Further extensions of a student-related optimal control problem

In a recent paper, Parlar discussed some extensions of "a student-related optimal control problem". originally proposed by Raggett et al. Parlar made two extensions in his paper by assuming: (1) the rate of change of knowledge is a linear function of the work rate, which has upper and lower bounds: and (2) the student is lazy but ambitious, and always attempts to gain maximum knowledge with minimum effort. In this paper, we shall discuss some modifications of these assumptions and apply the maximum principle to derive the optimal solutions to these modified optimal control problems. In addition, we shall apply the phase-diagram technique to plot the relationship between the state and adjoint variables. The plotting of phase-diagrams presents us with a pictorial view of the variation of the optimal solutions with the change in problem parameters. As a result, considerable insight can be gained about the practical significance of the various problem parameters.