Pure Hilbert Algebras with Infimum
In [6], iH-algebras were introduced in order to indicate an equational version of the class of Hilbert algebras where each pair of elements has infimum. These authors also proved that this variety hasthe class of Curry's implicative semilattices ([9]) as a proper subvariety. On the other hand, in [4] a special class of Hilbert algebras associated with ordered sets, which they called order algebras, were investigated. These algebras were also studied in [1] under the name of pure Hilbert algebras.Bearing in mind the above results, in this paper we introduce the notion of pure Hilbert algebras with infimum (or ipH-algebras, for short). Furthermore, we characterize the lattice of ipH-congruences and we determine the subdirectly irreducible ipH-algebras. Besides, we prove that subdirectly irreducible ipH-algebras are alsosubdirectly irreducible iH-algebras.
Congruences and Idealas in Hilbert Algebras
The concept of ideal for Hilbert algebras is introduced. It is presented a construction of a congruence having given ideal as its class. Moreover, it is shown that every congruence on a Hilbert algebra has this form.
L1 Adaptive Controller for Attitude Control of Multirotors
In this work we show an application of L1 Adaptive control theory for attitude control of UAVs. We implement the flight control system on a multirotor to show robustness and precise attitude tracking in the presence of modeling uncertainties and environmental disturbances. We choose backstepping control architecture, since the kinematics and dynamics of multirotors in most cases can be written in strict feedback form. We further exploit the fact that the kinematics of the plant, while free of uncertainties, is nonlinear, which makes it highly suitable for dynamic inversion control at each level of backstepping. On the other hand, plant dynamics is uncertain and is affected by environmental disturbances such as wind gusts, unmodeled dynamics etc. Therefore, we consider 3 variants of the control architecture. The first method uses backstepping to determine the moment demand and augments it with the L1 adaptive controller to account for uncertainties and provide robustness with guaranteed transient performance. The second architecture apply the concept of L1 adaptive backstepping to the same problem; and the third architecture uses L1 backstepping for quaternion representation of the system dynamics, which helps to avoid the singularities associated with Euler angles.