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This paper concerns the numerical procedure for solving hybrid optimalcontrol problems with sliding modes. A sliding mode is coped withdifferential-algebraic equations (DAEs) and that guarantees accurate trackingof the sliding motion surface. In the second part of the paper we demonstratethe correspondence between the discrete adjoint equations and the discretizedversion of the continuous adjoint equations in the case of system equationsdescribed by DAEs. We show that the discrete adjoint state trajectoriesconverge to their continuous counterparts. Next, we describe the application ofthe proposed procedure to three optimal control problems. The first problemconcerns optimal control of a simple mechanical system with dry friction. Thesecond problem is related to the planning of a haemodialysis process. The thirdproblem concerns the optimal steering of a racing car.

Numerical procedure for optimal control of hybrid systems with sliding modes, Part II