Lagrangian and Hamiltonian Methods For Nonlinear Control 2006 : Proceedings From the 3rd IFAC Workshop, Nagoya, Japan, July 2006

Preface......Page 5 List of Contributors......Page 6 Contents......Page 12 1 Introduction......Page 15 2 Closed-Loop Dynamics of Multi-joint Reaching Movement......Page 18 3 Riemannian Metrics and Stability on a Manifold......Page 20 4 Middle-Range Reaching......Page 24 5 Virtual Spring/Damper Hypothesis......Page 27 6 Theoretical Proof of Transferability......Page 28 7 3-D Grasping Under Nonholonomic Constraints......Page 31 8 Lagrange’s Equation of the Overall Fingers-Object System......Page 34 9 Control for Stable Blind Grasping......Page 37 10 Stability on a Constraint Manifold......Page 39 11 Conclusions......Page 40 1 Introduction......Page 43 2 Riemannian Optimization......Page 44 3 Applications......Page 48 1 Introduction and Motivation......Page 60 2 Background......Page 61 3Synchronization......Page 63 4 Conclusions......Page 70 1 Introduction......Page 73 2 Problem Description and Notation......Page 74 3 Discretization of First-Order Structures......Page 75 5 Energy Flow Discretization......Page 80 6Examples......Page 81 7 Conclusions......Page 84 1 Introduction......Page 86 2 Mathematical Preliminaries......Page 87 3 Decomposition of Self-adjoint Subsystems......Page 90 4 Boundary Conditions and Reconstruction of Virtual Lagrangian......Page 92 5Example......Page 94 6 Conclusions......Page 96 1 Introduction......Page 98 2 Preliminaries......Page 99 3MainResults......Page 101 4Example......Page 107 1 Introduction......Page 110 2 Background......Page 111 3 Impedance Matching Through a Storing Element......Page 113 4 The Transfer Interconnection Structure......Page 115 5 Simulations......Page 119 6 Conclusions......Page 120 1 Introduction......Page 122 2 Basic IDA-PBC Theory......Page 124 3 The Four-Tank System......Page 125 4 Simulations and Experiments......Page 130 5 Discussion and Conclusion......Page 132 1 Introduction......Page 134 2 Preliminaries......Page 135 3 Power-Based Description for a Class of Mechanical Systems......Page 137 4 The Inverted Pendulum on a Cart......Page 141 5 C......Page 143 1 Introduction and Background......Page 145 2 Power–Shaping Control......Page 148 3 The Tunnel Diode......Page 150 4 Concluding Remarks......Page 155 Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes......Page 157 1 Introduction......Page 158 2 Background on IDA–PBC and Problem Formulation......Page 159 3 Generating an Homogeneous Kinetic Energy PDE......Page 161 4 Solving the Original PDEs......Page 163 5 The Pendulum on a Cart Example......Page 164 6 Conclusions......Page 165 1 Introduction......Page 167 2 PBC with Simultaneous Energy Shaping and Damping Injection......Page 168 3 Induction Motor Control Via SIDA–PBC......Page 170 4 Total Energy–Shaping of a Doubly–Fed Induction Generator......Page 174 5 Conclusions......Page 178 1 Introduction......Page 180 2 Input Disturbance Suppression Problem and Its Adaptive Solution......Page 182 3 An Example: Magnetic Levitation System......Page 185 4 Conclusions......Page 189 1 Introduction......Page 192 2 Lagrangian Hybrid Systems......Page 194 3 Functional Routhian Reduction......Page 196 4 Controlled Symmetries Applied to 2D Bipedal Walkers......Page 198 5 Functional Routhian Reduction Applied to 3D Bipedal Walkers......Page 201 1 Introduction......Page 206 2 Iterative Learning Control Based on Variational Symmetry......Page 207 3 Extension of ILC for Time Derivatives......Page 209 4 Optimal Gait Generation......Page 211 5 Simulation......Page 214 6 Conclusion......Page 216 1 Introduction......Page 218 2 Conservative Contact Systems......Page 219 3 Interconnection of Port Contact Systems......Page 221 4 Conclusion......Page 226 5 Appendix: Reminder on Contact Geometry......Page 228 1 Introduction: Euclidean Cases......Page 230 2 Non-Euclidean Rolling Problems......Page 232 3 Hamiltonians and Extremal Equations......Page 234 4 Integrability......Page 237 1 Introduction......Page 241 2 Induced Dirac Structures......Page 242 3 Implicit Lagrangian Systems......Page 244 4 Implicit Hamiltonian Systems......Page 246 5ExamplesofL–CCircuits......Page 249 6 Conclusions......Page 254 1 Introduction......Page 256 2TheMethod......Page 257 3 Numerical Example......Page 262 4 Conclusion......Page 264 1 Introduction......Page 266 2 Newton–Euler–Lagrange Equations......Page 267 3 Second Order Principal Subspace Flows......Page 270 1 Introduction......Page 275 2 Convergence of Regularized Optimal Values......Page 276 3 Order of Singularity: Problem Setting......Page 277 4 The Singular Linear-Quadratic Case......Page 278 5 Singularity of Nonlinear Control-A.ne Problems......Page 279 6 SketchoftheProofoftheTheorem1......Page 280 7 Non-commutative Driftless Case: General Result......Page 283 1 Introduction......Page 286 2 Statement of the Result......Page 287 3 Hamiltonian Methods......Page 291 1......Page 293 2 Control System Model......Page 297 3 System Dynamics......Page 298 4 Quantum Control Objectives......Page 299 5 Hamiltonian Engineering......Page 300 1 Introduction......Page 309 2 Dynamics of PINCHING......Page 310 4 Theoretical Proof of Feasibility of Blind Grasping......Page 313 5 Numerical Simulation of 2-D Case......Page 316 6 Conclusions......Page 318 1 Introduction......Page 321 2 Background......Page 322 3 Intrinsic Tracking Control......Page 325 4 Conclusions......Page 331 1 Introduction......Page 333 2 Linear Force Model......Page 334 3 Nonlinear Force Model......Page 336 5 Relative Equilibrium Stability......Page 338 6FinalRemarks......Page 342 1 Introduction......Page 344 2 Energy Shaping and Pumping-Damping......Page 345 3 Di.erent Choices of the Energy Function......Page 347 4 A Stability Criterion......Page 353 5 Conclusions......Page 354 1 Introduction......Page 356 2 Problem Description......Page 357 3 Design with Direct Mechanical Damping Injection......Page 359 4 Simulation Research and Results......Page 362 5 Conclusions......Page 366 1 Introduction......Page 368 2 Averaged System......Page 369 3 Associated Riemannian Metric......Page 370 4 Integrability......Page 371 5 Numerical Results......Page 373 1 Introduction......Page 377 2 Equations of Motion for Underwater Vehicles......Page 378 3 A.ne-Connection Control Systems and Decoupling Vector Fields......Page 381 4 Singular Extremals......Page 383 6 Thanks......Page 386 1 Introduction......Page 388 2 Port Hamiltonian Systems......Page 389 3 Exact Structured Singular Value......Page 391 4 Robust Stability Analysis......Page 395 5 Conclusion......Page 396 Author Index......Page 398 This proceedings volume documents the 3rd IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control (LHMNLC'06) that was held in Nagoya, Japan, on July 19-21, 2006. The?rst workshop in this series was chaired and organized by ProfessorsN. E. Leonard and R. Ortega, and was held in Princeton, USA, in March 2000. The second one was chaired and organized by Professors A. Astol?, F. Gordillo and A.J. van der Schaft, and was held in Seville, Spain, in April 2003. A vibrantsynergyis documented between areassuch as nonlinear controland optimal control theory, di?erential and Riemannian geometry, Lagrangian and Hamiltonian mechanics, nonsmooth optimization, and dynamical systems. The articles in this volume focus on technological areas including not only control of mechanical systems, but also geometricoptimization, networkedcontrol, control of chemical processes, robotic locomotion, quantum systems, multi-agent s- tems, and robotic grasping and telemanipulation. Novel scienti?c contribution are proposed in a wide variety of techniques including synchronization, control Lyapunov functions, energy and power-based control, optimization algorithms, fault-tolerantcontrol, geometricreduction theory, and iterativelearning control, to name a few. Financial support for the workshop was provided by the 21st Century COE Program (Tokyo Institute of Technology) "Innovation of Creative Engineering through the Development of Advanced Robotics," the Suzuki Foundation, the Daiko Foundation and the University of Nagoya. We also would like to thank all the participants to the workshop, all the members of the national and - ternational organizing committees, the IFAC Secretariat, the IFAC Publications Committee, and the Springer-Verlag review board for the LNCIS series