Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations

By Lars Grüne, Manuel Schaller, Anton Schiela. 2020

70 citations recorded by the source corpus.

Abstract We analyze the sensitivity of linear quadratic optimal control problems governed by general evolution equations with bounded or admissible control operator. We show, that if the problem is stabilizable and detectable, the solution of the extremal equation can be bounded by the right-hand side including initial data with the bound being independent of the time horizon. Consequently, the influence of perturbations of the extremal equations decays exponentially in time. This property can for example be used to construct efficient space and time discretizations for a Model Predictive Control scheme. Furthermore, a turnpike property for unbounded but admissible control of general semigroups can be deduced.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/efb4ab19217d88f1a33240b1cdeb4af85165f11b