emgr - The Empirical Gramian Framework

System Gramian matrices are a well-known encoding for properties of input-output systems such as controllability, observability or minimality. These so-called system Gramians were developed in linear system theory for applications such as model order reduction of control systems. Empirical Gramian are an extension to the system Gramians for parametric and nonlinear systems as well as a data-driven method of computation. The empirical Gramian framework - emgr - implements the empirical Gramians in a uniform and configurable manner, with applications such as Gramian-based (nonlinear) model reduction, decentralized control, sensitivity analysis, parameter identification and combined state and parameter reduction

Custom optimization algorithms for efficient hardware implementation

The focus is on real-time optimal decision making with application in advanced control systems. These computationally intensive schemes, which involve the repeated solution of (convex) optimization problems within a sampling interval, require more efficient computational methods than currently available for extending their application to highly dynamical systems and setups with resource-constrained embedded computing platforms. A range of techniques are proposed to exploit synergies between digital hardware, numerical analysis and algorithm design. These techniques build on top of parameterisable hardware code generation tools that generate VHDL code describing custom computing architectures for interior-point methods and a range of first-order constrained optimization methods. Since memory limitations are often important in embedded implementations we develop a custom storage scheme for KKT matrices arising in interior-point methods for control, which reduces memory requirements significantly and prevents I/O bandwidth limitations from affecting the performance in our implementations. To take advantage of the trend towards parallel computing architectures and to exploit the special characteristics of our custom architectures we propose several high-level parallel optimal control schemes that can reduce computation time. A novel optimization formulation was devised for reducing the computational effort in solving certain problems independent of the computing platform used. In order to be able to solve optimization problems in fixed-point arithmetic, which is significantly more resource-efficient than floating-point, tailored linear algebra algorithms were developed for solving the linear systems that form the computational bottleneck in many optimization methods. These methods come with guarantees for reliable operation. We also provide finite-precision error analysis for fixed-point implementations of first-order methods that can be used to minimize the use of resources while meeting accuracy specifications. The suggested techniques are demonstrated on several practical examples, including a hardware-in-the-loop setup for optimization-based control of a large airliner.Open Acces

Data based predictive control: Application to water distribution networks

In this thesis, the main goal is to propose novel data based predictive controllers to cope with complex industrial infrastructures such as water distribution networks. This sort of systems have several inputs and out- puts, complicate nonlinear dynamics, binary actuators and they are usually perturbed by disturbances and noise and require real-time control implemen- tation. The proposed controllers have to deal successfully with these issues while using the available information, such as past operation data of the process, or system properties as fading dynamics. To this end, the control strategies presented in this work follow a predic- tive control approach. The control action computed by the proposed data- driven strategies are obtained as the solution of an optimization problem that is similar in essence to those used in model predictive control (MPC) based on a cost function that determines the performance to be optimized. In the proposed approach however, the prediction model is substituted by an inference data based strategy, either to identify a model, an unknown control law or estimate the future cost of a given decision. As in MPC, the proposed strategies are based on a receding horizon implementation, which implies that the optimization problems considered have to be solved online. In order to obtain problems that can be solved e ciently, most of the strategies proposed in this thesis are based on direct weight optimization for ease of implementation and computational complexity reasons. Linear convex combination is a simple and strong tool in continuous domain and computational load associated with the constrained optimization problems generated by linear convex combination are relatively soft. This fact makes the proposed data based predictive approaches suitable to be used in real time applications. The proposed approaches selects the most adequate information (similar to the current situation according to output, state, input, disturbances,etc.), in particular, data which is close to the current state or situation of the system. Using local data can be interpreted as an implicit local linearisation of the system every time we solve the model-free data driven optimization problem. This implies that even though, model free data driven approaches presented in this thesis are based on linear theory, they can successfully deal with nonlinear systems because of the implicit information available in the database. Finally, a learning-based approach for robust predictive control design for multi-input multi-output (MIMO) linear systems is also presented, in which the effect of the estimation and measuring errors or the effect of unknown perturbations in large scale complex system is considered

Numerical methods for advection-diffusion-reaction equations and medical applications

The purpose of this thesis is twofold, firstly, the study of a relaxation procedure for numerically solving advection-diffusion-reaction equations, and secondly, a medical application. Concerning the first topic, we extend the applicability of the Cattaneo relaxation approach to reformulate time-dependent advection-diffusion-reaction equations, that may include stiff reactive terms, as hyperbolic balance laws with stiff source terms. The resulting systems of hyperbolic balance laws are solved by extending the applicability of existing high-order ADER schemes, including well-balanced and non-conservative schemes. Moreover, we also present a new locally implicit version of the ADER method to solve general hyperbolic balance laws with stiff source terms. The relaxation procedure depends on the choice of a relaxation parameter $\epsilon$. Here we propose a criterion for selecting $\epsilon$ in an optimal manner, relating the order of accuracy $r$ of the numerical scheme used, the mesh size $\Delta x$ and the chosen $\epsilon$. This results in considerably more efficient schemes than some methods with the parabolic restriction reported in the current literature. The resulting present methodology is validated by applying it to a blood flow model for a network of viscoelastic vessels, for which experimental and numerical results are available. Convergence-rates assessment for some selected second-order model equations, is carried out, which also validates the applicability of the criterion to choose the relaxation parameter. The second topic of this thesis concerns the numerical study of the haemodynamics impact of stenoses in the internal jugular veins. This is motivated by the recent discovery of a range of extra cranial venous anomalies, termed Chronic CerbroSpinal Venous Insufficiency (CCSVI) syndrome, and its potential link to neurodegenerative diseases, such as Multiple Sclerosis. The study considers patient specific anatomical configurations obtained from MRI data. Computational results are compared with measured data

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

Modelos Paralelos para la Resolución de Problemas de Ingeniería Agrícola

El presente trabajo se inscribe en el campo de la computación paralela y, más en concreto, en el desarrollo y utilización de modelos computacionales en arquitecturas paralelas heterogéneas para la resolución de problemas aplicados. En la tesis abordamos una serie de problemas que están relacionados con la aplicación de la tecnología en el ámbito de las explotaciones agrícolas y comprenden: la representación del relieve, el manejo de información climática como la temperatura, y la gestión de recursos hídricos. El estudio y la solución a estos problemas en el área en la que se han estudiado tienen un amplio impacto económico y medioambiental. Los problemas basan su formulación en un modelo matemático cuya solución es costosa desde el punto de vista computacional, siendo incluso a veces inviable. La tesis consiste en implementar algoritmos paralelos rápidos y eficientes que resuelven el problema matemático asociado a estos problemas en nodos multicore y multi-GPU. También se estudia, propone y aplican técnicas que permiten a las rutinas diseñadas adaptarse automáticamente a las características del sistema paralelo donde van a ser instaladas y ejecutadas con el objeto de obtener la versión más cercana posible a la óptima a un bajo coste. El objetivo es proporcionar un software a los usuarios que sea portable, pero a la vez, capaz de ejecutarse eficientemente en la ordenador donde se esté trabajando, independientemente de las características de la arquitectura y de los conocimientos que el usuario pueda tener sobre dicha arquitectura.Do Carmo Boratto, M. (2015). Modelos Paralelos para la Resolución de Problemas de Ingeniería Agrícola [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/48529TESI

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 Problems. The conference is organized by the Department of Mechanical Engineering of the Universitat Politècnica de Catalunya (UPC) in Barcelona. The organizers would like to thank the authors for submitting their contributions, the keynote lecturers for accepting the invitation and for the quality of their talks, the awards and scientific committees for their support to the organization of the conference, and finally the topic organizers for reviewing all extended abstracts and selecting the awards nominees.Postprint (published version

Solving time-invariant differential matrix Riccati equations using GPGPU computing

Differential matrix Riccati equations (DMREs) enable to model many physical systems appearing in different branches of science, in some cases, involving very large problem sizes. In this paper, we propose an adaptive algorithm for time-invariant DMREs that uses a piecewise-linearized approach based on the Padé approximation of the matrix exponential. The algorithm designed is based upon intensive use of matrix products and linear system solutions so we can seize the large computational capability that modern graphics processing units (GPUs) have on these types of operations using CUBLAS and CULATOOLS libraries (general purpose GPU), which are efficient implementations of BLAS and LAPACK libraries, respectively, for NVIDIA © GPUs. A thorough analysis showed that some parts of the algorithm proposed can be carried out in parallel, thus allowing to leverage the two GPUs available in many current compute nodes. Besides, our algorithm can be used by any interested researcher through a friendly MATLAB © interface.Peinado Pinilla, J.; Alonso-Jordá, P.; Ibáñez González, JJ.; Hernández García, V.; Do Carmo Boratto, M. (2014). Solving time-invariant differential matrix Riccati equations using GPGPU computing. Journal of Supercomputing. 70(2):623-636. doi:10.1007/s11227-014-1111-3623636702Anderson E et al (1994) LAPACK users’ guide. SIAM, PhiladelphiaArias E, Hernández V, Ibáñez J, Peinado J (2007) A fixed point-based BDF method for solving Riccati equations. Appl Math Comput 188(2):1319–1333Benner P, Mena H (2004) BDF methods for large-scale differential Riccati equations. In: 16th International symposium on mathematical theory of network and systems (MTNS2004), Katholieke Universiteit Leuven, BelgiumBenner P, Mena H (2013) Rosenbrock methods for solving Riccati differential equations. 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SIAM J Numer Anal 29(3):781–815EM Photonics (2011) CULATOOLS, R12 ednHernández V, Ibáñez J, Arias E, Peinado J (2008) A GMRES-based BDF method for solving differential Riccati equations. Appl. Math. Comput. 196(2):613–626Horn RA, Johnson CR (1991) Topics in matrix analysis. Cambridge University Press, LondonIbáñez J, Hernández V (2010) Solving differential matrix Riccati equations by a piecewise-linearized method based on the conmutant equation. Comput Phys Commun 180:2103–2114Ibáñez J, Hernández V (2011) Solving differential matrix Riccati equations by a piecewise-linearized method based on diagonal Padé approximants. Comput Phys Commun 182:669–678Ibáñez J, Hernández V, Arias E, Ruiz P (2009) Solving initial value problems for ordinary differential equations by two approaches: BDF and piecewise-linearized methods. Comput Phys Commun 180(5):712–723Kenney CS, Leipnik RB (1985) Numerical integration of the differential matrix Riccati equation. 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