Accurate multivariable arbitrary piecewise model regression of McKibben and Peano muscle static and damping force behavior

Machines that efficiently and safely interact with the uncertainty of the natural world need actuators with the properties of living creatures' muscles. However, the inherent nonlinearity of the static and damping properties that the most promising of these muscle-like actuators have makes them difficult to control. Our ability to accurately control these actuators requires accurate models of their behavior. One muscle-like actuator for which no accurate models have been specifically developed is the Peano muscle. This paper presents and validates a model generation algorithm, multivariable arbitrary piecewise model regression (MAPMORE), that produces accurate models for predicting the static and damping force behavior of Peano muscles, as well as of the popular McKibben muscle. MAPMORE builds a training data processing, muscle-specific model term dictionary, and piecewise function fusion framework around Billings et al's forward regression orthogonal least squares estimator algorithm. We demonstrate that MAPMORE's static and damping force models have a normalized root mean square error (NRMSE) of 48%–88% of the NRMSE of the most accurate of Peano and McKibben muscles' existing models. The improved accuracy of MAPMORE's models for these artificial muscles potentially aids the muscles' ability to be accurately controlled and hence is a step towards enabling machines that interact with the real world. Further steps could be made by improving MAPMORE's accuracy through the addition of hysteresis operator and lagged terms in the damping force dictionary

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Putting reaction-diffusion systems into port-Hamiltonian framework

Reaction-diffusion systems model the evolution of the constituents distributed in space under the influence of chemical reactions and diffusion [6], [10]. These systems arise naturally in chemistry [5], but can also be used to model dynamical processes beyond the realm of chemistry such as biology, ecology, geology, and physics. In this paper, by adopting the viewpoint of port-controlled Hamiltonian systems [7] we cast reaction-diffusion systems into the portHamiltonian framework. Aside from offering conceptually a clear geometric interpretation formalized by a Stokes-Dirac structure [8], a port-Hamiltonian perspective allows to treat these dissipative systems as interconnected and thus makes their analysis, both quantitative and qualitative, more accessible from a modern dynamical systems and control theory point of view. This modeling approach permits us to draw immediately some conclusions regarding passivity and stability of reaction-diffusion systems. It is well-known that adding diffusion to the reaction system can generate behaviors absent in the ode case. This primarily pertains to the problem of diffusion-driven instability which constitutes the basis of Turing’s mechanism for pattern formation [11], [5]. Here the treatment of reaction-diffusion systems as dissipative distributed portHamiltonian systems could prove to be instrumental in supply of the results on absorbing sets, the existence of the maximal attractor and stability analysis. Furthermore, by adopting a discrete differential geometrybased approach [9] and discretizing the reaction-diffusion system in port-Hamiltonian form, apart from preserving a geometric structure, a compartmental model analogous to the standard one [1], [2] is obtaine