Convergence of truncates in L1 optimal feedback control

Existing design methodologies based on infinite-dimensional linear programming generally require an iterative process often involving progressive increase of truncation length, in order to achieve a desired accuracy. In this chapter we consider the fundamental problem of determining a priori estimates of the truncation length sufficient for attainment of a given accuracy in the optimal objective value of certain infinite-dimensional linear programs arising in optimal feedback control. The treatment here also allows us to consider objective functions lacking interiority of domain, a problem which often arises in practice.