Methods to Deal with Control Variable Path Constraints in Dynamic Optimization Problems

Many researchers have reported their methods to handle state variable path constraints in dynamic optimization problems. However, very few of them mentioned the techniques to handle control variable path constraints specifically. This paper firstly introduces two methods to deal with control variable path constraints, then presents a novel smoothed quadratic penalty function method that can solve dynamic optimization problems with both control and state variable path constraints at the same time. The control variable parameterization strategy is used to solve the resulting problems. Two separate cases are considered where testing of case1 demonstrates the characteristics of the three methods, while testing of Case 2 indicates the effectiveness and the superiority of the proposed smoothed penalty function method.