Control Theory: A Mathematical Perspective on Cyber-Physical Systems

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently the control field is facing new challenges motivated by application domains that involve networks of systems. Examples are interacting robots, networks of autonomous cars or the smart grid. In order to address the new challenges posed by these application disciplines, the special focus of this workshop has been on the currently very active field of Cyber-Physical Systems, which forms the underlying basis for many network control applications. A series of lectures in this workshop was devoted to give an overview on current theoretical developments in Cyber-Physical Systems, emphasizing in particular the mathematical aspects of the field. Special focus was on the dynamics and control of networks of systems, distributed optimization and formation control, fundamentals of nonlinear interconnected systems, as well as open problems in control

Contact and HiL interaction in multibody based machinery simulators

[Abstract] Multibody simulators allow to predict and evaluate the motion of machines and mechanisms under the action of the user and the interaction with the simulated environment. Interactive simulators guided by a human or a piece of hardware must be efficient enough to compute the state of the system in real time. ?erefore, employing fast and sufficiently accurate techniques is a must. In this work, generic tools for the implementation of this kind of simulators are provided. Efficient multibody formulations are reviewed for implementing real-time simulators. ?e index-3 Augmented Lagrange formulation with projections of velocities and accelerations is selected, due to its efficiency and stability. ?e integration of the equations of motion follows the Generalized-a method, which provides high-frequency dissipation, and can be unconditionally stable and secondorder accurate if suitable integrator parameters are chosen. Contact modeling and detection is essential for computing the interaction among the mechanisms and the simulated environment. Normal and tangential contact force models are presented. For the normal contact, a Hertz-type Hunt- Crossley model is chosen. ?e tangential force model is based on Coulomb’s law, and includes stiction and viscous friction effects. Both models were compared with the output of the Bowden-Leben stick-slip experiment. A real-time, simplified terrain model featuring digging forces for excavator simulators is also discussed. Several techniques are shown for detecting colliding bodies at run-time. ?e collision detection process is divided into two stages. ?e first one is a broad range and coarse grained process, where potentially colliding pairs of objects are discovered. Spatial and hierarchical division techniques as Octrees, BSP-trees and Directed Acyclic Graphs are presented for this purpose. In the second stage, fine-detailed contact properties are computed from each pair of bodies. Several models are presented for testing object enclosing volumes or more complex surfaces discretized as triangular meshes. State-of-the-art, Commercial Off ?e Shelf hardware devices are presented as the physical foundation of a simulator. Industrial-quality controllers, projection screens and audio devices are reviewed for this purpose. ?e implementation details for the use of those devices are also considered. Network communication procedures between the simulator and monitoring nodes are discussed, too. Finally, a particular implementation of all the techniques described in previous chapters is presented in the form of an interactive excavator simulator, which features all the degrees of freedom of the machine, and is able to perform earthmoving operations in a realistic environment. Monitoring capabilities are also available, and any training session can be defined by user scripts. ?e techniques described in this document constitute a generic and efficient compendium of algorithms that are well-fi?ed for medium or low-end computational systems, as desktop or even laptop computers

Adapting Hybrid Monte Carlo methods for solving complex problems in life and materials sciences

Efficient sampling is the key to success of molecular simulation of complex physical systems. Still, a unique recipe for achieving this goal is unavailable. Hybrid Monte Carlo (HMC) is a promising sampling tool offering a smart, free of discretization errors, propagation in phase space, rigorous temperature control, and flexibility. However, its inability to provide dynamical information and its weakness in simulations of reasonably large systems do not allow HMC to become a sampler of choice in molecular simulation of complex systems. In this thesis, we show that performance of HMC can be dramatically improved by introducing in the method the splitting numerical integrators and importance sampling. We propose a novel splitting integration scheme called Adaptive Integration Approach or AIA, which leads to very promising improvements in accuracy and sampling in HMC simulations. Given a simulation problem and a time step, AIA automatically chooses the optimal scheme out of the family of two-stage splitting integrators. A system-specific integrator identified by our approach is optimal in the sense that it provides the best conservation of energy for harmonic forces. The role of importance sampling on the performance of HMC is studied through the modified Hamiltonian Monte Carlo (MHMC) methods, sampling with respect to a modified or shadow Hamiltonian. The particular attention is paid to Generalized Shadow Hybrid Monte Carlo (GSHMC), introduced by Akhmatskaya and Reich in 2008. To improve the performance of MHMC in general and GSHMC in particular, we develop and test the new multi-stage splitting integrators, specially formulated for sampling with respect to modified Hamiltonians. The novel adaptive two-stage integration approach or MAIA, specifically derived for MHMC is presented. We also discuss in detail the adaptation of GSHMC to the NPT ensemble and provide the thorough analysis of its performance. Moreover, for the first time, we formulate GSHMC in the grand canonical ensemble. A general framework, useful for an extension of other Hybrid Monte Carlo methods to the grand canonical ensemble, is also provided. The software development is another fundamental part of the present work. The algorithms presented in this thesis are implemented in MultiHMC-GROMACS, an in-house version of the popular software package GROMACS. We explain the details of such implementation and give useful recommendations and hints for implementation of the new algorithms in other software packages. In summary, in this thesis, we propose the new numerical algorithms that are capable of improving the accuracy and sampling efficiency of molecular simulations with Hybrid Monte Carlo methods. We show that equipping the Hybrid Monte Carlo algorithm with extra features makes it even a “smarter” sampler and, no doubts, a strong competitor to the well-established molecular simulation techniques such as molecular dynamics (MD) and Monte Carlo. The up to 60 times increase in sampling efficiency of GSHMC over MD, due to the new algorithms in simulations of selected systems, supports such a belief.MTM2013-46553-C3-1-

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: ● Formulations and Numerical Methods ● Efficient Methods and Real-Time Applications ● Flexible Multibody Dynamics ● Contact Dynamics and Constraints ● Multiphysics and Coupled Problems ● Control and Optimization ● Software Development and Computer Technology ● Aerospace and Maritime Applications ● Biomechanics ● Railroad Vehicle Dynamics ● Road Vehicle Dynamics ● Robotics ● Benchmark ProblemsPostprint (published version