Table Of ContentStochastics, Control and Robotics
Stochastics, Control and Robotics
Harish Parthasarathy
Professor
Electronics & Communication Engineering
Netaji SubHh.a Ps aInrtshtiatustaer oaft hTyechnology (NSIT)
New Delhi, Delhi-110078
Firstpublished2021
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Brief Contents
1. Classical Robotics and Quantum Stochastics 1–128
2. Electromagnetus and Related Partial Differential Equation 129–149
3. Radon and Group Theoretic Transforms with Robotics
Applications 151–175
4. Stochastic Filtering and Control, Interacting Particles 177–221
5. Classical and Quantum Robotics 223–253
6. Large Deviations, Classical and Quantum General
Relativity with GPS Application 255–338
7. Quantum Signal Processing 339–476
Detailed Contents
1. Classical Robotics and Quantum Stochastics 1–128
[1] A Problem in Robotics with Current Carrying Links 1
[2] Quantum Filtering 4
[3] Evan’s Hudson Flow 8
[4] Quantum Version of a Gauss-Markov Process 10
[5] Problems on the δ-Function 13
[6] Conditional Expectation in Quantum Filtering 16
[7] K.R. Parthasarathy Quantum Markov Processes 18
[8] Quantum Stochastic Lyapunov Theory 20
[9] Let P be a Solution to the Martingale Problem π(x, a, b), i.e. 27
[10] Problem from Revuz and Yor 28
[11] Gough and Kostler Paper on Quantum Filtering
Some Remarks 28
[12] Quantization of Master. Slave Robot Motion Using
Evans-Hudson Flows 33
[13] Problem From KRP QSC 37
[14] Moment Generating Function for Certain Quantum
Random Variables 41
[15] Belavkin Filtering Contd. 42
[16] Modelling Noise in Quantum Mechanical Systems 43
[17] Belavkin has Derived a Quantum Stochastic Differential
Equation (qsde) for (cid:31)X(t t) 48
[18] Waveguide Modes 50
[19] Estimating the Initial State from Measurements of an
Observable after the State Passes through a Sequence
of Quantum Channels 56
[20] Quantum Poisson Random Variable 57
viii Detailed Contents Detailed Contents ix
[21] Quantum Relative Entropy Evolution 59 [5] n-Dimensional Helmholtz Green’s Funtion 140
[22] Gauge Group Invariance of a Wave Eqn. 60 [6] Edge Diffusion 141
[23] Problem 61 [7] Waves in Metamaterials 141
[24] Quantum Oscillator Perturbed by an Electromagnetic Field 61 [8] Stroock Partial Differential Equations for Probabilities
ϕ(cid:31) Function, u(cid:31) Sobolev Distribution 148
[25] Quantization of Mechanical Systems 64
3. Radon and Group Theoretic Transforms with Robotics
[26] Quantum Filtering 66
Applications 151–175
[27] Perspective Projection by Camera Attached to a Robot 71
[1] Modern Trends in Signal Processing by
[28] Proof of The Positivity of Quantum Relative Entropy 72 Harish Parthasarathy, NSIT 151
[29] Entropy of a Quantum System 73 [2] Radon-Transform Based Image Processing 152
[30] Dirac Eqn. Based Temperature Estimation of Black-Body [3] Image Processing Using Invariants of the Permutation
Temperature Field 76 Group 155
[31] Quantum Image Processing on a C∞- Manifold 81 [4] Radon Transform of Rotated and Translated Image Field 157
[32] Belavkin Contd. (Quantum Non-Linear Filtering) 82 [5] Estimating the Rotation Applied to the 3-D Robot Links
from Electromagnetic Field Pattern 158
[33] Remarks on Theorems from V. Kac. Infinite Dimensional
Lic Algebra. P.87 83 [6] Kinetic Energy of a Two Link Robot 159
[34] Quantum Mutual Information 84 [7] Vector Potential Generated by a 2-Link Robot 164
[35] Scattering Theory Applied to Quantum Gate Design 86 [8] Group Associated with Robot Motion 166
[36] Quantization of the Simple Exclusion Model 93 [9] Radon Transform 168
[37] Quantum Version of Nearest Neighbour Interactions 96 [10] Campbelt Baker-Hausdorff Formula 169
[38] Remarks and Comments on “Collected Papers of S.R.S [11] Problem on Rigid Body Motion 171
Varadhan” Vol. 4, Particle System and Their Large Deviations 101
[12] Remarks on Theorems from V. Kac. Infinite Dimensional
[39] Quantum String Theory 103 Lic Algebra. P.87 171
[40] Quantum Shannon Theory Contd. 108 [13] Theta a Function From Group Theory P 252 (V.Kac) 172
[41] Basics of Cq-Information Theory 111 [14] Iwasava Decomposition 175
[42] Typical Sequences and Error Probability in Classical 4. Stochastic Filtering and Control, Interacting Particles 177–221
and Quantum Coding 114
[1] Bernoulli Filters 177
[43] Quantum Image Processing Some Basic Problems 125
[2] A Problem in Large Deviation Theory 179
2. Electromagnetus and Related Partial Differential Equation 129–149
[3] Large Deviations in Image Trajectory on a Screen Taken
[1] Computation of the Perturbe Characteristics Frequencies by a Robot Camera in Motion 180
in a Cavity Resonator with in Homogeneous Dielectric
[4] P406 Revuz and Yor 184
and Permittivity 129
[5] Problem from “Continuous Martingales and Brownian
[2] Numerical Methods for pde 133
Motion” by Revuz and Yor 188
[3] Tracking of Moving Targets Using a Camera Attached to the
[6] Problem from Revuz and Yor 189
Tip of a 2 = Link Robot 137
[7] Collected Papers of Varadhan-Interacting Particle System,
[4] Problem 140
Vol. 4. Hamiltonian System and Hydrodynamical Equations 191
Detailed Contents ix
[5] n-Dimensional Helmholtz Green’s Funtion 140
[6] Edge Diffusion 141
[7] Waves in Metamaterials 141
[8] Stroock Partial Differential Equations for Probabilities
ϕ(cid:31) Function, u(cid:31) Sobolev Distribution 148
3. Radon and Group Theoretic Transforms with Robotics
Applications 151–175
[1] Modern Trends in Signal Processing by
Harish Parthasarathy, NSIT 151
[2] Radon-Transform Based Image Processing 152
[3] Image Processing Using Invariants of the Permutation
Group 155
[4] Radon Transform of Rotated and Translated Image Field 157
[5] Estimating the Rotation Applied to the 3-D Robot Links
from Electromagnetic Field Pattern 158
[6] Kinetic Energy of a Two Link Robot 159
[7] Vector Potential Generated by a 2-Link Robot 164
[8] Group Associated with Robot Motion 166
[9] Radon Transform 168
[10] Campbelt Baker-Hausdorff Formula 169
[11] Problem on Rigid Body Motion 171
[12] Remarks on Theorems from V. Kac. Infinite Dimensional
Lic Algebra. P.87 171
[13] Theta a Function From Group Theory P 252 (V.Kac) 172
[14] Iwasava Decomposition 175
4. Stochastic Filtering and Control, Interacting Particles 177–221
[1] Bernoulli Filters 177
[2] A Problem in Large Deviation Theory 179
[3] Large Deviations in Image Trajectory on a Screen Taken
by a Robot Camera in Motion 180
[4] P406 Revuz and Yor 184
[5] Problem from “Continuous Martingales and Brownian
Motion” by Revuz and Yor 188
[6] Problem from Revuz and Yor 189
[7] Collected Papers of Varadhan-Interacting Particle System,
Vol. 4. Hamiltonian System and Hydrodynamical Equations 191
