Edgar N. Sanchez

LMI-based approach for asymptotically stability analysis of delayed neural networks

This paper derives some sufficient conditions for asymptotic stability of neural networks with constant or time-varying delays. The Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) approach are employed to investigate the problem. It shows how some well-known results can be refined and generalized in a straightforward manner. For the case of constant time delays, the stability criteria are delay-independent; for the case of time-varying delays, the stability criteria are delay-dependent. The results obtained in this paper are less conservative than the ones reported so far in the literature and provides one more set of criteria for determining the stability of delayed neural networks.

Input-to-state stability (ISS) analysis for dynamic neural networks

In this paper a novel approach to assess the stability of dynamic neural networks is presented. Using a Lyapunov function, we determine conditions to guarantee input-to-state stability (ISS) which also ensures global asymptotic stability (GAS). The applicability of these conditions is illustrated by two examples.

Differential neural networks for Robust nonlinear control : identification, state estimation and trajectory tracking

Theoretical Study: Neural Networks Structures Nonlinear System Identification: Differential Learning Sliding Mode Identification: Algebraic Learning Neural State Estimation Passivation via Neuro Control Neuro Trajectory Tracking Neurocontrol Applications: Neural Control for Chaos Neuro Control for Robot Manipulators Identification of Chemical Processes Neuro Control for Distillation Column General Conclusions and Future Work Appendices: Some Useful Mathematical Facts Elements of Qualitative Theory of ODE Locally Optimal Control and Optimization.

Discrete-Time Adaptive Backstepping Nonlinear Control via High-Order Neural Networks

This paper deals with adaptive tracking for discrete-time multiple-input-multiple-output (MIMO) nonlinear systems in presence of bounded disturbances. In this paper, a high-order neural network (HONN) structure is used to approximate a control law designed by the backstepping technique, applied to a block strict feedback form (BSFF). This paper also includes the respective stability analysis, on the basis of the Lyapunov approach, for the whole controlled system, including the extended Kalman filter (EKF)-based NN learning algorithm. Applicability of the scheme is illustrated via simulation for a discrete-time nonlinear model of an electric induction motor.

Combining fuzzy, PID and regulation control for an autonomous mini-helicopter

This paper reports on the synthesis of different flight controllers for an X-Cell mini-helicopter. They are developed on the basis of the most realistic mathematical model currently available. Two hybrid intelligent control systems, combining computational intelligence methodologies with other control techniques, are investigated. For both systems, Mamdani-type fuzzy controllers determine the set points for altitude/attitude control. These fuzzy controllers are designed using a simple rule base. The first scheme consists of conventional SISO PID controllers for z-position and roll, pitch and yaw angles. In the second scheme, two of the previous PID controllers are used for roll and pitch, and a linear regulator is added to control altitude and yaw angle. These control schemes mimic the action of an expert pilot. The designed controllers are tested via simulations. It is shown that the designed controllers exhibit good performance for hover flight and control positioning at slow speed.

Takagi-Sugeno fuzzy scheme for real-time trajectory tracking of an underactuated robot

This paper presents an approach to achieve trajectory tracking for nonlinear systems. Combining the linear regulator theory with Takagi-Sugeno (T-S) fuzzy methodology; an algorithm is described for the trajectory tracking. The main contribution of the paper includes a real-time application of this algorithm to a specific two-rigid-link underactuated robot, called the Pendubot.

Real-Time Discrete Neural Block Control Using Sliding Modes for Electric Induction Motors

This paper deals with real-time adaptive tracking for discrete-time induction motors in the presence of bounded disturbances. A high-order neural-network structure is used to identify the plant model, and based on this model, a discrete-time control law is derived, which combines discrete-time block-control and sliding-mode techniques. This paper also includes the respective stability analysis for the whole system with a strategy to avoid adaptive weight zero-crossing. The scheme is implemented in real time using a three-phase induction motor.

Discrete-Time High Order Neural Control

The objective of this work is to present recent advances in the theory of neural control for discrete-time nonlinear systems with multiple inputs and multiple outputs. The results that appear in each chapter include rigorous mathematical analyses, based on the Lyapunov approach, that guarantee its properties; in addition, for each chapter, simulation results are included to verify the successful performance of the corresponding proposed schemes. In order to complete the treatment of these schemes, the final chapter presents experimental results related to their application to a electric three phase induction motor, which show the applicability of such designs. The proposed schemes could be employed for different applications beyond the ones presented in this book. The book presents solutions for the output trajectory tracking problem of unknown nonlinear systems based on four schemes. For the first one, a direct design method is considered: the well known backstepping method, under the assumption of complete sate measurement; the second one considers an indirect method, solved with the block control and the sliding mode techniques, under the same assumption. For the third scheme, the backstepping technique is reconsidering including a neural observer, and finally the block control and the sliding mode techniques are used again too, with a neural observer. All the proposed schemes are developed in discrete-time. For both mentioned control methods as well as for the neural observer, the on-line training of the respective neural networks is performed by Kalman Filtering.

Discrete-Time Neural Sliding-Mode Block Control for a DC Motor With Controlled Flux

An adaptive discrete-time tracking controller for a direct current motor with controlled excitation flux is presented. A recurrent neural network is used to identify the plant model; this neural identifier is trained with an extended Kalman filter algorithm. Then, the discrete-time block-control and sliding-mode techniques are used to develop the trajectory tracking. This paper also includes the respective stability analysis for the whole closed-loop system. The effectiveness of the proposed control scheme is verified via real-time implementation.

Nonlinear System Approximation by Neural Networks: Error Stability Analysis

In this article we analyze nonlinear system approximation by Dynamic Neural Networks with the same state space dimension as the system. The state approximation error is formulated, and by means of ...