Computing Switching Times in Bang-Bang Control

During the past half-century, many optimization problems have arisen in fields such as management, engineering, computer science, production, industry, and economics. Often one needs to optimize (minimize or maximize) certain objective subject to some constraints. Some optimization problems involve optimal control, which are more complex and involving a dynamic system. This paper introduces a special transformation of time scale for an oscillator problem (A typical optimal control problem) whose dynamic system could be described as a second order differential equation. The computational algorithms for these kinds of optimal control problems are described as well as the analysis of the result of the test example. The traditional problem solving in searching optimal control policy is replaced by computing the optimal switching times of the control in the algorithms. While the control switches in the optimal time intervals, the system reaches the optimum.