Academic interests
 CyberPhysical systems
 Networked control
 Connected and intelligent transportation systems
 Hybrid systems: modelling, simulation, design and validation
Courses taught
Google scholar page
https://scholar.google.com/citations?user=VrWL7wAAAAJ&hl=no&oi=ao
Projects
CriSp (Forsknigsrådet): Finding a CRItical SPeed function ahead of a road section for vehicles in motion
SafeSmart (KK stiftelsen)
Software
<script src="https://codeocean.com/widget.js?slug=2880063" async></script><script src="https://codeocean.com/widget.js?slug=2880063" async></scriptMATLAB code for simulating a class of switched affine systems Associated paper slides lecture video
Tags:
CyberPhysical Systems,
Internet of Things,
Hybrid systems,
The Digital Society,
DigiTech
Publications

Berger, Guillaume O. & Rabi, Maben
(2021).
Bounds on set exit times of affine systems, using Linear Matrix Inequalities.
IFACPapersOnLine.
ISSN 24058963.
54(5),
p. 283–288.
doi:
10.1016/j.ifacol.2021.08.512.
Full text in Research Archive
Show summary
Efficient computation of trajectories of switched affine systems becomes possible, if for any such hybrid system, we can manage to efficiently compute the sequence of switching times. Once the switching times have been computed, we can easily compute the trajectories between two successive switches as the solution of an affine ODE. Each switching time can be seen as a positive real root of an analytic function, thereby allowing for efficient computation by using root finding algorithms. These algorithms require a finite interval, within which to search for the switching time. In this paper, we study the problem of computing upper bounds on such switching times, and we restrict our attention to stable timeinvariant affine systems. We provide semidefinite programming models to compute upper bounds on the time taken by the trajectories of an affine ODE to exit a set described as the intersection of a few generalized ellipsoids. Through numerical experiments, we show that the resulting bounds are tighter than bounds reported before, while requiring only a modest increase in computation time.

Rabi, Maben
(2021).
Relay SelfOscillations for Second Order, Stable, Nonminimum Phase Plants.
IEEE Transactions on Automatic Control.
ISSN 00189286.
66(9),
p. 4282–4288.
doi:
10.1109/TAC.2020.3030893.
Show summary
We study a relay feedback system (RFS) having an ideal relay element and a linear, timeinvariant, secondorder plant. The relay element is modeled as an ideal on – off switch. And the plant is modeled using a transfer function that as follows: first, is Hurwitz stable, second, is proper, third, has a positive real zero, andfourth, has a positive dc gain. We analyze this RFS using a statespace description, with closedform expressions for the state trajectory from one switching time to the next. We prove that the state transformation from one switching time to the next, first, has a Schur stable linearization, and first, is a contraction mapping. Then using the Banach contraction mapping theorem, we prove that all trajectories of this RFS converge asymptotically to a unique limit cycle. This limit cycle is symmetric, and is unimodal as it has exactly two relay switches per period. This result helps understand the behavior of the relay autotuning method, when applied to secondorder plants with no time delay. We also treat the case where the plant either has no finite zero, or has exactly one zero that is negative.


Bocharova, Irina E.; Kudryashov, Boris D.; Rabi, Maben; Lyamin, Nikita; Dankers, Wouter & Frick, Erik
[Show all 7 contributors for this article]
(2019).
Modeling Packet Losses in Communication Networks.
IEEE International Symposium on Information Theory. Proceedings.
ISSN 21578095.
p. 1012–1016.
doi:
10.1109/ISIT.2019.8849400.
Show summary
An approach to constructing discrete models of packet losses suitable for a wide variety of communication network applications is studied. It is based on estimating parameters of probabilistic automata described via socalled pseudoMarkov chains. The new technique is applied both to approximating a discrete time analog process at the output of known channel models and to the experimental data stream. Comparison of models is performed by computing probabilities of more than m losses out of n transmitted packets (P (≥ m, n)). It is shown that for the Rician fading channel with exponential correlation and correlation determined by a Bessel filter, the obtained ranktwo and rankthree discrete modes, respectively, provide high accuracy coincidence of P (≥ m, n) performances. The rankthree discrete model computed on the experimental data stream obtained from the LTE network provides significantly better approximation of P (≥ m, n) performance than that obtained by the BaumWelch algorithm.

Bocharova, Irina E.; Kudryashov, Boris D.; Lyamin, Nikita; Frick, Erik; Rabi, Maben & Vinel, Alexey
(2019).
Low Delay InterPacket Coding in Vehicular Networks.
Future Internet.
ISSN 19995903.
11(10).
doi:
10.3390/fi11100212.
Full text in Research Archive
Show summary
In Cooperative Intelligent Transportation Systems (CITSs), vehicles need to wirelessly connect with Roadside units (RSUs) over limited durations when such pointtopoint connections are possible. One example of such communications is the downloading of maps to the CITS vehicles. Another example occurs in the testing of CITS vehicles, where the tested vehicles upload trajectory records to the roadside units. Because of realtime requirements, and limited bandwidths, data are sent as User Datagram Protocol (UDP) packets. We propose an interpacket error control coding scheme that improves the recovery of data when some of these packets are lost; we argue that the coding scheme has to be one of convolutional coding. We measure performance through the session averaged probability of successfully delivering groups of packets. We analyze two classes of convolution codes and propose a lowcomplexity decoding procedure suitable for network applications. We conclude that Reed–Solomon convolutional codes perform better than Wyner–Ash codes at the cost of higher complexity. We show this by simulation on the memoryless binary erasure channel (BEC) and channels with memory, and through simulations of the IEEE 802.11p DSRC/ITSG5 network at the CITS test track AstaZero.
View all works in Cristin


Rabi, Maben
(2020).
The usefulness of Mathematics to Engineers: a few examples from Robotics and Control systems.

Rabi, Maben
(2020).
Piecewise analytic trajectory computation for polyhedral switching between stable affine systems.
Show summary
Our problem is to compute trajectories of a hybrid system that switches between stable affine ODEs, with switching triggered by hyperplane crossings. Instead of integrating over relatively short time steps, we propose to analytically calculate the affine ODE trajectories between switching times. Our algorithm computes the switching times themselves by Chebyshev interpolation of the analytic trajectory pieces, and polynomial root finding. We shrink the interpolation time intervals using bounds on the times needed by the affine ODE trajectories to enter Lyapunov sublevel sets. Based on the Chebfun package, we give a MATLAB implementation of our algorithm. We find that this implementation simulates Relay feedback systems as accurately and sometimes faster than conventional algorithms.

Bocharova, Irina E.; Kudryashov, Boris D.; Rabi, Maben; Lyamin, Nikita; Dankers, Wouter & Frick, Erik
[Show all 7 contributors for this article]
(2019).
Modeling Packet Losses in Communication Networks.
Show summary
An approach to constructing discrete models of packet losses suitable for a wide variety of communication network applications is studied. It is based on estimating parameters of probabilistic automata described via socalled pseudoMarkov chains. The new technique is applied both to approximating a discrete time analog process at the output of known channel models and to the experimental data stream. Comparison of models is performed by computing probabilities of more than m losses out of n transmitted packets (P (≥ m, n)). It is shown that for the Rician fading channel with exponential correlation and correlation determined by a Bessel filter, the obtained ranktwo and rankthree discrete modes, respectively, provide high accuracy coincidence of P (≥ m, n) performances. The rankthree discrete model computed on the experimental data stream obtained from the LTE network provides significantly better approximation of P (≥ m, n) performance than that obtained by the BaumWelch algorithm.

Haugen, Øystein & Rabi, Maben
(2019).
Internet of Things.
View all works in Cristin
Published June 13, 2019 2:53 PM
 Last modified Feb. 10, 2022 10:01 AM