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Relative Heading based Pattern Generation

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IFAC-PapersOnLine 2017年第1期50卷 12759-12764页

作者： Agarwal, Shashank Tripathy, Twinkle Borkar, Aseem Sinha, Arpita Shashank Agarwal Twinkle Tripathy Arpita Sinha and Aseem Borkar are with Systems and Control Engineering Group at IIT Bombay India

The objective of this paper is to generate planar patterns using a unicycle based robot. These patterns are annular and centred around a fixed point in the plane, which is termed as center point. The center could be any landmark for various purposes of target monitoring, exploration etc. The patterns are defined in terms of maximum and minimum radial distance from the center. The paper proposes a control strategy based on relative heading of the robot with respect to center. Analysis has been performed to guarantee the generation of annular patterns by imposing conditions over initial conditions and control law parameters. Verification of the theoretical results has been performed by means of simulation. Further, the control strategy has been implemented on a mobile robot to validate the results. © 2017

关键词： control theory

Automated synthesis of fixed structure QFT prefilter using piecewise linear approximation based linear programming optimization techniques

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IFAC-PapersOnLine 2016年第1期49卷 349-354页

作者： Nataraj, P.S.V. Makwana, Dipesh Systems and Control Engineering Group IIT Bombay India

Prefilter synthesis is one of the important design steps of Horowitz's quantitative feedback theory (QFT) to robust feedback system synthesis. The prefilter is designed to achieve tracking specifications. In this paper, a new, computationally efficient approach for automation of the prefilter design step is proposed. A linear programming based algorithm is proposed for the automatic synthesis of fixed structure QFT prefilter. In present work, prefilter synthesis problem is posed as a piecewise linear approximation based linear programming problem and solved with GUROBI optimizer *** proposed method is validated using a benchmark problem and a simple, low order prefilter is obtained in quick time. © 2016, IFAC (International Federation of Automatic control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Piecewise linear techniques Feedback Linear programming Robust control Automatic synthesis Computationally efficient Linear programming optimization Linear programming problem Order sets Piecewise linear approximations Prefilter designs Quantitative feedback theory

Vector Field Guidance for Convoy Monitoring Using Elliptical Orbits

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arXiv 2017年

作者： Borkar, Aseem V. Borkar, Vivek S. Sinha, Arpita Interdisciplinary Program in Systems and Control Engineering IIT Bombay India Department of Electrical Engineering IIT Bombay India

— We propose a novel vector field based guidance scheme for tracking and surveillance of a convoy, moving along a possibly nonlinear trajectory on the ground, by an aerial agent. The scheme first computes a time varying ellipse that encompasses all the targets in the convoy using a simple regression based algorithm. It then ensures convergence of the agent to a trajectory that repeatedly traverses this moving ellipse. The scheme is analyzed using perturbation theory of nonlinear differential equations and supporting simulations are provided. Some related implementation issues are discussed and advantages of the scheme are highlighted. Copyright © 2017, The Authors. All rights reserved.

关键词： Perturbation techniques

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Chirp Mixing

arXiv 2017年

作者： Khaneja, Navin Systems and Control Engineering IIT Bombay Powai400076 India

In this paper, we develop the theory of chirp mixing. The working principle is simple, given coupled homonuclear spins with offsets in range [−B, B], we adiabatically sweep through the resonances. This achieves cross polarization between the z magnetization of the coupled spins. We repeat this basic operation many times with a supercycle to achieve appropriate mixing time. When we sweep through the resonances, midway between the resonances of the coupled spin I and S, the effective field seen by two spins is the same and hence they precess at same frequency around their effective fields. This means the coupling, which normally gets averaged due to the chemical shift difference is no more averaged for a short time and we get mixing. In this paper, we develop these basic ideas. By virtue of its design, the chirp mixing is much more broadband compared to state of the art methods. The proposed methodology is demonstrated on 13C mixing in a sample of Alanine. Copyright © 2017, The Authors. All rights reserved.

关键词： Mixing

Structure-preserving discrete-Time optimal maneuvers of a wheeled inverted pendulum

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arXiv 2017年

作者： Phogat, Karmvir Singh Banavar, Ravi Chatterjee, Debasish Systems & Control Engineering IIT Bombay Mumbai400076 India

The Wheeled Inverted Pendulum (WIP) is a nonholonomic, underactuated mechanical system, and has been popularized commercially as the Segway. Designing optimal control laws for point-To-point state-Transfer for this autonomous mechanical system, while respecting momentum and torque constraints as well as the underlying manifold, continues to pose challenging problems. In this article we present a successful effort in this direction: We employ geometric mechanics to obtain a discrete-Time model of the system, followed by the synthesis of an energy-optimal control based on a discrete-Time maximum principle applicable to mechanical systems whose configuration manifold is a Lie group. Moreover, we incorporate state and momentum constraints into the discrete-Time control directly at the synthesis stage. The control is implemented on a WIP with parameters obtained from an existing prototype;the results are highly encouraging, as demonstrated by numerical experiments. Copyright © 2017, The Authors. All rights reserved.

关键词： Mechanics

Electron conduction in solid state via time varying wavevectors

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arXiv 2017年

作者： Khaneja, Navin Systems and Control Engineering IIT Bombay Powai400076 India

In this paper, we study electron wavepacket dynamics in electric and magnetic fields. We rigorously derive the semiclassical equations of electron dynamics in electric and magnetic fields. We do it both for free electron and electron in a periodic potential. We do this by introducing time varying wavevectors k(t). In the presence of magnetic field, our wavepacket reproduces the classical cyclotron orbits once the origin of the Schröedinger equation is correctly chosen to be center of cyclotron orbit. In the presence of both electric and magnetic fields, our equations for wavepacket dynamics differ from classical Lorentz force equations. We show that in a periodic potential, on application of electric field, the electron wave function adiabatically follows the wavefunction of a time varying Bloch wavevector k(t), with its energies suitably shifted with time. We derive the effective mass equation and discuss conduction in conductors and insulators. Copyright © 2017, The Authors. All rights reserved.

关键词： Electrons

A complete characterization of optimal dictionaries for least squares representation

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arXiv 2017年

作者： Sheriff, Mohammed Rayyan Chatterjee, Debasish Systems and Control Engineering Iit Bombay Powai Mumbai400076 India

Dictionaries are collections of vectors used for representations of elements in Euclidean spaces. While recent research on optimal dictionaries is focussed on providing sparse (i.e., 0-optimal,) representations, here we consider the problem of finding optimal dictionaries such that representations of samples of a random vector are optimal in an 2-sense. For us, optimality of representation is equivalent to minimization of the average 2-norm of the coefficients used to represent the random vector, with the lengths of the dictionary vectors being specified a priori. With the help of recent results on rank-1 decompositions of symmetric positive semidefinite matrices and the theory of majorization, we provide a complete characterization of 2-optimal dictionaries. Our results are accompanied by polynomial time algorithms that construct 2-optimal dictionaries from given data. Copyright © 2017, The Authors. All rights reserved.

关键词： Polynomial approximation

Conservation of energy, density of states and spin lattice relaxation

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arXiv 2017年

作者： Khaneja, Navin Department of Systems and Control Engineering IIT Bombay Powai400076 India

The starting point of all NMR experiments is a spin polarization which develops when we place the sample in static magnetic field B0. There are excess of spins aligned along B0 (spin up with lower energy) than spins aligned opposite (spin down with higher energy) to the field B0. A natural question is what is the source of this excess spin polarization because relaxation mechanisms can flip a up spin to a down spin and vice-versa. The answer lies in the density of states. When a molecule with spin down flips to spin up it loses energy. This energy goes into increasing the kinetic energy of the molecule in the gas/solution phase. At this increased kinetic energy, there are more rotational-translational states accessible to the molecule than at lower energy. This increases the probability the molecule will spend in spin up state (higher kinetic energy state). This is the source of excess polarization. In this paper, we use an argument based on equipartition of energy to explicitly count the excess states that become accessible to the molecule when its spin is flipped from down to up. Using this counting, we derive the familiar Boltzmann distribution of the ratio of up vs down spins. Although prima facie, there is nothing new in this paper, we find the mode counting argument for excess states interesting. Furthermore, the paper stresses the fact that spin polarization arises from higher density of states at increased kinetic energy of molecules. Copyright © 2017, The Authors. All rights reserved.

关键词： Molecules

Discrete time pontryagin maximum principle for optimal control problems under state-action-frequency constraints

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arXiv 2017年

作者： Paruchuri, Pradyumna Chatterjee, Debasish Systems and Control Engineering IIT Bombay Powai Mumbai400076 India

We establish a Pontryagin maximum principle for discrete time optimal control problems under the following three types of constraints: a) constraints on the states pointwise in time, b) constraints on the control actions pointwise in time, and c) constraints on the frequency spectrum of the optimal control trajectories. While the first two types of constraints are already included in the existing versions of the Pontryagin maximum principle, it turns out that the third type of constraints cannot be recast in any of the standard forms of the existing results for the original control system. We provide two different proofs of our Pontryagin maximum principle in this article, and include several special cases fine-tuned to control-affine nonlinear and linear system models. In particular, for minimization of quadratic cost functions and linear time invariant control systems, we provide tight conditions under which the optimal controls under frequency constraints are either normal or *** Codes 49K21 Copyright © 2017, The Authors. All rights reserved.

关键词： Maximum principle