Singular Bang-Bang Control For Uncertain Systems

Optimal control plays an important role in both theory and applications. For the investigation of Bang-Bang control, the case may be singular, which is called singular Bang-Bang problem. For a model of an optimal control system, if the switching function that determines the values of the control function is consistently zero within a time interval, then the model belongs to a singular case. The optimal solution of a singular Bang-Bang problem usually consists of Bang-Bang arcs and singular arcs. If the system is influenced by uncertain factors, it can be described by an uncertain differential equation. This thesis mainly investigates the singular Bang-Bang control problem for control systems based on uncertain differential equations.The goal of this thesis is to determine the control functions of singular uncertain optimal control models. The Hamiltonian function is established through backward uncertain differential equations when the switching function is consistently zero in a control interval for a continuous-time model. Furthermore, the singular optimal control function is solved by making use of the fact that the optimal value of the Hamilton function is zero in a singular control interval. This thesis develops a method that determines a singular optimal control interval for a model where the drift term of an uncertain system and objective function are both linear in the control variables. In a singular control interval, a method of solving a singular optimal control is developed for the model. In an example, the singular optimal control function is solved by the obtained results. At the same time, another example shows that the methods of this thesis may be not suitable to all models.