**Reference:**

L. Busoniu,
D. Ernst,
B. De Schutter, and
R. Babuska,
"Approximate dynamic programming with a fuzzy parameterization,"
*Automatica*, vol. 46, no. 5, pp. 804-814, May 2010.

**Abstract:**

Dynamic programming (DP) is a powerful paradigm for general, nonlinear
optimal control. Computing exact DP solutions is in general only
possible when the process states and the control actions take values
in a small discrete set. In practice, it is necessary to approximate
the solutions. Therefore, we propose an algorithm for approximate DP
that relies on a fuzzy partition of the state space, and on a
discretization of the action space. This *fuzzy Q-iteration*
algorithm works for deterministic processes, under the discounted
return criterion. We prove that fuzzy Q-iteration asymptotically
converges to a solution that lies within a bound of the optimal
solution. A bound on the suboptimality of the solution obtained in a
finite number of iterations is also derived. Under continuity
assumptions on the dynamics and on the reward function, we show that
fuzzy Q-iteration is consistent, i.e., that it asymptotically obtains
the optimal solution as the approximation accuracy increases. These
properties hold both when the parameters of the approximator are
updated in a synchronous fashion, and when they are updated
asynchronously. The asynchronous algorithm is proven to converge at
least as fast as the synchronous one. The performance of fuzzy
Q-iteration is illustrated in a two-link manipulator control problem.

Online version of the paper

Corresponding technical report: pdf file (1.48 MB)

@article{BusErn:09-047,

author={L. Bu{\c{s}}oniu and D. Ernst and B. {D}e Schutter and R. Babu{\v{s}}ka},

title={Approximate dynamic programming with a fuzzy parameterization},

journal={Automatica},

volume={46},

number={5},

pages={804--814},

month=may,

year={2010},

doi={10.1016/j.automatica.2010.02.006}

}

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