Maben Rabi

• Langstrand, Jens-Patrick Andre Bjerk & Rabi, Maben (2023). Estimating road friction from kinematic summaries at curved sections. In Mastellone, Silvia (Eds.), Proceedings of the 2023 IEEE Conference on Control Technology and Applications (CCTA). IEEE conference proceedings. ISSN 979-8-3503-3544-6. p. 307–314. doi: 10.1109/CCTA54093.2023.10253194. Show summary

  We present a system for estimating the friction of the pavement surface at any curved road section, by arriving at a consensus estimate, based on data from vehicles that have recently passed through that section. This estimate can help following vehicles. To keep costs down, we depend only on standard automotive sensors, such as the IMU, and sensors for the steering angle and wheel speeds. Our system’s workflow consists of: (i) processing measurements from vehicular sensors, (ii) transmitting short kinematic summaries from vehicles to a road side unit (RSU), using V2X communication, and (iii) estimating the friction coefficients, by running a machine learning regressor at the RSU, on summaries from individual vehicles, and then combining several such estimates.We study two key questions: (i) should each individual road section have a local friction coefficient regressor, or can we use a global regressor that covers all the possible road sections? and (ii) how accurate are the resulting regressor estimates? We test the performance of design variations of our system, using simulations of normal driving scenarios at curved road sections, using the commercial package Dyna4. We consider a single vehicle type with varying levels of tyre wear, and a range of road friction coefficients. We find that: (a) only a marginal loss of accuracy is incurred in using a global regressor as compared to local regressors, (b) the consensus estimate at the RSU has a worst case error of about ten percent, if the combination is based on at least fifty recently passed vehicles, and (c) our regressors have root mean square (RMS) errors that are less than five percent. The RMS error rate of our system is half as that of a commercial friction estimation service [7].But when tested with data from extreme driving manoeuvres that were unseen in the training data, our regressor performs an order of magnitude worse than on data from normal driving runs on curved road sections. Still our regressor’s RMS errors on such test data are no worse than the state of the art Artificial Neural Network regressors [18], [30].

• Rabi, Maben; Wu, Junfeng; Singh, Vyoma & Johansson, Karl Henrik (2023). Estimating a scalar log-concave random variable, using a silence set based probabilistic sampling, 2023 American Control Conference (ACC 2023). IEEE (Institute of Electrical and Electronics Engineers). ISSN 979-8-3503-2806-6. p. 4759–4765. doi: 10.23919/ACC55779.2023.10156312. Show summary

  We study the probabilistic sampling of a random variable, in which the variable is sampled only if it falls outside a given set, which is called the silence set. This helps us to understand optimal event-based sampling for the special case of IID random processes, and also to understand the design of a sub-optimal scheme for other cases. We consider the design of this probabilistic sampling for a scalar, log-concave random variable, to minimize either the mean square estimation error, or the mean absolute estimation error. We show that the optimal silence interval: (i) is essentially unique, and (ii) is the limit of an iterative procedure of centering. Further we show through numerical experiments that super-level intervals seem to be remarkably near-optimal for mean square estimation. Finally we use the Gauss inequality for scalar unimodal densities, to show that probabilistic sampling gives a mean square distortion that is less than a third of the distortion incurred by periodic sampling, if the average sampling rate is between 0.3 and 0.9 samples per tick.

• Berger, Guillaume O. & Rabi, Maben (2021). Bounds on set exit times of affine systems, using Linear Matrix Inequalities. IFAC-PapersOnLine. ISSN 2405-8963. 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 time-invariant affine systems. We provide semi-definite 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 Self-Oscillations for Second Order, Stable, Nonminimum Phase Plants. IEEE Transactions on Automatic Control. ISSN 0018-9286. 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, time-invariant, second-order 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 state-space description, with closed-form 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 second-order 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.

• Rabi, Maben (2020). Piece-wise analytic trajectory computation for polytopic switching between stable affine systems. In Ames, Aaron & Seshia, Sanjit (Ed.), HSCC '20: Proceedings of the 23rd International Conference on Hybrid Systems: Computation and Control. Association for Computing Machinery (ACM). ISSN 978-1-4503-7018-9. doi: 10.1145/3365365.3382204. 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 certain Lyapunov sub-level 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. IEEE International Symposium on Information Theory. Proceedings. ISSN 2157-8095. 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 so-called pseudo-Markov 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 rank-two and rank-three discrete modes, respectively, provide high accuracy coincidence of P (≥ m, n) performances. The rank-three 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 Baum-Welch algorithm.

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• Rabi, Maben (2021). Remoteness is no hindrance to academic excellence. Hindu. ISSN 0971-751X. Show summary

  Excellence in education depends on the quality of mentorship and not on the size or location of campuses.

• Rabi, Maben (2020). The usefulness of Mathematics to Engineers: a few examples from Robotics and Control systems.
• Rabi, Maben (2020). Piece-wise 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 sub-level 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 so-called pseudo-Markov 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 rank-two and rank-three discrete modes, respectively, provide high accuracy coincidence of P (≥ m, n) performances. The rank-three 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 Baum-Welch algorithm.

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