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Iterative Path Integral Method for Nonlinear Stochastic Optimal Control
Published on Oct 16, 20126728 Views
So far, we have been studying nonlinear stochastic control. For example, in [1, 2, 3], we have proposed an asymptotically stabilization method based on properties of physical systems such as passivity
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Iterative Path Integral Method for Nonlinear Stochastic Optimal Control00:00
Outline00:19
Outline: Introduction00:43
Collaborators00:45
Motivation: Gait generation via learning control of Hamiltonian systems - 101:07
Motivation: Gait generation via learning control of Hamiltonian systems - 203:23
Motivation: Gait generation via learning control of Hamiltonian systems - 303:42
Objective and our approach - 104:19
Objective and our approach - 204:42
Objective and our approach - 305:19
Outline: Stochastic optimal control based on path integrals06:08
Problem setting (finite time optimal control problem) - 106:17
Problem setting (finite time optimal control problem) - 206:52
Problem setting (finite time optimal control problem) - 307:12
Problem setting (finite time optimal control problem) - 407:29
Outline of path integral optimal control method - 108:03
Outline of path integral optimal control method - 208:19
Outline of path integral optimal control method - 308:27
Outline of path integral optimal control method - 408:34
Outline of path integral optimal control method - 508:41
Exponential transformation and particular assumptions - 109:00
Exponential transformation and particular assumptions - 209:16
Exponential transformation and particular assumptions - 309:23
Exponential transformation and particular assumptions - 409:36
Exponential transformation and particular assumptions - 510:10
Feynman-Kac formula and explicit solution to the PDE - 110:19
Feynman-Kac formula and explicit solution to the PDE - 210:53
Optimal feedback input in path integral control method - 111:02
Optimal feedback input in path integral control method - 211:13
Optimal feedback input in path integral control method - 311:26
Optimal feedback input in path integral control method - 411:44
Outline: Iterative path integral optimal control12:29
The objective of the iterative path integral method - 112:39
The objective of the iterative path integral method - 213:31
Idea of the proposed method15:21
Result 1. Iteration law of the iterative path integral control16:13
Structure of the proposed PDE - 117:09
Structure of the proposed PDE - 217:50
Structure of the proposed PDE - 318:02
Structure of the proposed PDE - 418:26
Structure of the proposed PDE - 518:50
Structure of the proposed PDE - 619:15
Numerical computation with Monte Carlo20:09
Property of the convergence solution - 122:31
Property of the convergence solution - 222:43
Property of the convergence solution - 323:04
Convergence theorem of iterative path integral method - 123:39
Convergence theorem of iterative path integral method - 223:50
Example: 1-link robot manipulator with noise25:19
Numerical results28:26
Outline: Conclusion30:08
Summary30:09