RESUMEN
In this paper, we propose a new optimal control model for uncertain systems with jump. In the model, the background-state variables are incorporated, where the background-state variables are governed by an uncertain differential equation. Meanwhile, the state variables are governed by another uncertain differential equation with jump, in which both the background-state variables and the control variables are involved. Under the optimistic value criterion, using uncertain dynamic programming method, we establish the principle and the equation of optimality. As an application, the optimal investment strategy and optimal payment rate for DC pension plans are given, where the corresponding background-state variables represent the salary process. This application in DC pension plans illustrates the effectiveness of the proposed model.
RESUMEN
In this paper, optimal control problems for uncertain discrete-time singular systems and uncertain continuous-time singular systems are considered under optimistic value criterion. The above singular systems are assumed to be regular and impulse-free, and optimistic value method is employed to optimize uncertain objective functions. Firstly, based on Bellman's principle of optimality, a recurrence equation is presented for settling optimal control problems subject to uncertain discrete-time singular systems. Then, by applying the principle of optimality and uncertainty theory, an equation of optimality for an optimal control model subject to an uncertain continuous-time singular system is derived. The optimal control problem can be settled through solving the equation of optimality. Two numerical examples and a dynamic input-output model are given to show the effectiveness of the results obtained.