their ability for generalization, self-organization and self-learning [3].

Many architectures of neural networks are used. Among them, the most common and the most popular architecture is the multilayered perceptron, implemented with the standardized backpropagation algorithm. If the initial set of weights is not selected properly, this algorithm, employing a gradient descent search technique is seriously prone to getting trapped in local optimum solutions.

However, the calculations could slowly occurred and may even overflow or fluctuate between the optima. These limitations encouraged researchers to look for more powerful optimizations techniques that can help reach the optimal solution in an improved fashion, guarantee the convergence of control system and increase the learning speed [3].

for machinery fault detection [15]. Finally, in [16] the authors used PSO to tune the

*Tuning Artificial Neural Network Controller Using Particle Swarm Optimization Technique…*

The PSO is well used in control system, for instance, in [17], the parameters of PID are tuned by ANN where their weights are optimized using PSO method to avoid any local minima/maxima in its searching procedure. In [18], the authors proposed a design of decentralized load-frequency controller for interconnected power systems with ac-dc parallel using PSO algorithm. The experiment result illustrated that their method have rapid dynamic response ability. In [19], the PSO

*D<sup>δ</sup>* controller

radial basis function networks for modeling of MIG welding process.

*DOI: http://dx.doi.org/10.5772/intechopen.96424*

algorithm is implemented to optimize the own five parameters of *PI<sup>λ</sup>*

control of nonlinear time-varying discrete system.

structures.

conclusion of this chapter.

**2. Problem statement**

as given in **Figure 1**.

**Figure 1.**

**5**

*The architecture of indirect neural control.*

via El-Khazali's approach in order to minimize several error functions satisfying some step response specifications such as the set of time domain and frequency domain constraints; overshoot, rise time and settling time. In [20], a comparative analysis of PSO algorithms is carried out, where two PSO algorithms, namely PSO with linearly decreasing inertia weight (LDW-PSO), and PSO algorithm with constriction factor approach (CFA-PSO), are independently tested for different PID

In this chapter, a comparison of the performance of the PSO optimized neural network with the standard back-propagation is presented for the adaptive indirect

The present chapter is organized as follows. After this introduction, section 2 reviews the problem statement. Furthermore, in section 3 the neural network optimization methods are shown. In Section 4, tuning neural network controller using classical approach is presented. However, the section 5 details tuning neural network controller using PSO approach. An example of nonlinear system is studied, in section 6, to illustrate the proposed efficiency of the method. Section 7 gives the

The indirect adaptive control that is used, in this chapter, is composed of two blocks: a block of neural network model and a block of control system. The proposed control system is a neural network controller. At the simulation, it is assume that the neural network controller parameter's depending of the model parameter's

In this architecture of indirect control, *r k*ð Þ is the desired value, *u k*ð Þ is the control law from the controller, *y k*ð Þ is the output of the nonlinear system, *yr k*ð Þ is the output of the neural network model, *e k*ð Þ is the identification error, ^*ec*ð Þ*k* is the estimated tracking error, *ec*ð Þ*k* is the tracking error and *k* is the discrete time. The aim of this chapter is to find a control law *u k*ð Þ to the nonlinear system, given by the Eq. (1), based on the tuning neural network controller's parameters in order that the system output *y k*ð Þ tracks, where possible, the desired value *r k*ð Þ.

A lot of optimization techniques of neural network are widely used. Among them, particle swarm optimization (PSO), the subject of this chapter, studied in different papers like in [3], and originates from the behavioral simulation of fish schooling and bird flocking. The conceptual model, at some point in the evolution of the algorithm, was an optimizer following which a number of parameters extraneous to optimization were eliminated leading to the basic PSO algorithm [3].

This technique is used in many applications of neural network optimization like identification, control and modeling. For instance, in [4], the authors used the PSO based neural network optimization for prediction of diameter errors in a boring machine. In their work, they established an improvement in the quality of optimization of the neural networks and error compensations with the use of the PSO algorithm, which achieves a better machining precision with fewer numbers of iterations.

The PSO algorithm is proposed to get optimal the parameters of ANN. This algorithm is well used because it has convergent result and not require many iterations, so in relative calculation relative quick. PSO is a population-based approach, which uses the swarm intelligence generated by the cooperation and competition between the particles in a swarm. It has been emerged successfully to a wide variety of search and optimization problems.

For example, in [5], the authors compared the performance of the PSO technique with other EAs for both continuous and discrete optimization problems in terms of processing time, convergence speed, and quality of the results. In addition, in [6], the authors proposed a PSO learning algorithm that self-generates radial basis function neural network (RBFN) to deal with three non-linear problems. This proposed PSO allows a high accuracy within a short training time when determining RBFN with small number of radial basis functions. Then, in [7], a PSO algorithm was developed by the authors to find the optimum process parameters which satisfy given limit, tool wear and surface roughness values and maximize the productivity at the same time. Also, in [8], the authors described an evolutionary algorithm for evolving the ANN which was based on the PSO technique. Both the architecture and the weights of the ANN were adaptively adjusted according to the quality of the neural network until the best architecture or a terminating criterion was reached. Moreover, the performance of the basic PSO algorithm with the constriction PSO on some test functions of different dimensions was compared by [9] and they found that the use of constriction PSO with mutation provided significant improvement in certain cases.

Further, in [10], it is presented an improved PSO algorithm for neural network training employing a population diversity method to avoid premature convergence. Furthermore, in [11], the authors used the PSO technique to optimize the grinding process parameters such as wheel and workpiece speed, depth and lead of dressing, etc. subjected to suitable constraints with the objective of minimizing the production cost and obtaining the finest possible surface finish. As well as, by comparing the PSO algorithm results with genetic algorithms and quadratic programming techniques, the PSO algorithm gives the global optimum solution with the objective to obtain minimum cost of manufacturing, [12]. Equally, in [13], the authors applied ANN - PSO approach for selection of optimum process parameters for minimizing burr size in drilling process. Besides that, the PSO algorithm was applied for optimization of multi objective problem in tile manufacturing process [14] and also

### *Tuning Artificial Neural Network Controller Using Particle Swarm Optimization Technique… DOI: http://dx.doi.org/10.5772/intechopen.96424*

for machinery fault detection [15]. Finally, in [16] the authors used PSO to tune the radial basis function networks for modeling of MIG welding process.

The PSO is well used in control system, for instance, in [17], the parameters of PID are tuned by ANN where their weights are optimized using PSO method to avoid any local minima/maxima in its searching procedure. In [18], the authors proposed a design of decentralized load-frequency controller for interconnected power systems with ac-dc parallel using PSO algorithm. The experiment result illustrated that their method have rapid dynamic response ability. In [19], the PSO algorithm is implemented to optimize the own five parameters of *PI<sup>λ</sup> D<sup>δ</sup>* controller via El-Khazali's approach in order to minimize several error functions satisfying some step response specifications such as the set of time domain and frequency domain constraints; overshoot, rise time and settling time. In [20], a comparative analysis of PSO algorithms is carried out, where two PSO algorithms, namely PSO with linearly decreasing inertia weight (LDW-PSO), and PSO algorithm with constriction factor approach (CFA-PSO), are independently tested for different PID structures.

In this chapter, a comparison of the performance of the PSO optimized neural network with the standard back-propagation is presented for the adaptive indirect control of nonlinear time-varying discrete system.

The present chapter is organized as follows. After this introduction, section 2 reviews the problem statement. Furthermore, in section 3 the neural network optimization methods are shown. In Section 4, tuning neural network controller using classical approach is presented. However, the section 5 details tuning neural network controller using PSO approach. An example of nonlinear system is studied, in section 6, to illustrate the proposed efficiency of the method. Section 7 gives the conclusion of this chapter.
