In addition to novel results of your research activities, also contributions in the form of work-in-progress reports will be highly appreciated.
If you are interested in participating in this seminar, either as a speaker or as a listener to the forthcoming presentations, please fill in the following form and provide us with a registration request. You will then get the login data for the planned online meeting in a personal e-mail message. Note that the participation in this seminar will be fully free of charge.
The exact starting date of the International Online Seminar on Interval Methods in Control Engineering will be announced on this web page as well as on the Reliable Computing mailing list. Moreover, we plan to make all presentations publicly available for which we receive the explicit consent of the speaker(s).
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Hugo Rémin
Université Angers, France
Hugo Rémin holds a PhD in robotics from the University of Angers, within the LARIS laboratory. His doctoral research, conducted in collaboration with CEA Pays de la Loire, focuses on trajectory planning for robotic tomography, with a particular emphasis on large-scale parts. He is also interested in the characterization of configuration spaces using interval analysis.
Topological spaces are used in almost all branch of modern mathematics, it is of importance in robotics as the free configuration space of a robot is a topological space. Thus knowing underlying topological properties on the free configuration space can be used in motion planning.
In this talk, our focus is on computing the number of path-connected components of spaces defined by generic non-linear inequalities. With our approach we are able to guarantee whether a trajectory between two configurations is feasible or not. Previous research includes formal methods limited to semi-algebraic sets and, most relevant to this paper, an algorithm on the same spaces as our focus running in O(2^{2n}) time using star domains and interval analysis. Here we show that by using contractibility over star domain a substantial improvement on the time complexity can be accomplished. An algorithm is presented with a time complexity of O(2^{n}) and the results are shown on examples.
Chair for Reliability Engineering, TU Dortmund, Germany
Zhejiang University, Hangzhou, China
Instituto Tecnológico de La Laguna, Torreón, Coahuila, México
Héctor Ríos earned his PhD in Electrical Engineering, specializing in Automatic Control, from the National Autonomous University of Mexico in 2014, working with Professors Leonid Fridman and Jorge Dávila. He then pursued a postdoctoral fellowship with the Non-A team at Inria Lille (2014–2015), working alongside Professors Denis Efimov and Laurentiu Hetel. From 2015 to 2016, he continued his research at the Department of Electrical & Computer Engineering at
the University of California, Santa Barbara, collaborating with Professor Andrew R. Teel.
Since October 2016, he has been a SECIHTI Research Fellow at the Instituto Tecnológico de La Laguna, Mexico. He is a Level II member of the National System of Researchers in Mexico (SNII), a Senior Member of IEEE, a member of the IEEE Conference Editorial Board, and an Associate Editor for Nonlinear Analysis: Hybrid Systems and the International Journal of Adaptive Control and Signal Processing.
Throughout his career, he has authored or co-authored over 170 publications, including journal articles, book chapters, and conference papers. His research interests include the observation of linear, nonlinear, and hybrid systems, fault diagnosis, sliding-mode control and its applications, control for constrained systems, and robust control for unmanned aerial and ground vehicles.
This presentation shows a robust control design for the blood glucose regulation problem in patients with diabetes mellitus type–1. The proposed switching control approach is based on an interval predictor–based state–feedback, which takes into account the state and input constraints of the insulin–glucose system dynamics (Bergman minimal model), i.e., positive states and input, and minimum and maximum values of the blood glucose level and the insulin infusion rate. The method deals with interpatient variabilities and unannounced food intake. Additionally, the switching structure of the control law allows us to switch off the state–feedback controller, stopping the insulin injection for proper glucose level regulation. Some simulation results, over a cohort of 4 virtual type 1 diabetes mellitus adult patients, illustrate the performance of the proposed robust controller.
Department of Computing and Software, McMaster University Hamilton, Ontario, Canada
Ned Nedialkov is a Professor in the Department of Computing and Software at McMaster University and Associate Director of the School of Computational Science and Engineering. He holds a Ph.D. in Computer Science from the University of Toronto.
His research focuses on numerical methods for ordinary differential equations (ODEs) and differential-algebraic equations (DAEs), with interests in interval numerical methods, automatic differentiation, multibody dynamics, and mathematical software development. He is the author of VNODE-LP, a validated ODE solver, and a co-author of the DAE solver DAETS and the structural analyzer DAESA.
He contributed to the IEEE 1788™-2015 and 1788.1™-2017 interval arithmetic standards, serving as Assistant Editor and Senior Technical Editor, respectively.
A Taylor method for solving an ordinary differential equation (ODE) initial-value problem computes a truncated Taylor series (TS) expansion of the solution at a given point and advances the solution by summing the TS with an appropriate step size. To find Taylor coefficients for the solution, automatic differentiation is typically employed, which requires implementing formulas for the four basic arithmetic operations (BAOs) and standard functions (such as exp, sin) on Taylor polynomials. For instance, for exp, this involves evaluating v(t) = exp(u(t)), where u(t) and v(t) are TS, through a recurrence relation.
Many commonly used functions satisfy simple ODEs that involve only BAOs. For example, exp(u(t)) satisfies v' = v * u'. We introduce a novel sub-ODE method that directly incorporates the ODEs of such functions into the evaluation process. This approach streamlines implementation: each function that satisfies a simple ODE is added to the "Taylor library" with a few lines of code, eliminating the need for separate recurrence formulas. Furthermore, our computational kernel consists of just the four BAOs, plus a new "sub-ODE operator".
However, embedding sub-ODEs typically transforms the original ODE into a differential-algebraic system. We present results showing that this approach is theoretically sound, regardless of the number of sub-ODEs incorporated.
Finally, we introduce our sub-ODE-based MATLAB ODE solver and show that its performance compares favorably with existing solvers from the MATLAB ODE suite.
Joint work with John Pryce, Cardiff University, UK
ENSTA, Brest, France
Maël Godard received a double degree in Autonomous Robotics, from ENSTA Bretagne, and in Dynamical Systems and Signals, from Polytech Angers, in 2023. He is currently a Ph.D. student at ENSTA, in the Lab-STICC laboratory, ROBEX team. His research is focused on the a priori validation of robotic missions.
In this presentation, we propose to use parallelepipeds to enclose the image of a sphere by a nonlinear function, with examples in two and three dimensions.
We will consider the cases where the function is known, and when it is the flow function of a dynamical system. The CAPD library will be used for guaranteed integration when needed, in combination with the CODAC library.
ENSTA, Institut Polytechnique de Paris, France
In this seminar, we present a novel method for constructing discrete abstractions for discrete-time, continuous-state systems. Traditional approaches focus on building a discrete bisimulation that represents all possible combinations of states and inputs. This results in highly complex models due to the need to account for all possible behaviors. Instead, we propose to relax the requirement of completeness in order to obtain models that are deterministic, and this readily realizable, and less complex. Our method strikes a balance between system granularity and computational efficiency. Furthermore, we leverage linearization and linear feedback control, which allows us to treat systems exhibiting sufficiently contractive cycles, while related approaches are limited to globally contractive systems. We demonstrate the utility of our approach through numerical experiments, highlighting its applicability in domains where properties such as safety and reversibility are critical.
This work with Gwendal Priser and Elena Vanneaux has been published at Reachability Problems 2024.