Describe the procedure for solving optimal control problem using Pontryagin’s minimum principle.
Answers
Answer:
Explanation:
Optimal control of any process can be achieved either in open or closed loop. In the following two chapters we concentrate mainly on the first class. The first chapter is devoted to definition of open-loop optimal control (dynamic optimisation) problems. Next, the chapter is concerned with practical ways (techniques) that can be used to solve such problems. It also discusses closed-loop implementation, handling of disturbances, and nonlinear state-feedback control. We introduce three basic parts of an optimal control problem (OCP): an objective functional, constraint functions, and a process model and their common mathematical forms. The objective functional, optimisation criterion, or performance index represents mathematical expression of phenomenon whose minimum (or maximum) we want to attain. The constraint functions of various types determine a search space of decision (optimisation) variables whose time evolutions or values are searched for. The process model function ties inputs, states, and outputs of the process together and determines a search domain for the optimisation procedure in a similar way as the constraint functions do.