Abstract : Necessary conditions for optimal control problems involving implicit control systems and with possible nonsmooth data has been derived under bounded slope conditions in [1]. Here, we investigate how such conditions apply to various particular cases of implicit control systems. In particular, we extend the analysis in [3], where application to some optimal control problems with semi-explicit Differential Algebraic Equations (DAE's) are explored. Noteworthy, we consider DAE's systems with index higher then 1. We go a step further and we extend necessary conditions for mixed constrained problem derived in [3] under interiority conditions and convexity of the velocity sets can to cover implicit control systems.
