Global complete observability and output-to-state stability imply the existence of a globally convergent observer

We consider systems which are globally completely observable and output-to-state stable. The former property guarantees the existence of coordinates such that the dynamics can be expressed in observability form. The latter property guarantees the existence of a state norm observer and therefore the possibility of bounding any continuous state functions. Both properties allow to conceptually build an observer from an approximation of an exponentially attractive invariant manifold in the space of the system state and an output driven dynamic extension. The proposed observer provides convergence to zero of the estimation error within the domain of definition of the solutions. The work of A. Astolfi is partly supported by the Leverhulme Trust.     

Asymptotic stabilization of some equilibria of an underactuated underwater vehicle

The stabilization problem for selected relative equilibria of an underactuated rigid body, modelling a simple underwater vehicle, moving in an ideal fluid is addressed. State feedback control laws achieving local asymptotic stability of a forward motion and of a diving/rising with forward/reverse motion are proposed. The control design exploits the Hamiltonian nature of the system to be controlled and it is based on the so-called interconnection and damping assignment (IDA) procedure. Simulation results complete the work.     

Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes

Total energy shaping is a controller design methodology that achieves (asymptotic) stabilization of mechanical systems endowing the closed-loop system with a Lagrangian or Hamiltonian structure with a desired energy function - that qualifies as Lyapunov function for the desired equilibrium. The success of the method relies on the possibility of solving two PDEs which identify the kinetic and potential energy functions that can be assigned to the closed loop. Particularly troublesome is the partial differential equation (PDE) associated to the kinetic energy which is nonlinear and inhomogeneous and the solution, that defines the desired inertia matrix, must be positive-definite. In this note, we prove that we can eliminate or simplify the forcing term in this PDE by modifying the target dynamics and introducing a change of coordinates in the original system. Furthermore, it is shown that, in the particular case of transformation to the Lagrangian coordinates, the possibility of simplifying the PDEs is determined by the interaction between the Coriolis and centrifugal forces and the actuation structure. The examples of pendulum on a cart and Furuta's pendulum are used to illustrate the results.     

Rationally designed inhibitors as tools for comparing the mechanism of squalene-hopene cyclase with oxidosqualene cyclase

The inhibition of squalene-hopene cyclase (SHC) (E.C. 5.4.99.-), an enzyme of bacterial membranes catalyzing the formation of pentacyclic sterol-like triterpenes, was studied by using different classes of compounds originally developed as inhibitors of oxidosqualene cyclase (OCS) (E.C. 5.4.99.7), the enzyme of eukaryotes responsible for the formation of tetracyclic precursors of sterols. The mechanism of cyclization of squalene by SHC, beginning with a protonation of the 2,3 double bond by an acidic residue of the enzyme, followed by a series of electrophilic additions of the carbocationic intermediates to the double bonds, is similar to the mechanism of cyclization of 2,3-oxidosqualene by OSC. The inhibitors studied included: (i) analogs of the carbocationic intermediates formed during cyclization, such as aza-analogs of squalene and 2,3-oxidosqualene; (ii) affinity-labeling inhibitors bearing a methylidene reactive group; and (iii) vinyldioxidosqualenes and vinylsulfide derivatives of the substrates. Comparison of the results obtained with the two enzymes, SHC and OSC, showed that many of the most effective inhibitors of OSC were also able to inhibit SHC, while some derivatives acted as specific inhibitors. Differences could be easily explained on the basis of the different substrate specificity of the two enzymes.     

THROO: a Tracked Hybrid Rover to Overpass Obstacles

In this paper, the design, simulation and experimental tests are presented for THROO: a Tracked Hybrid Rover, which has been developed to Overpass Obstacles. The proposed mobile robot has 3-DOFs and it is capable of straight motion, turning ability and two operations, namely rover-like motion with tracks on flat terrain and walking-like motion with track and legs to overpass obstacles to move on uneven terrain. The leg mechanism is composed of a four-bar linkage, which has been synthesized according to the desired features. In particular, the Burmester problem, which aims at finding the geometric parameters of a four-bar linkage required for a prescribed set of finitely separated poses are solved for the case understudy. Dynamic simulations have been carried out and a prototype has been built. The proposed results show the hybrid rover ability to overpass obstacles, for which size is comparable or greater than the track high.     

Synthesis and catalytic activity of optically active polymers containing oxime groups

Optically active polymers containing oxime groups have been prepared: (i) by partial quaternization of poly(4-vinyl pyridine) (P4VP) with phenacyloxime bromide and with (+)-(S)-1-bromo-2-methylbutane; and (ii) by reaction of the copolymer from 4VP and (+)-(S)-5-methyl-1-hepten-3-one with hydroxylamine. These polymers have been used as catalysts for the esterolysis of esters of p-nitrophenol with non-chiral and with chiral acids. The kinetic parameters of the catalytic process are markedly dependent on the structure of polymer and substrate. A moderate chiral discrimination of the antipodes of p-nitrophenyl 2-methylbutanoate is observed with the catalyst obtained from the copolymer of 4VP with (+)-(S)-5-methyl-1-hepten-3-one.     

Access of the substrate to the active site of yeast oxidosqualene cyclase: an inhibition and site-directed mutagenesis approach

A structural model of Saccharomyces cerevisiae oxidosqualene cyclase (SceOSC) suggests that some residues of the conserved sequence Pro-Ala-Glu-Val-Phe-Gly (residues 524-529) belong to a channel constriction that gives access to the active-site cavity. Starting from the SceOSC C457D mutant, which lacks the cysteine residue next to the catalytic Asp456 residue Cys457 has been replaced but Asp456 is still there, we prepared two further mutants where the wild-type residues Ala525 and Glu526 were individually replaced by cysteine. These mutants, especially E526C, were very sensitive to the thiol-reacting agent dodecyl-maleimide. Moreover, both the specific activity and the thermal stability of E526C were severely reduced. A similar decrease of the enzyme functionality was obtained by replacing Glu526 with alanine, while substitution with the conservative residues aspartate or glutamine did not alter catalytic activity. Molecular modeling of the yeast wild-type OSC and mutants on the template structure of human OSC confirms that the channel constriction is an important aspect of the protein structure and suggests a critical structural role for Glu526.