Jaime Pacheco

Backpropagation to train an evolving radial basis function neural network

In this paper, a stable backpropagation algorithm is used to train an online evolving radial basis function neural network. Structure and parameters learning are updated at the same time in our algorithm, we do not make difference in structure learning and parameters learning. It generates groups with an online clustering. The center is updated to achieve the center is near to the incoming data in each iteration, so the algorithm does not need to generate a new neuron in each iteration, i.e., the algorithm does not generate many neurons and it does not need to prune the neurons. We give a time varying learning rate for backpropagation training in the parameters. We prove the stability of the proposed algorithm.

Uniform stable observer for the disturbance estimation in two renewable energy systems.

In this study, an observer for the states and disturbance estimation in two renewable energy systems is introduced. The restrictions of the gains in the proposed observer are found to guarantee its stability and the convergence of its error; furthermore, these results are utilized to obtain a good estimation. The introduced technique is applied for the states and disturbance estimation in a wind turbine and an electric vehicle. The wind turbine has a rotatory tower to catch the incoming air to be transformed in electricity and the electric vehicle has generators connected with its wheels to catch the vehicle movement to be transformed in electricity.

An stable online clustering fuzzy neural network for nonlinear system identification

In this paper, we propose a online clustering fuzzy neural network. The proposed neural fuzzy network uses the online clustering to train the structure, the gradient to train the parameters of the hidden layer, and the Kalman filter algorithm to train the parameters of the output layer. In our algorithm, learning structure and parameter learning are updated at the same time, we do not make difference in structure learning and parameter learning. The center of each rule is updated to obtain the center is near to the incoming data in each iteration. In this way, it does not need to generate a new rule in each iteration, i.e., it neither generates many rules nor need to prune the rules. We prove the stability of the algorithm.

Uniform stable radial basis function neural network for the prediction in two mechatronic processes

The stable neural networks are the models where their variables and parameters remain bounded through the time and where the overfitting is avoided. A model with overfit has many parameters relative to the number of data, and it has poor predictive performance because it overreacts to minor fluctuations in the data. This paper presents a method to obtain a stable algorithm for the learning of a radial basis function neural network. The method consists of: 1) the radial basis function neural network is linearized, 2) the algorithm for the learning of the radial basis function neural network is introduced, 3) stability of the mentioned technique is assured, 4) convergence of the suggested method is guaranteed, and 5) boundedness of parameters in the focused technique is assured. The above mentioned method is applied for the learning of two mechatronic processes.

State estimation in MIMO nonlinear systems subject to unknown deadzones using recurrent neural networks

Abstract This paper deals with the problem of state observation by means of a continuous-time recurrent neural network for a broad class of MIMO unknown nonlinear systems subject to unknown but bounded disturbances and with an unknown deadzone at each input. With respect to previous works, the main contribution of this study is twofold. On the one hand, the need of a matrix Riccati equation is conveniently avoided; in this way, the design process is considerably simplified. On the other hand, a faster convergence is carried out. Specifically, the exponential convergence of Euclidean norm of the observation error to a bounded zone is guaranteed. Likewise, the weights are shown to be bounded. The main tool to prove these results is Lyapunov-like analysis. A numerical example confirms the feasibility of our proposal.

Proportional Derivative Control with Inverse Dead-Zone for Pendulum Systems

A proportional derivative controller with inverse dead-zone is proposed for the control of pendulum systems. The proposed method has the characteristic that the inverse dead-zone is cancelled with the pendulum dead-zone. Asymptotic stability of the proposed technique is guaranteed by the Lyapunov analysis. Simulations of two pendulum systems show the effectiveness of the proposed technique.

Robust fault diagnosis of disturbed linear systems via a sliding mode high order differentiator

A fault estimator for linear systems affected by disturbances is proposed. Faults appearing explicitly in the state equation and in the system output (actuator faults and sensor faults) are considered. With this design neither the estimation of the state vector nor the estimation of the disturbances is required, implying that the structural conditions are less restrictive than the ones required to design an unknown input observer. Furthermore, the number of unknown inputs (faults plus disturbances) may be greater than the number of outputs. The faults are written as an algebraic expression of a high-order derivative of a function depending on the output. Thus, the reconstruction of the fault signals is carried out by means of a sliding mode high-order differentiator, which requires the derivative of the faults to have a bounded norm.

Trajectory planning and collisions detector for robotic arms

The major contributions of this paper are as follows: (1) the Gilbert–Johnson–Keerthi (GJK) algorithm is a collisions detector algorithm, a modified Gilbert–Johnson–Keerthi algorithm is presented, the proposed GJK algorithm uses a different distance, (2) some examples of GJK algorithm are presented, in the last example, the GJK distance algorithm is used to detect the collisions of a camera with its environment inside of a warehouse, the camera cannot cross any part of the structure of the warehouse, the camera needs to go around the structure, when the camera touches the structure, the camera goes to the right or to the left, (3) the time used in a cycle of work of the transelevator robotic arm is presented, it can be extended to other kind of robotic arms, (4) some examples of the time used in a cycle of work are presented, in the least example, the algorithm is used to control the time needed for the transelevator to go from one place to other one, (5) this paper presents a new trajectory planning algorithm which divides the trajectory in n periods, when n is equal to 2, the proposed algorithm is the same as other algorithms, but for n higher than 2, the proposed algorithm gives other optional trajectories, so the proposed algorithm lets the designer to take a better trajectory than with the previous algorithms, (6) some examples of the proposed trajectories planning algorithm are presented, in the least example, the proposed trajectory planning algorithm is used to control the movements of a transelevator inside of a warehouse.

System Identification Using Multilayer Differential Neural Networks: A New Result

In previous works, a learning law with a dead zone function was developed for multilayer differential neural networks. This scheme requires strictly a priori knowledge of an upper bound for the unmodeled dynamics. In this paper, the learning law is modified in such a way that this condition is relaxed. By this modification, the tuning process is simpler and the dead-zone function is not required anymore. On the basis of this modification and by using a Lyapunov-like analysis, a stronger result is here demonstrated: the exponential convergence of the identification error to a bounded zone. Besides, a value for upper bound of such zone is provided. The workability of this approach is tested by a simulation example.

Disturbance Rejection in Two Mechatronic Systems

In this investigation, a control for the disturbance rejection in mechatronic systems is designed. In the proposed strategy, the transfer function of the outputs and disturbances is forced to be zero by the control law to obtain an acceptable disturbance rejection. The proposed technique is verified by two examples.