This paper studies on aeroelastic control for the two-dimensional airfoil-flap system with unknown gust disturbances and model uncertainties. Open loop limit cycle oscillation (LCO) happens at the post-flutter speed. Structural stiffness of the aeroelastic system is represented by nonlinear polynomials. To robustly suppress aeroelastic vibration within finite time, a backstepping terminal sliding mode control (BTSMC) is proposed. In addition a learning rate is incorporating into the backstepping TSMC to adjusthow fast the aeroelastic response converges to zero. In order to overcome the limitation of the BTSMC design that it is dependent on prior knowledge, a nonlinear disturbance-observer (DO) is designed to estimate the variable observable disturbances. The closed-loop aeroelastic control system is proved to be globally asymptotically stable and converge within finite time by using Lyapunov theory. Simulation results of an aeroelastic two-dimensional airfoil with both trailing-edge (TE) and leading-edge (LE) control surfaces show that the proposed DO-BTSMC is effective for flutter suppression, even when subjected to gusts and parameter uncertainties.

Skid steer mobile robots are widely used in indoor and outdoor applications. However, accurate trajectory tracking control for this kind of robot is quite challenging due to the uncertainties arising from the complex behavior of frictional force, external disturbances, and undergoing fluctuations in the instantaneous center of rotation (ICR) during turning maneuvers. The uncertainties directly disturb velocities and make it impossible for the robot to track the command velocities, thus making the SSMR unable to follow the reference path. This paper proposes a nonsingular terminal sliding mode control (NTSMC) based on backstepping for a 4-wheel skid steer mobile robot to cope with the aforementioned challenges. The strategy seeks to mitigate the impact of external disturbances and model uncertainties by developing an adaptive law to estimate the integrated lumped outcome. Then, the finite time stability of the closed-loop system is proven using Lyapunov’s theory. The designed NTSMC input is continuous and has no noticeable chattering problem. It has also been noted from the analysis that the proposed control strategy is strongly robust against disturbance and modeling uncertainties. The proposed control scheme demonstrates effective trajectory tracking performance in the presence of disturbance and modeling uncertainties through simulations.

We reduplicate the Book “Dark Energy” by M. Li, X-D. Li, and Y. Wang, given zero-point energy calculation with an unexpected “length’ added to the ‘width’ of a graviton wave just prior to specifying the creation of ‘gravitons’, using the Rosen and Israelit model of a nonsingular universe. In doing so we are in addition to obtaining a wavelength 10^30 times greater than Planck’s length so we can calculate DE, may be able to with the help of the Rosen and Israelit model have a first approximation as to the arrow of time, and a universe with massive gravity. We have left the particulars of the nonsingular starting point undefined but state that the Rosen and Israelit model postulates initial temperatures of 10^-180 Kelvin and also a value of about Planck temperature, at 10^-3 centimeters radii value which may satisfy initial conditions asked by t’Hooft for describing an arrow of time. A key assumption is that the DE is formed at 10^-3 cm, after an expansion of 10^30 times in radii, from the Planck length radius nonsingular starting point. The given starting point for DE in this set of assumptions is where there is a change in the cosmic acceleration, to a zero value, according to Rosen and Israel, with time t = 1.31 times 10^-42 seconds. Which may be where we may specify a potential magnitude, V, which has ties into inflaton physics. The particulars of the model from Rosen and Israelit allow a solution to be found, without discussion of where that nonsingular starting point came from, a point the author found in need of drastic remedies and fixes.