Dynamic System Modelling and Analysis with MATLAB and Python

Jongrae Kim, PhD, is Associate Professor at the Institute of Design, Robotics & Optimization (iDRO), School of Mechanical Engineering, University of Leeds in the United Kingdom. He obtained his doctorate from the Department of Aerospace Engineering at Texas A&M University in the United States in 2002.

• Preface xiiiAcknowledgements xvAcronyms xviiAbout the Companion Website xix1 Introduction 11.1 Scope of the Book 11.2 Motivation Examples 21.2.1 Free-Falling Object 21.2.1.1 First Program in Matlab 41.2.1.2 First Program in Python 101.2.2 Ligand–Receptor Interactions 141.3 Organization of the Book 21Exercises 21Bibliography 222 Attitude Estimation and Control 232.1 Attitude Kinematics and Sensors 232.1.1 Solve Quaternion Kinematics 262.1.1.1 MATLAB 262.1.1.2 Python 292.1.2 Gyroscope Sensor Model 332.1.2.1 Zero-Mean Gaussian White Noise 332.1.2.2 Generate Random Numbers 342.1.2.3 Stochastic Process 402.1.2.4 MATLAB 412.1.2.5 Python 452.1.2.6 Gyroscope White Noise 492.1.2.7 Gyroscope RandomWalk Noise 502.1.2.8 Gyroscope Simulation 532.1.3 Optical Sensor Model 572.2 Attitude Estimation Algorithm 642.2.1 A Simple Algorithm 642.2.2 QUEST Algorithm 652.2.3 Kalman Filter 662.2.4 Extended Kalman Filter 752.2.4.1 Error Dynamics 762.2.4.2 Bias Noise 772.2.4.3 Noise Propagation in Error Dynamics 782.2.4.4 State Transition Matrix, Φ 842.2.4.5 Vector Measurements 842.2.4.6 Summary 862.2.4.7 Kalman Filter Update 862.2.4.8 Kalman Filter Propagation 872.3 Attitude Dynamics and Control 882.3.1 Dynamics Equation of Motion 882.3.1.1 MATLAB 912.3.1.2 Python 942.3.2 Actuator and Control Algorithm 952.3.2.1 MATLAB Program 982.3.2.2 Python 1012.3.2.3 Attitude Control Algorithm 1032.3.2.4 Altitude Control Algorithm 1052.3.2.5 Simulation 1062.3.2.6 MATLAB 1072.3.2.7 Robustness Analysis 1072.3.2.8 Parallel Processing 110Exercises 113Bibliography 1153 Autonomous Vehicle Mission Planning 1193.1 Path Planning 1193.1.1 Potential Field Method 1193.1.1.1 MATLAB 1223.1.1.2 Python 1263.1.2 Graph Theory-Based Sampling Method 1263.1.2.1 MATLAB 1283.1.2.2 Python 1293.1.2.3 Dijkstra’s Shortest Path Algorithm 1303.1.2.4 MATLAB 1303.1.2.5 Python 1313.1.3 Complex Obstacles 1343.1.3.1 MATLAB 1353.1.3.2 Python 1413.2 Moving Target Tracking 1453.2.1 UAV and Moving Target Model 1453.2.2 Optimal Target Tracking Problem 1483.2.2.1 MATLAB 1493.2.2.2 Python 1513.2.2.3 Worst-Case Scenario 1533.2.2.4 MATLAB 1573.2.2.5 Python 1593.2.2.6 Optimal Control Input 1643.3 Tracking Algorithm Implementation 1673.3.1 Constraints 1673.3.1.1 Minimum Turn Radius Constraints 1673.3.1.2 Velocity Constraints 1693.3.2 Optimal Solution 1723.3.2.1 Control Input Sampling 1723.3.2.2 Inside the Constraints 1753.3.2.3 Optimal Input 1773.3.3 Verification Simulation 180Exercises 182Bibliography 1824 Biological System Modelling 1854.1 Biomolecular Interactions 1854.2 Deterministic Modelling 1854.2.1 Group of Cells and Multiple Experiments 1864.2.1.1 Model Fitting and the Measurements 1884.2.1.2 Finding Adaptive Parameters 1904.2.2 E. coli Tryptophan Regulation Model 1914.2.2.1 Steady-State and Dependant Parameters 1944.2.2.2 Padé Approximation of Time-Delay 1954.2.2.3 State-Space Realization 1964.2.2.4 Python 2054.2.2.5 Model Parameter Ranges 2064.2.2.6 Model Fitting Optimization 2134.2.2.7 Optimal Solution (MATLAB) 2214.2.2.8 Optimal Solution (Python) 2234.2.2.9 Adaptive Parameters 2264.2.2.10 Limitations 2264.3 Biological Oscillation 2274.3.1 Gillespie’s Direct Method 2314.3.2 Simulation Implementation 2344.3.3 Robustness Analysis 241Exercises 245Bibliography 2465 Biological System Control 2515.1 Control Algorithm Implementation 2515.1.1 PI Controller 2515.1.1.1 Integral Term 2525.1.1.2 Proportional Term 2535.1.1.3 Summation of the Proportional and the Integral Terms 2535.1.1.4 Approximated PI Controller 2535.1.1.5 Comparison of PI Controller and the Approximation 2545.1.2 Error Calculation: ΔP 2605.2 Robustness Analysis: 𝜇-Analysis 2695.2.1 Simple Examples 2695.2.1.1 𝜇 Upper Bound 2725.2.1.2 𝜇 Lower Bound 2755.2.1.3 Complex Numbers in MATLAB/Python 2785.2.2 Synthetic Circuits 2805.2.2.1 MATLAB 2815.2.2.2 Python 2815.2.2.3 𝜇-Upper Bound: Geometric Approach 290Exercises 291Bibliography 2926 FurtherReadings2956.1 Boolean Network 2956.2 Network Structure Analysis 2966.3 Spatial-Temporal Dynamics 2976.4 Deep Learning Neural Network 2986.5 Reinforcement Learning 298Bibliography 298Appendix A Solutions for Selected Exercises 301A.1 Chapter 1 301Exercise 1.4 301Exercise 1.5 301A.2 Chapter 2 302Exercise 2.5 302A.3 Chapter 3 302Exercise 3.1 302Exercise 3.6 303A.4 Chapter 4 303Exercise 4.1 303Exercise 4.2 303Exercise 4.7 304A.5 Chapter 5 304Exercise 5.2 304Exercise 5.3 304Index 307