The term singular is used to denote optimal control problems in which the Pontryagin’s Minimum Principle (PMP based on the Hamiltonian function) does not deliver a clear information about the optimal control and its relation to the state and costate variables. Such problems are active in the various applications of optimal control problems.
In this presentation, I am going to introduce an applied viewpoint to some engineering problems in which the singularity has a tangible mean and we proceed to investigate it. As a matter of fact, we finally get a sense to formulate this issue via three standard functions: saturation, signup and dead-zone.