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The Decision Rule Approach to Optimal Control Design


S. Aschwanden

Semester Thesis, HS14 (10376)

Stochastic optimal control problems seek an optimal causal control policy that minimizes the expectation of a quadratic convex cost function. Feasible control policies need to satisfy linear state and control constraints. We consider stochastic linear discrete-time system dynamics. The problem requires that the constraints are for all uncertainties from a support set. Such problems are generally non-convex and computationally intractable. Recent findings show that re-parameterizing the feedback policies in terms of the disturbances results in a convex program. The re-parameterization states that we can represent causal affine feedback policies depending on measurements as causal affine policies using feedback information from accessible uncertainties. The resulting convex optimization problem is computationally tractable and its size is a polynomial function of the problem data. Nevertheless, the restriction on affine feedback policies can admit massively suboptimal policies. We present a technique to improve the affine approximation using the decision rule approach. By applying lifting techniques to the uncertainties, we reparameterise and map the problem to a higher-dimensional space. Furthermore, we seek optimal affine feedback control policies for the lifted problem. The lifting allows us to preserve favourable scaling properties while increasing the flexibility of the controller. As a result, we obtain piecewise affine control policies on the original space which boost the performance with respect to the affine controller. Finally, we use duality arguments to quantify the suboptimality of the piecewise affine controller


Type of Publication:

(13)Semester/Bachelor Thesis

A. Georghiou

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2014:IFA_5066
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