The multilayer perceptrons (MLPs) are widely used in many fields, however, singularities in the parameter space may seriously influence the learning dynamics of MLPs and cause strange learning behaviors. Given that the singularities are the subspaces of the parameter space where the Fisher information matrix (FIM) degenerates, the FIM plays a key role in the study of the singular learning dynamics of the MLPs. In this paper, we obtain the analytical form of the FIM for unipolar activation function-based MLPs where the input subjects to the Gaussian distribution with general covariance matrix and the unipolar error function is chosen as the activation function. Then three simulation experiments are taken to verify the validity of the obtained results.

The existence of singularities often affects the learning dynamics in feedforward neural networks. In this paper, based on theoretical analysis results, we numerically analyze the learning dynamics of radial basis function (RBF) networks near singularities to understand to what extent singularities influence the learning dynamics. First, we show the explicit expression of the Fisher information matrix for RBF networks. Second, we demonstrate through numerical simulations that the singularities have a significant impact on the learning dynamics of RBF networks. Our results show that overlap singularities mainly have influence on the low dimensional RBF networks and elimination singularities have a more significant impact to the learning processes than overlap singularities in both low and high dimensional RBF networks, whereas the plateau phenomena are mainly caused by the elimination singularities. The results can also be the foundation to investigate the singular learning dynamics in deep feedforward neural networks.

In this paper, a fully nonlinear aircraft dynamic model in the presence of wind is introduced. Assuming the wind vortex hypothesis, the equations of motion are formulated in a novel nonlinear control system form that is affine in control input for the chosen aircraft model. A sliding mode controller is subsequently developed where the position of the throttle is used to control the air velocity and the aileron, elevator, and rudder deflections are employed to control the rest of the dynamics. It is shown that the full state converges to the desired values even in the presence of the uncertainties imposed by the wind. The applicability of the controller design is illustrated through simulations in the presence of uncertainties.

This paper presents a three-axis attitude control algorithm for small satellites using only magnetic actuation. Such satellites are controllable only in two axes that are perpendicular to the local geomagnetic field vector at any point in time since the control torque can only be generated perpendicular to the geomagnetic field vector. We first model the attitude kinematics and dynamics in the geomagnetic frame in the form of an underactuated system. We then develop a three-axis magnetic attitude control algorithm using the theory of slowly-varying systems. The effectiveness of the proposed control law is illustrated through a computer simulation.

This paper studies the sloshing suppression problem in point-to-point liquid container transfer via a planar Prismatic-Prismatic-Revolute (PPR) robot. The most prominent liquid sloshing modes are modeled using a mechanical analogy based on multiple mass-spring elements. The control inputs are two forces and a torque applied to the prismatic joints and the revolute joint, respectively. The control objective is to control the robot end-effector movement while suppressing the sloshing modes. A Lyapunov-based feedback controller is designed to achieve the control objective. In contrast to the full-state feedback controller we developed in our previous work, the partial-state feedback controller described in this paper does not use slosh state information. The effectiveness of the controller is demonstrated through a simulation example.