Mohamed Djemel

Two coupled neural-networks-based solution of the Hamilton-Jacobi-Bellman equation

Abstract: This work is aimed at looking into the determination of optimal neuro-feedback control for discrete time nonlinear systems. The basic idea consists in the use of two coupled neural networks to approximate the solution of the Hamilton-Jacobi-Bellman equation (HJB) and to obtain a robust feedback closed-loop control law. The used learning algorithm is a modified version of the backpropagation one. As an illustration, a numerical nonlinear discrete time example is considered. Simulation results show the effectiveness of the proposed method.

Hierarchical control for discrete large-scale complex systems by intelligent controllers

This paper presents a new method to approximate optimal control strategies of discrete time large-scale nonlinear systems using intelligent approaches. The idea is based on the decomposition principle of the global system into interconnected subsystems for which nonlinearities are located in the interconnection terms. Then, the mixed coordination procedure between different subsystems is formulated as a hierarchical method for the solution of large-scale optimal control problems. So, for each subsystem, local optimal feedback gains are expressed in terms of the interconnection vector. For this purpose, neural networks and fuzzy logic controllers have been constructed in order to identify these gains. A comparison with the differential dynamic programming procedure as a reference method is done. Simulation results of two numerical examples show that the proposed method yields to satisfactory performances, and the robustness of the proposed approaches has been tested.

Stability Analysis of Neural Networks-Based System Identification

This paper treats some problems related to nonlinear systems identification. A stability analysis neural network model for identifying nonlinear dynamic systems is presented. A constrained adaptive stable backpropagation updating law is presented and used in the proposed identification approach. The proposed backpropagation training algorithm is modified to obtain an adaptive learning rate guarantying convergence stability. The proposed learning rule is the backpropagation algorithm under the condition that the learning rate belongs to a specified range defining the stability domain. Satisfying such condition, unstable phenomena during the learning process are avoided. A Lyapunov analysis leads to the computation of the expression of a convenient adaptive learning rate verifying the convergence stability criteria. Finally, the elaborated training algorithm is applied in several simulations. The results confirm the effectiveness of the CSBP algorithm.

Decomposition and hierarchical control for discrete complex systems by fuzzy logic controllers

This paper proposes a method to compute sub-optimal control strategies of discrete time large-scale non-linear systems by fuzzy logic controllers. The method is based on the principle of decomposition of the global system into inter-connected subsystems. We consider that the non-linearities are located in the interconnections terms. Then, a mixed method of coordination procedure between different subsystems is formulated. So, for each subsystem, local optimal feedback gains are expressed as a function of the interconnection vector. Within this approach, first order Tkagi-Sugeno fuzzy logic systems have been constructed in order to identify these gains. Simulation results of a rotary crane show the effectiveness of the method and the robustness of the proposed approach.

On the neuro-genetic approach for determining optimal control of a rotary crane

The aim of this paper considers the determination of optimal control trajectories of a complex process. The proposed method is based on the decomposition of the system into interconnected subsystems. We consider the cases where subsystems are linear in terms of their state and control vectors. For this reason, a neural network is identified which compute local gains. Genetic algorithms are used to optimize the networks weights. Simulation results show that the proposed approximations yield satisfactory performances.

On the fuzzy modeling of uncertain nonlinear systems

This paper deals with fuzzy modeling of nonlinear systems affected by bounded uncertainties. The proposed model is composed of two parts: a linear uncertain part and a nonlinear part. The linear uncertain part is obtained by system linearization around some operating points. Nonlinear part parameters are estimated through the use of the descent gradient method. Finally, two examples are treated to illustrate the effectiveness of the proposed modeling method.

Fuzzy predictive control of nonlinear systems

This paper presents two strategies of nonlinear predictive control based on a Takagi-Sugeno fuzzy model. The first one introduces a fuzzy logic-based modeling methodology, where a nonlinear system is divided into a number of linear subsystems. So the linear model based predictive control (MPC) technique is used for each subsystem. In the second one, the fuzzy model is considered as a nonlinear model of the system and the control signal is obtained by minimizing either the cumulative differences or the instant difference between set-point and fuzzy model output. The efficiency of these two fuzzy model predictive control (FMPC) approaches is demonstrated through two examples.

Decomposition and hierarchical control for discrete large scale system using neural networks

This paper presents a method to compute sub-optimal control strategies of discrete time large scale nonlinear systems by neural networks. The method is based on the principle of decomposition of the global system into interconnected subsystems for which we consider that non-linearities are located in the interconnection terms. Then, a mixed method is considered to coordinate between different subsystems in order to compute the optimal control. So, for each subsystem, local optimal feedback gains are expressed in terms of the interconnection vector. For this purpose, neural networks have been used in order to identify these gains. Simulation results of a rotary crane show that the proposed method yields to satisfactory performances. The robustness of the proposed approach is analysed.

Design of optimal fuzzy logic controller with genetic algorithms

This paper looks into the determination of optimal trajectories of a nonlinear model of a two-link articulated manipulator. In a first step, genetic algorithms are used to generate an optimal control sequence which is used to bring the manipulator robot into a desired position. In a second step, genetic algorithms optimize the parameters of membership functions to facilitate the realization of a Sugeno fuzzy logic based optimal controller. Simulation results show that the second step gives suboptimal solutions, however the first step yields to optimal solutions which are very sensitive with respect to the parameter variation of the system.

Robust sliding mode control for nonlinear uncertain discrete-time systems

This paper deals with robust sliding mode control for nonlinear uncertain discrete-time systems. The dynamics of a such system are approximated by a model including two parts: the first one is a linear uncertain expression and the second part is a nonlinear static term assimilated to an additive perturbation. Then, a robust sliding mode control is synthesized basing on this model. Finally, two simulation examples are presented to show the validity of the proposed control design.