Acta Cybernetica

Preface + In memoriam of Nicolas Delanoue

Luc Jaulin, Sébastien Lahaye, Andreas Rauh, Steffen Schön — Thu, 21 Nov 2024 00:00:00 +0100

The Summer Workshop on Interval Methods (SWIM) is an annual scientific meeting initiated in 2008 with a special focus on promoting interval analysis techniques and their applications to a broader community of researchers. Since 2008, SWIM has become a multi-disciplinary keystone event for researchers dealing with various aspects of interval and set-based methods.

A Constraint Programming Approach for Polytopic Simulation of Ordinary Differential Equations

Mon, 01 Apr 2024 00:00:00 +0200

This paper presents a constraint-based approach to compute the reachable tube of nonlinear differentiable equations. A set of initial values for the equations is considered and defined by a polytope represented as intersections of zonotopes. Guaranteed numerical integration based on zonotopic computation is used to compute reachable tubes. In order to efficiently build polytopes defined by the intersection of several zonotopes, we use a previously developed abstract domain to represent reachable tubes. The proposed contribution allows to compute more expressive reachable tubes more efficiently than methods based only on boxes, and therefore could improve verification/validation processes in robotics application for example. The approach is evaluated on examples taken from literature and we present two applications of this work.

Verified Bit and Power Allocation for MIMO Systems: A Comparison of SVD Based Techniques With GMD

Ekaterina Auer, Andreas Ahrens — Thu, 21 Mar 2024 00:00:00 +0100

Methods with result verification have been applied in different practical contexts, for example, in such diverse areas as robotics, computer graphics, or chemistry. Such methods help to verify the result of a computer simulation, additionally taking into account possibly present bounded uncertainty in a deterministic way. Modeling and simulation of multiple-input multiple-output (MIMO) systems has not received much attention from this angle. Nowadays, increasing the capacity of communication links by using the MIMO mechanism is an essential part of various wireless communication standards.

In this paper, we consider the channel separation stage in the overall modeling and simulation process for MIMO systems and compare the singular value decomposition (SVD) and the geometric mean decomposition (GMD) based approaches from the point of view of the achievable bit error ratio (BER) under good and poor scattering conditions. As a special focus, we use interval methods to verify the result and to deal with the appearing epistemic uncertainty. Additionally, we consider resource allocation in detail, which mostly makes sense only for the SVD approach since the goal of the GMD based one is to avoid it. However, this has been studied only asymptotically until now and needs confirmation. We propose a combined analytical-numerical approach to simulate resource allocation relying on verified techniques. The theoretical results are illustrated and the comparison is performed using simulated data for an uncorrelated and a correlated MIMO system with four receiving and four transmitting antennas.

Robust Control and Actuator Fault Detection Based on an Iterative LMI Approach: Application on a Quadrotor

Oussama Benzinane, Andreas Rauh — Thu, 21 Mar 2024 00:00:00 +0100

Linear Matrix Inequalities (LMIs) have recently gained momentum due to the increasing performance of computing hardware. Many current research activities rely on the advantages of this growth in order to design controllers with provable stability and performance guarantees. To guarantee robustness despite actuator faults, model uncertainty, nonlinearities, and measurement noise, a novel iterative LMI approach is presented to design an observer-based state feedback controller allowing for simultaneous optimization of the control and observer gains. A comparison with a combination of an Extended Kalman Filter (EKF) and a Linear-Quadratic Regulator (LQR) has been conducted, inherently providing guaranteed stability for the closed loop only when the separation principle holds, which is not the case in this study. Both approaches are applied on a quadrotor, where reliable detection and compensation of the faults in the presence of measurement noise is demonstrated.

A New Interval Arithmetic to Generate the Complementary of Contractors

Pierre Filiol, Theotime Bollengier, Luc Jaulin, Jean Christophe Le Lann — Thu, 21 Mar 2024 00:00:00 +0100

Contractor algebra is used to characterize a set defined as a composition of sets defined by inequalities. It mainly uses interval methods combined with constraint propagation. This algebra includes the classical operations we have for sets such as the intersection, the union and the inversion. Now, it does not include the complement operator. The reason for this is probably related to the interval arithmetic itself. In this paper, we show that if we change the arithmetic used for intervals adding a single flag, similar to not a number, we are able to include easily the complement in the algebra of contractors.

Exponential State Enclosure Techniques for the Implementation of Validated Model Predictive Control

Mohamed Fnadi, Andreas Rauh — Wed, 20 Mar 2024 00:00:00 +0100

The design task of predictive controllers for uncertain systems is commonly formulated on the basis of their kinematic and/or dynamic models. These models are assumed to be expressed as initial value problems (IVPs) for finite-dimensional sets of nonlinear ordinary differential equations (ODEs). If constraints for the admissible state trajectories are formulated, bounds for these trajectories need to be computed by numerical procedures to obtain guaranteed enclosures of all possible states at each time step that contain the solution of the exact IVP-ODEs. Uncertainties in both the initial states and system parameters are considered in this paper by means of bounded interval variables. For this kind of system representation, we apply an exponential enclosure approach to determine guaranteed enclosures of all reachable states. This approach is embedded in a novel manner into the framework of a guaranteed nonlinear model predictive control (NMPC) to acquire optimal and safe control domains along a receding horizon. The NMPC problem is solved at each time step considering several constraints which are crucial for the system's safety and stability, namely, bounds on the state trajectories and the control signals. The capabilities of the combination of the exponential enclosure technique with the set-based NMPC strategy are illustrated through simulations using a nonlinear inverted pendulum.

Set-Valued Approach for the Online Identification of the Open-Circuit Voltage of Lithium-Ion Batteries

Marit Lahme, Andreas Rauh — Wed, 20 Mar 2024 00:00:00 +0100

To describe the dynamic behavior of lithium-ion batteries using the terminal current and the terminal voltage as input and output of the battery, equivalent circuit models are used, which comprise series resistances, RC sub-networks and a state of charge dependent voltage source. The parameters of the battery model are influenced by aging effects as well as other factors such as the state of charge and the cell temperature. Although those variations can be estimated with the help of an augmented state vector, the typically applied approaches do not allow for a direct identification of nonlinear dependencies of circuit elements on the state of charge or other influence factors. Therefore, a two-stage identification routine for identifying those nonlinear dependencies using an interval observer and an interval contraction scheme is proposed in this paper. The identification routine was successfully applied to identify the open-circuit voltage characteristic of a lithium-ion battery. Numerical simulations are used to evaluate the identification quality of the identification routine.

The Codac Library

Simon Rohou, Benoît Desrochers, Fabrice Le Bars — Thu, 21 Mar 2024 00:00:00 +0100

Codac (Catalog Of Domains And Contractors) is a C++/Python library providing tools for constraint programming over reals, trajectories and sets. It has many applications in parameter estimation, guaranteed integration or robot localization and provides reliable outputs by computing sets of feasible solutions according to the constraints defining the problem. This paper provides a brief overview of the library and its Contractor Network approach, illustrated on a convincing robotic application.

RISC-V Based Hardware Acceleration of Interval Contractor Primitives in the Context of Mobile Robotics

Pierre Filiol, Theotime Bollengier, Luc Jaulin, Jean-Christophe Le Lann — Thu, 24 Oct 2024 00:00:00 +0200

Localization tasks, generally modeled as Constraint Satisfaction Problem (CSP), are recurring problems in mobile robotics. Known approaches rely on software libraries which all have their advantages but also their limitations, among which non-optimal computing performances. This paper proposes a different approach which consists in extending the RISC-V ISA to provide hardware support for interval primitives.

GPU-Accelerated, Interval-Based Parameter Identification Methods Illustrated Using the Two-Compartment Problem

Lorenz Gillner, Ekaterina Auer — Thu, 24 Oct 2024 00:00:00 +0200

Interval methods are helpful in the context of scientific computing for reliable treatment of problems with bounded uncertainty. Most traditional interval algorithms, however, were designed for sequential execution while internally depending on processor-specific instructions for directed rounding. Nowadays, many-core processors and dedicated hardware for massively parallel data processing have become the de facto standard for high-performance computers. Interval libraries have yet to adapt to this heterogeneous computing paradigm. In this article, we investigate the parallelization of interval methods with an emphasis on modern graphics processors. Using a parameter identification scenario in combination with newly developed or enhanced GPU-based interval software, we evaluate different methods for reducing the size of large interval search domains. For the first time, algorithmic differentiation can be used with intervals on the GPU. Different versions of interval optimization algorithms are compared wrt. their functionality, run times, and energy consumption.

Asymptotically Minimal Contractors Based on the Centered Form

Luc Jaulin — Thu, 24 Oct 2024 00:00:00 +0200

This paper proposes a new interval-based contractor for nonlinear equations which is minimal when dealing with narrow boxes. The method is based on the centered form classically used by interval algorithms combined with a Gauss Jordan band diagonalization preconditioning. As an illustration in stability analysis, we propose to compute the set of all parameters of a characteristic function of linear time-delayed equations which have at least one zero in the imaginary axis. Our approach is able compute a guaranteed and accurate enclosure of the solution set faster than existing approaches.