Matching in the method of controlled Lagrangians and IDA-passivity based control

This paper reviews the method of controlled Lagrangians and the interconnection and damping assignment passivity based control (IDA-PBC)method. Both methods have been presented recently in the literature as means to stabilize a desired equilibrium point of an Euler-Lagrange system, respectively Hamiltonian system, by searching for a stabilizing structure preserving feedback law. The conditions under which two Euler-Lagrange or Hamiltonian systems are equivalent under feedback are called the matching conditions (consisting of a set of nonlinear PDEs). Both methods are applied to the general class of underactuated mechanical systems and it is shown that the IDA-PBC method contains the controlled Lagrangians method as a special case by choosing an appropriate closed-loop interconnection structure. Moreover, explicit conditions are derived under which the closed-loop Hamiltonian system is integrable, leading to the introduction of gyroscopic terms. The $\lambda$-method as introduced in recent papers for the controlled Lagrangians method transforms the matching conditions into a set of linear PDEs. In this paper the method is extended, transforming the matching conditions obtained in the IDA-PBC method into a set of quasi-linear and linear PDEs.\u

Singular reduction of implicit Hamiltonian systems

This paper develops the reduction theory of implicit Hamiltonian systems admitting a symmetry group at a singular value of the momentum map. The results naturally extend those known for (explicit) Hamiltonian systems described by Poisson brackets.Comment: 29 pages, no figures, submitte

Multi-Parameter Analysis of Biobanked Human Bone Marrow Stromal Cells Shows Little Influence for Donor Age and Mild Comorbidities on Phenotypic and Functional Properties

Heterogeneous populations of human bone marrow-derived stromal cells (BMSC) are among the most frequently tested cellular therapeutics for treating degenerative and immune disorders, which occur predominantly in the aging population. Currently, it is unclear whether advanced donor age and commonly associated comorbidities affect the properties of ex vivo-expanded BMSCs. Thus, we stratified cells from adult and elderly donors from our biobank (n = 10 and n = 13, mean age 38 and 72 years, respectively) and compared their phenotypic and functional performance, using multiple assays typically employed as minimal criteria for defining multipotent mesenchymal stromal cells (MSCs). We found that BMSCs from both cohorts meet the standard criteria for MSC, exhibiting similar morphology, growth kinetics, gene expression profiles, and pro-angiogenic and immunosuppressive potential and the capacity to differentiate toward adipogenic, chondrogenic, and osteogenic lineages. We found no substantial differences between cells from the adult and elderly cohorts. As positive controls, we studied the impact of in vitro aging and inflammatory cytokine stimulation. Both conditions clearly affected the cellular properties, independent of donor age. We conclude that in vitro aging rather than in vivo donor aging influences BMSC characteristics

A joined geometric structure for Hamiltonian and gradient control systems

status: publishe

Power balancing for a new class of non-linear systems and stabilization of RLC circuits

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The matching conditions of controlled Lagrangians and IDA-passivity based control

This paper discusses the matching conditions resulting from the controlled Lagrangians method and the interconnection and damping assignment passivity based control (IDA-PBC) method. Both methods have been presented recently in the literature as means to stabilize a desired equilibrium point of an Euler±Lagrange, respectively Hamiltonian, system. In the context of mechanical systems with symmetry, the original controlled Lagrangians method is reviewed, and an interpretation of the matching assumptions in terms of the matching of kinetic and potential energy is given. Secondly, both methods are applied to the general class of underactuated mechanical systems and it is shown that the controlled Lagrangians method is contained in the IDA-PBC method. The $\lambda$-method as described in recent papers for the controlled Lagrangians method, transforming the matching conditions (a set of non-linear PDEs) into a set of linear PDEs, is discussed. The method is used to transform the matching conditions obtained in the IDA-PBC method into a set of quadratic and linear PDEs. Finally, the extra freedom obtained in the IDA-PBC method (with respect to the controlled Lagrangians method) is used to discuss the integrability of the closed-loop system. Explicit conditions are derived under which the closed-loop Hamiltonian system is integrable, leading to the introduction of gyroscopic terms

Power port concepts in robotics: the geometrical-physical approach

status: publishe