In real-time problems, the possibilities of having a precise mathematical model describing the dynamics of the nonlinear system are scarce. Besides, the measurements invariably are tainted with noise which makes the problem of estimating the actual states of the system more difficult. The most common way of solving this issue involves the application of the Kalman Filter (KF) or the Extended Kalman Filter (EKF), for linear and nonlinear systems, respectively; although in both cases, the estimation heavily relies on linear techniques. In a different way, the James-Stein Filter provides a robust approach to estimate linear and nonlinear systems under parametric uncertainties of the mathematical model. In this brief note, a slightly different James-Stein State Estimator (JSSE), named Modified James- Stein State Estimator (JSSE-M), is presented as an alternative to filtering the states of nonlinear systems within a control scheme. The main contribution of this work is the comparison of performance between KF, EKF, JSSE, and JSSE-M when they are used on a relatively complex nonlinear system which is extremely dependent on its parameters, namely the quadrotor. In this sense, some interesting comparisons focused on both, the effectiveness and processing time are provided.

In this study, a modified linear technique is proposed for the controllability and observability of robotic arms, the modified linear technique consists of the following steps: a transformation is used to rewrite a nonlinear time-variant model as a linear time-variant model, this linear time-variant model is evaluated at origin to obtain a linear time-invariant model, and the rank condition tests the controllability and observability of the linear time-invariant model. The modified linear technique is better than the linearization technique because the modified linear technique does not use the Jacobian approximation, while the linearization technique needs the Jacobian approximation. The modified linear technique is better than the linear technique because the modified linear technique can be applied to robotic arms with rotational and prismatic joints, while the linear technique can only be applied to robotic arms with rotational joints.

In this article, an argument Kalman filter is exposed for the fast updating of a neural network. The argument Kalman filter is developed based on the extended Kalman filter, but the recommended scheme has the next two advantages: first, it has less computational complexity because it only employs the Jacobian argument instead of the full Jacobian, second, its gain is ensured to be uniformly stable based on the Lyapunov approach. The commented scheme is applied for the modeling of two Takagi-Sugeno fuzzy models.

In this work, it is theoretically demonstrated that a quadrotor can track trajectories using a low-cost GPS with signal losses in unpredictable instants. The lack of a continuous altitude output and the signal loss are solved with certain limitations using two-hybrid linear observers. This type of observer is originally employed to compensate for data loss in computer networks. This was possible due to the sufficient conditions for uniform global asymptotic stability theorems of hybrid systems with persistent jumping. This concept is based on a dynamic hybrid system that guarantees a jumping condition with a Lyapunov function constant when the system flows and decreases during jumps. The quadrotor was modeled like a linear time-invariant system. The results are presented using simulations.

Sliding mode control is a robust technique that is used to overcome difficulties such as parameter variations, unmodeled dynamics, external disturbances, and payload changes in the position-tracking problem regarding robots. However, the selection of the gains in the controller could produce bigger forces than are required to move the robots, which requires spending a large amount of energy. In the literature, several approaches were used to manage these features, but some proposals are complex and require tuning the gains. In this work, a sliding mode controller was designed and optimized in order to save energy in the position-tracking problem of a two-degree-of-freedom SCARA robot. The sliding mode controller gains were optimized usinga Bat algorithm to save energy by minimizing the forces. Finally, two controllers were designed and implemented in the simulation, and as a result, adequate controller gains were found that saved energy by minimizing the forces.