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This paper extends a theoretical approach to optimal control problems (OCPs) governed by a class of control systems with discontinuous right hand sides. A possible application of the framework developed in this paper is constituted by the conventional sliding mode dynamic processes. The general theory of the general constrained OCPs is finally used as an analytic basis for some conceptual numerically tractable schemes from a wide family of computational methods for OCPs. The proposed analytic method guarantees consistency of the resulting approximations related to the sophisticated initial infinite-dimensional optimization problem and can provide a fundament for some concrete implementable algorithms.