Hermitian K-theory and 2-regularity for totally real number fields

We completely determine the 2-primary torsion subgroups of the hermitian K-groups of rings of 2-integers in totally real 2-regular number fields. The result is almost periodic with period 8. We also identify the homotopy fibers of the forgetful and hyperbolic maps relating hermitian and algebraic K-theory. The result is then exactly periodic of period 8. In both the orthogonal and symplectic cases, we prove the 2-primary hermitian Quillen-Lichtenbaum conjecture.Comment: To appear in Mathematische Annale

PID, BFO-optimized PID, and PD-FLC control of a two-wheeled machine with two-direction handling mechanism: a comparative study

In this paper; three control approaches are utilized in order to control the stability of a novel five-degrees-of-freedom two-wheeled robotic machine designed for industrial applications that demand a limited-space working environment. Proportional–integral–derivative (PID) control scheme, bacterial foraging optimization of PID control method, and fuzzy logic control method are applied to the wheeled machine to obtain the optimum control strategy that provides the best system stabilization performance. According to simulation results, considering multiple motion scenarios, the PID controller optimized by bacterial foraging optimization method outperformed the other two control methods in terms of minimum overshoot, rise time, and applied input forces