Pontryagin’s Maximum Principle

Some control systems need to maximize a certain outcome while minimizing the cost. For example, a rocket propulsion system intends to reach the maximum altitude with the least fuel. In such systems, the cost minimization concept in optimal control is changed to outcome maximization, and the particular optimal control design process can be implemented using Pontryagin’s maximum principle. This chapter presents the maximum principle based on the Hamiltonian and demonstrates its application through several exercises. The bang–bang control and control switching, which are outcomes of the maximum principle, are also presented.