A Class of Optimal Control Problems of Systems Governed by the First Order Linear Dynamic Equations on Time Scales

摘要

This paper is mainly concerned with a class of optimal control problems of systems governed by the first order linear dynamic equations on time scales with quadratic cost functional. At first, we briefly recall the time scales calculus which was initiated by Stefan Hilger in order to create a theory that can unify discrete and continuous analysis: basic definition, basic theorems and basic properties etc. Next, two important function spaces on time scales, C_(rd)([a,b],R) and L_T~2([a,b],R) are discussed, and their completeness is shown. Based on the discussion on classical solution, the weak solution of linear dynamic equations is introduced.