Series Preface |
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xiii | |
Preface |
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xv | |
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1 | (28) |
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1.1 Notation and Basic Definitions |
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1 | (2) |
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3 | (7) |
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1.2.1 Linear Tracking Systems |
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7 | (2) |
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1.2.2 Linear Time-Invariant Tracking Systems |
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9 | (1) |
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1.3 Guidance and Control of Flight Vehicles |
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10 | (3) |
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1.4 Special Tracking Laws |
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13 | (11) |
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1.4.1 Proportional Navigation Guidance |
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13 | (3) |
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1.4.2 Cross-Product Steering |
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16 | (3) |
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1.4.3 Proportional-Integral-Derivative Control |
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19 | (5) |
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1.5 Digital Tracking System |
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24 | (1) |
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25 | (1) |
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26 | (2) |
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28 | (1) |
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2 Optimal Control Techniques |
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29 | (74) |
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29 | (2) |
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2.2 Multi-variable Optimization |
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31 | (2) |
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2.3 Constrained Minimization |
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33 | (8) |
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2.3.1 Equality Constraints |
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34 | (4) |
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2.3.2 Inequality Constraints |
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38 | (3) |
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2.4 Optimal Control of Dynamic Systems |
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41 | (3) |
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2.4.1 Optimality Conditions |
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43 | (1) |
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2.5 The Hamiltonian and the Minimum Principle |
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44 | (4) |
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2.5.1 Hamilton-Jacobi-Bellman Equation |
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45 | (2) |
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2.5.2 Linear Time-Varying System with Quadratic Performance Index |
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47 | (1) |
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2.6 Optimal Control with End-Point State Equality Constraints |
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48 | (4) |
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2.6.1 Euler-Lagrange Equations |
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50 | (1) |
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50 | (2) |
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2.7 Numerical Solution of Two-Point Boundary Value Problems |
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52 | (9) |
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54 | (3) |
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57 | (4) |
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2.8 Optimal Terminal Control with Interior Time Constraints |
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61 | (2) |
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2.8.1 Optimal Singular Control |
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62 | (1) |
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63 | (6) |
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2.9.1 Neighboring Extremal Method and Linear Quadratic Control |
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64 | (5) |
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2.10 Stochastic Processes |
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69 | (8) |
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2.10.1 Stationary Random Processes |
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75 | (2) |
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2.10.2 Filtering of Random Noise |
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77 | (1) |
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77 | (4) |
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2.12 Robust Linear Time-Invariant Control |
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81 | (15) |
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82 | (7) |
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2.12.2 H2/H∞ Design Methods |
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89 | (7) |
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96 | (2) |
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98 | (3) |
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101 | (2) |
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3 Optimal Navigation and Control of Aircraft |
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103 | (92) |
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3.1 Aircraft Navigation Plant |
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104 | (11) |
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3.1.1 Wind Speed and Direction |
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110 | (2) |
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3.1.2 Navigational Subsystems |
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112 | (3) |
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3.2 Optimal Aircraft Navigation |
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115 | (13) |
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3.2.1 Optimal Navigation Formulation |
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116 | (3) |
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3.2.2 Extremal Solution of the Boundary-Value Problem: Long-Range Flight Example |
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119 | (2) |
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3.2.3 Great Circle Navigation |
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121 | (7) |
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3.3 Aircraft Attitude Dynamics |
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128 | (8) |
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3.3.1 Translational and Rotational Kinetics |
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132 | (3) |
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3.3.2 Attitude Relative to the Velocity Vector |
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135 | (1) |
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3.4 Aerodynamic Forces and Moments |
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136 | (3) |
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3.5 Longitudinal Dynamics |
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139 | (6) |
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3.5.1 Longitudinal Dynamics Plant |
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142 | (3) |
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3.6 Optimal Multi-variable Longitudinal Control |
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145 | (2) |
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3.7 Multi-input Optimal Longitudinal Control |
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147 | (1) |
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3.8 Optimal Airspeed Control |
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148 | (25) |
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3.8.1 LQG/LTR Design Example |
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149 | (11) |
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160 | (6) |
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3.8.3 Altitude and Mach Control |
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166 | (7) |
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3.9 Lateral-Directional Control Systems |
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173 | (10) |
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3.9.1 Lateral-Directional Plant |
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173 | (4) |
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3.9.2 Optimal Roll Control |
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177 | (3) |
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3.9.3 Multi-variable Lateral-Directional Control: Heading-Hold Autopilot |
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180 | (3) |
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3.10 Optimal Control of Inertia-Coupled Aircraft Rotation |
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183 | (6) |
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189 | (3) |
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192 | (2) |
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194 | (1) |
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4 Optimal Guidance of Rockets |
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195 | (82) |
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195 | (1) |
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4.2 Optimal Terminal Guidance of Interceptors |
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195 | (4) |
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4.3 Non-planar Optimal Tracking System for Interceptors: 3DPN |
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199 | (9) |
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4.4 Flight in a Vertical Plane |
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208 | (3) |
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4.5 Optimal Terminal Guidance |
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211 | (5) |
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4.6 Vertical Launch of a Rocket (Goddard's Problem) |
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216 | (3) |
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4.7 Gravity-Turn Trajectory of Launch Vehicles |
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219 | (9) |
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4.7.1 Launch to Circular Orbit: Modulated Acceleration |
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220 | (7) |
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4.7.2 Launch to Circular Orbit: Constant Acceleration |
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227 | (1) |
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4.8 Launch of Ballistic Missiles |
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228 | (9) |
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4.8.1 Gravity-Turn with Modulated Forward Acceleration |
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232 | (1) |
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4.8.2 Modulated Forward and Normal Acceleration |
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233 | (4) |
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4.9 Planar Tracking Guidance System |
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237 | (10) |
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4.9.1 Stability, Controllability, and Observability |
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241 | (2) |
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4.9.2 Nominal Plant for Tracking Gravity-Turn Trajectory |
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243 | (4) |
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4.10 Robust and Adaptive Guidance |
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247 | (3) |
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4.11 Guidance with State Feedback |
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250 | (4) |
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4.11.1 Guidance with Normal Acceleration Input |
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250 | (4) |
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4.12 Observer-Based Guidance of Gravity-Turn Launch Vehicle |
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254 | (12) |
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4.12.1 Altitude-Based Observer with Normal Acceleration Input |
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255 | (5) |
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4.12.2 Bi-output Observer with Normal Acceleration Input |
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260 | (6) |
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4.13 Mass and Atmospheric Drag Modeling |
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266 | (8) |
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274 | (1) |
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275 | (1) |
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275 | (2) |
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5 Attitude Control of Rockets |
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277 | (20) |
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277 | (1) |
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5.2 Attitude Control Plant |
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277 | (4) |
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5.3 Closed-Loop Attitude Control |
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281 | (1) |
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281 | (1) |
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5.5 Pitch Control of Rockets |
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282 | (12) |
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282 | (1) |
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5.5.2 Pitch Guidance and Control System |
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283 | (5) |
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5.5.3 Adaptive Pitch Control System |
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288 | (6) |
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5.6 Yaw Control of Rockets |
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294 | (1) |
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295 | (1) |
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295 | (1) |
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296 | (1) |
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6 Spacecraft Guidance Systems |
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297 | (60) |
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297 | (1) |
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297 | (8) |
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298 | (1) |
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6.2.2 Perifocal and Celestial Frames |
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299 | (2) |
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301 | (3) |
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6.2.4 Lagrange's Coefficients |
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304 | (1) |
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6.3 Spacecraft Terminal Guidance |
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305 | (29) |
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6.3.1 Minimum Energy Orbital Transfer |
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307 | (4) |
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311 | (2) |
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313 | (9) |
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6.3.4 Lambert Guidance of Rockets |
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322 | (5) |
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6.3.5 Optimal Terminal Guidance of Re-entry Vehicles |
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327 | (7) |
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6.4 General Orbital Plant for Tracking Guidance |
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334 | (5) |
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6.5 Planar Orbital Regulation |
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339 | (6) |
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6.6 Optimal Non-planar Orbital Regulation |
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345 | (7) |
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352 | (1) |
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352 | (3) |
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355 | (2) |
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7 Optimal Spacecraft Attitude Control |
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357 | (34) |
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357 | (1) |
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7.2 Terminal Control of Spacecraft Attitude |
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357 | (7) |
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7.2.1 Optimal Single-Axis Rotation of Spacecraft |
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358 | (6) |
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7.3 Multi-axis Rotational Maneuvers of Spacecraft |
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364 | (11) |
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7.4 Spacecraft Control Torques |
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375 | (4) |
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7.4.2 Reaction Wheels, Momentum Wheels and Control Moment Gyros |
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311 | (67) |
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7.4.3 Magnetic Field Torque |
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378 | (1) |
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7.5 Satellite Dynamics Plant for Tracking Control |
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379 | (1) |
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7.6 Environmental Torques |
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380 | (3) |
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7.6.1 Gravity-Gradient Torque |
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382 | (1) |
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7.7 Multi-variable Tracking Control of Spacecraft Attitude |
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383 | (6) |
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7.7.1 Active Attitude Control of Spacecraft by Reaction Wheels |
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385 | (4) |
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389 | (1) |
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389 | (1) |
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390 | (1) |
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Appendix A Linear Systems |
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391 | (10) |
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391 | (1) |
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392 | (1) |
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A.3 Solution to Linear State Equations |
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392 | (2) |
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A.3.1 Homogeneous Solution |
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393 | (1) |
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393 | (1) |
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A.4 Linear Time-Invariant System |
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394 | (1) |
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A.5 Linear Time-Invariant Stability Criteria |
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395 | (1) |
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A.6 Controllability of Linear Time-Invariant Systems |
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395 | (1) |
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A.7 Observability of Linear Time-Invariant Systems |
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395 | (1) |
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396 | (1) |
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A.9 Singular Value Decomposition |
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396 | (1) |
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A.10 Linear Time-Invariant Control Design |
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397 | (3) |
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A.10.1 Regulator Design by Eigenstructure Assignment |
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397 | (1) |
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A.10.2 Regulator Design by Linear Optimal Control |
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398 | (1) |
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A.10.3 Linear Observers and Output Feedback Compensators |
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398 | (2) |
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400 | (1) |
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401 | (8) |
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401 | (1) |
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B.2 Stability in the Sense of Lagrange |
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402 | (2) |
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B.3 Stability in the Sense of Lyapunov |
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404 | (4) |
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B.3.1 Asymptotic Stability |
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406 | (1) |
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B.3.2 Global Asymptotic Stability |
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406 | (1) |
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407 | (1) |
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B.3.4 Krasovski's Theorem |
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408 | (1) |
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B.3.5 Lyapunov Stability of Linear Systems |
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408 | (1) |
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408 | (1) |
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Appendix C Control of Underactuated Flight Systems |
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409 | (24) |
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C.1 Adaptive Rocket Guidance with Forward Acceleration Input |
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409 | (6) |
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C.2 Thrust Saturation and Rate Limits (Increased Underactuation) |
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415 | (2) |
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C.3 Single- and Bi-output Observers with Forward Acceleration Input |
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417 | (15) |
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432 | (1) |
Index |
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