weiwei_ilqg_CDC43

Weiwei_ilqg_CDC43 - 43rd IEEE Conference on Decision and Control(submitted A generalized iterative LQG method for locally-optimal feedback control

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A generalized iterative LQG method for locally-optimal feedback control of constrained nonlinear stochastic systems Emanuel Todorov and Weiwei Li Abstract — This paper presents an iterative Linear- Quadratic-Gaussian (ILQG) method for nonlinear stochastic systems subject to control constraint. Such local iterative methods have only been applied to deterministic unconstrained problems in the past. We derive a linear control law by minimizing a novel quadratic approximation to the optimal cost-to-go function. The performance of the algorithm is illustrated in a limited-torque pendulum problem, as well as a complex biomechanical control problem involving an arm model with 10 state dimensions and 6 muscle actuators. 43rd IEEE Conference on Decision and Control (submitted) I. INTRODUCTION Optimal control theory has received a lot of attention in the last 50 years, and has found numerous applications in both science and engineering. Despite many theoretical and algorithmic advances, however, solving complex optimal control problems in practice remains a challenge [14]. When the control problem of interest does not fall in one of the few classes of analytically tractable problems, one has to resort to general-purpose approximation methods. Most existing approximation methods attempt to design a control law that is global (i.e. applicable to all states of the controlled plant), and are based on the Hamilton- Jacobi-Bellman equations and the idea of dynamic program- ming. For continous systems, the only numerical methods guaranteed to converge to the globally-optimal solution [13] involve discretizations of the state and control spaces, and run into the curse of dimensionaly. Generalizations to continuous high-dimensional spaces typically involve function approximations whose properties are not yet well understood [15]. An alternative to global optimization is provided by local methods, that only f nd sub-optimal solutions but do so ef f ciently without running into the curse of dimensional- ity. What these methods have in common is the idea of constructing a non-parametric discrete-time representation of the open-loop control sequence, and improving it it- eratively by using only local information. Such methods are typically related to Pontryagin’s Maximum Principle – which provides a necessary condition that optimal state- control trajectories for deterministic systems must satisfy. Trajectories consistent with the Maximum Principle can be found by solving a set of ODEs under boundary-value This work is supported by NIH Grant 1-R01-NS045915-01. Emanuel Todorov is with the faculty of the Cognitive Science Depart- ment, University of California San Diego. Weiwei Li is with the Deparment of Mechanical and Aerospace Engi-
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This note was uploaded on 02/04/2012 for the course ECE 222 taught by Professor Goengi during the Spring '11 term at Maryland.

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Weiwei_ilqg_CDC43 - 43rd IEEE Conference on Decision and Control(submitted A generalized iterative LQG method for locally-optimal feedback control

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