Linear-quadratic mean-field-type games with multiple input constraints

In this letter, we study a class of constrained linear-quadratic mean-field-type games. The considered system dynamics are described including some mean-field terms, i.e., the expectation of both the system states and the control inputs. We obtain a semi-explicit solution for the problem by using the direct method in combination with some auxiliary dynamics that guarantee the satisfaction of the multiple input coupled constraints. Finally, a proof-of-concept example is presented in order to show the appropriate performance of the proposed approach.