Page 118 |
Save page Remove page | Previous | 118 of 289 | Next |
|
small (250x250 max)
medium (500x500 max)
Large (1000x1000 max)
Extra Large
large ( > 500x500)
Full Resolution
All (PDF)
|
This page
All
|
x˙ = Ax + Bu or nonlinear dynamical systems of the form x˙ = f (x) + G(x)u in
which fi(x)<M||x||. Examples of nonlinear functions that satisfy the linear growth
condition are functions such as cos(x), sin(x). The dynamical systems under con-sideration
can be stable or unstable, for as long as their vector field satisfies the
linear growth condition then they ”qualify” for the application of the Feynman-Kac
lemma.
• But what happens for the case of dynamical systems in which the vector field f (x)
cannot be bounded ,x ! "n such as for example the function f (x) = x2? The
answer to this question is related to the locality condition. In particular if we know
that the dynamical system under consideration operates in a pre-specified region
of the state space then an upper bound for the vector field can almost always be
found. Consequently the conditions of boundedness in combination with the relaxed
condition of locality are important for the application of Feynman-Kac lemma to a
rather general class of systems.
• Finally, our view in applying the Feynman Kac lemma and the path integral control
formalism is for systems in which an initial set of state space trajectories is given or
generated after an initial control policy has been applied. Thus these systems are
initially controlled and clearly their vector field cannot be unbounded as a function
of the state.
We will continue this discussion of the application of Feynman - Lemma for optimal
control and planning for the chapter of path integral control formalism. In the next section
we will try to identify the most important special case of the Feynman Kac lemma.
104
Object Description
| Title | Iterative path integral stochastic optimal control: theory and applications to motor control |
| Author | Theodorou, Evangelos A. |
| Author email | etheodor@usc.edu; theo0027@umn.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Computer Science |
| School | Viterbi School of Engineering |
| Date defended/completed | 2011-01-11 |
| Date submitted | 2011 |
| Restricted until | Unrestricted |
| Date published | 2011-04-29 |
| Advisor (committee chair) | Schaal, Stefan |
| Advisor (committee member) |
Valero-Cuevas, Francisco Sukhatme, Gaurav S. Todorov, Emo Schweighofer, Nicolas |
| Abstract | Motivated by the limitations of current optimal control and reinforcement learning methods in terms of their efficiency and scalability, this thesis proposes an iterative stochastic optimal control approach based on the generalized path integral formalism. More precisely, we suggest the use of the framework of stochastic optimal control with path integrals to derive a novel approach to RL with parameterized policies. While solidly grounded in value function estimation and optimal control based on the stochastic Hamilton Jacobi Bellman (HJB) equation, policy improvements can be transformed into an approximation problem of a path integral which has no open algorithmic parameters other than the exploration noise. The resulting algorithm can be conceived of as model-based, semi-model-based, or even model free, depending on how the learning problem is structured. The new algorithm, Policy Improvement with Path Integrals (PI2), demonstrates interesting similarities with previous RL research in the framework of probability matching and provides intuition why the slightly heuristically motivated probability matching approach can actually perform well. Applications to high dimensional robotic systems are presented for a variety of tasks that require optimal planning and gain scheduling.; In addition to the work on generalized path integral stochastic optimal control, in this thesis we extend model based iterative optimal control algorithms to the stochastic setting. More precisely we derive the Differential Dynamic Programming algorithm for stochastic systems with state and control multiplicative noise. Finally, in the last part of this thesis, model based iterative optimal control methods are applied to bio-mechanical models of the index finger with the goal to find the underlying tendon forces applied for the movements of, tapping and flexing. |
| Keyword | stochastic optimal control; reinforcement learning,; robotics |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m3804 |
| Contributing entity | University of Southern California |
| Rights | Theodorou, Evangelos A. |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | cisadmin@lib.usc.edu |
| Filename | etd-Theodorou-4581 |
| Archival file | uscthesesreloadpub_Volume14/etd-Theodorou-4581.pdf |
Description
| Title | Page 118 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text |
x˙ = Ax + Bu or nonlinear dynamical systems of the form x˙ = f (x) + G(x)u in
which fi(x) |
