The paper considers an optimal control problem of the typewhere the set M of admissible controls consists of all measurable vector‐functions h, which can take only two values h1 or h2. It is shown that the relaxation of this problem can be explicitly computed by rank‐one laminates.
Raitums, U. (2008). Relaxation of a weakly discontinuous functional depending on one control function. Mathematical Modelling and Analysis, 13(1), 79-85. https://doi.org/10.3846/1392-6292.2008.13.79-85
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where the set M of admissible controls consists of all measurable vector‐functions h, which can take only two values h1 or h2. It is shown that the relaxation of this problem can be explicitly computed by rank‐one laminates.