Imam Sutrisno

Lyapunov learning algorithm for Quasi-ARX neural network to identification of nonlinear dynamical system

In this note, we present the modeling of nonlinear dynamical systems with Quasi-ARX neural network using Lyapunov algorithm in learning process. This work exploits the idea on learning algorithm in nonlinear kernel part of Quasi-ARX model to improve stability and fast convergence of error. The proposed algorithm is then employed to model and predict a classical nonlinear system with input dead zone and nonlinear dynamic systems, exhibiting the effectiveness of proposed algorithm. Based on the result of simulation, the proposed algorithm can make the error in process learning become fast convergence, ultimately bounded, and the error distributed uniformly.

Modified fuzzy adaptive controller applied to nonlinear systems modeled under quasi-ARX neural network

In this article, a fuzzy adaptive controller approach is presented for nonlinear systems. The proposed quasi-ARX neural network based on Lyapunov learning algorithm is used to update its weight for prediction model as well as to modify fuzzy adaptive controller. The improving performances of the Lyapunov learning algorithm are stable in the learning process of the controller and able to increase the accuracy of the controller as well as fast convergence of error. The simulations are intended to show the effectiveness of the proposed method.

Deep searching for parameter estimation of the linear time invariant (LTI) system by using Quasi-ARX neural network

This work exploits the idea on how to search parameter estimation and increase its convergence speed for the Liner Time Invariant (LTI) system. The convergence speed of parameter estimation is the one problem and plays an important role in the adaptive controller to increase performance. The well-known algorithm is the recursive least square algorithm. However, the speed of convergence is still low and is influenced by the number of sampling, which is represented by the limited availability for the information vector. We offer a new method to increase the convergence speed by applying Quasi-ARX model. Quasi-ARX model performs two steps identification process by presenting parameter estimation as a function over time. The first, parameters estimation of macro-part sub-model are searched by the least square error, and the second is to sharpen the searching by performing backpropagation learning of multi layer parceptron network.

Quasi‐ARX neural network based adaptive predictive control for nonlinear systems

In this paper, a new switching mechanism is proposed based on the state of dynamic tracking error so that more information will be provided –not only the error but also a one up to pth differential error will be available as the switching variable. The switching index is based on the Lyapunov stability theory. Thus the switching mechanism can work more effectively and efficiently. A simplified quasi-ARX neural-network (QARXNN) model presented by a state-dependent parameter estimation (SDPE) is used to derive the controller formulation to deal with its computational complexity. The switching works inside the model by utilizing the linear and nonlinear parts of an SDPE. First, a QARXNN is used as an estimator to estimate an SDPE. Second, by using SDPE, the state of dynamic tracking error is calculated to derive the switching index. Additionally, the switching formula can use an SDPE as the switching variable more easily. Finally, numerical simulations reveal that the proposed control gives satisfactory tracking and disturbance-rejection performances. Experimental results demonstrate its effectiveness.

An adaptive predictive control based on a quasi-ARX neural network model

A quasi-ARX (quasi-linear ARX) neural network (QARXNN) model is able to demonstrate its ability for identification and prediction highly nonlinear system. The model is simplified by a linear correlation between the input vector and its nonlinear coefficients. The coefficients are used to parameterize the input vector performed by an embedded system called as state dependent parameter estimation (SDPE), which is executed by multi layer parceptron neural network (MLPNN). SDPE consists of the linear and nonlinear parts. The controller law is derived via SDPE of the linear and nonlinear parts through switching mechanism. The dynamic tracking controller error is derived then the stability analysis of the closed-loop controller is performed based Lyapunov theorem. Linear based adaptive robust control and nonlinear based adaptive robust control is performed with the switching of the linear and nonlinear parts parameters based Lyapunov theorem to guarantee bounded and convergence error.

An improved adaptive switching control based on quasi-ARX neural network for nonlinear systems

In this paper, an improved switching mechanism based on quasi-linear auto regressive exogenous (quasi-ARX) neural network (QARXNN) is presented for the adaptive control of nonlinear systems. The proposed switching control is composed of a QARXNN-based prediction model and an improved switching mechanism using two new adaptive control laws, first is moving average filter law and second is new switching law. Since the control result of nonlinear predictor is better than the linear predictor in most of the time, the adaptive control with a simple switching mechanism has many useless switching during the processing. Hence, the improved smooth switching mechanism is proposed to replace the original switching mechanism; it can improve the performance by reducing the useless switching while guaranteeing stability of the system control. The simulations show that the efficiency of the proposed control method is satisfied in stability, improve control accuracy and robustness.

Nonlinear Model-Predictive Control Based on Quasi-ARX Radial-Basis Function-Neural-Network

A nonlinear model-predictive control (NMPC) is demonstrated for nonlinear systems using an improved fuzzy switching law. The proposed moving average filter fuzzy switching law (MAFFSL) is composed of a quasi-ARX radial basis function neural network (RBFNN) prediction model and a fuzzy switching law. An adaptive controller is designed based on a NMPC. a MAFFSL is constructed based on the system switching criterion function which is better than the (ON/OFF) switching law and a RBFNN is used to replace the neural network (NN) in the quasi-ARX black box model which is understood in terms of parameters and is not an absolute black box model, in comparison with NN. The proposed controller performance is verified through numerical simulations to demonstrate the effectiveness of the proposed method.

Implementation of Lyapunov learning algorithm for fuzzy switching adaptive controller modeled under Quasi-ARX Neural Network

This paper presents a fuzzy adaptive controller applied to a non linear system modeled under a Quasi-linear ARX Neural Network, with stability proof by using the Lyapunov approach. This work exploits the new idea to use Lyapunov function to train multi-input multi-output neural network on the core-part sub-model. The proposed controller is designed between a non linear controller and linear controller based on fuzzy switching algorithm. Finally improving performances of the Lyapunov learning algorithm are stable in the learning process, fast convergence of error, and able to increase the accuracy of the controller.