Title :
Approximate dynamic programming with Gaussian processes
Author :
Deisenroth, Marc P. ; Peters, Jan ; Rasmussen, Carl E.
Author_Institution :
Dept. of Eng., Cambridge Univ., Cambridge
Abstract :
In general, it is difficult to determine an optimal closed-loop policy in nonlinear control problems with continuous-valued state and control domains. Hence, approximations are often inevitable. The standard method of discretizing states and controls suffers from the curse of dimensionality and strongly depends on the chosen temporal sampling rate. In this paper, we introduce Gaussian process dynamic programming (GPDP) and determine an approximate globally optimal closed-loop policy. In GPDP, value functions in the Bellman recursion of the dynamic programming algorithm are modeled using Gaussian processes. GPDP returns an optimal state- feedback for a finite set of states. Based on these outcomes, we learn a possibly discontinuous closed-loop policy on the entire state space by switching between two independently trained Gaussian processes. A binary classifier selects one Gaussian process to predict the optimal control signal. We show that GPDP is able to yield an almost optimal solution to an LQ problem using few sample points. Moreover, we successfully apply GPDP to the underpowered pendulum swing up, a complex nonlinear control problem.
Keywords :
Gaussian processes; closed loop systems; dynamic programming; optimal control; state feedback; GPDP; Gaussian processes; LQ problem; dynamic programming; nonlinear control problems; optimal closed loop policy; optimal state feedback; temporal sampling rate; Bayesian methods; Control systems; Dynamic programming; Function approximation; Gaussian processes; Machine learning; Nonlinear dynamical systems; Optimal control; Sampling methods; State-space methods;
Conference_Titel :
American Control Conference, 2008
Conference_Location :
Seattle, WA
Print_ISBN :
978-1-4244-2078-0
Electronic_ISBN :
0743-1619
DOI :
10.1109/ACC.2008.4587201