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This paper is concerned with the design of control policies from exampledatasets. The case considered is when just a black box description of thesystem to be controlled is available and the system is affected by actuationconstraints. These constraints are not necessarily fulfilled by the (possibly,noisy) example data and the system under control is not necessarily the same asthe one from which these data are collected. In this context, we introduce anumber of theoretical results to compute a control policy from example datasetsthat: (i) makes the behavior of the closed-loop system similar to the oneillustrated in the data; (ii) guarantees compliance with the constraints. Werecast the control problem as a finite-horizon optimal control problem and givean explicit expression for its optimal solution. Moreover, we turn our findingsinto an algorithmic procedure. The procedure gives a systematic tool to computethe policy. The effectiveness of our approach is illustrated via a numericalexample, where we use real data collected from test drives to synthesize acontrol policy for the merging of a car on a highway.

On a probabilistic approach to synthesize control policies from example datasets