Existence results for Isaacs equations with local conditions and related semilinear Cauchy problems

TL;DR

This paper establishes existence results for classical solutions to generalized Isaacs equations, including those with local coefficient conditions, relevant in robust control and state-dependent control constraints.

Contribution

It extends existing results by allowing local conditions on coefficients and applies to a broader class of control-related equations.

Findings

Proved existence of classical solutions for generalized Isaacs equations.

Extended results to equations with local coefficient conditions.

Applicable to control problems with state-dependent constraints.

Abstract

Our goal is to prove existence results for classical solutions to some general nondegenerate Cauchy problems which are natural generalizations of Isaacs equations. For the latter we are able to extend our results by admitting local conditions for coefficients. Such equations appear naturally for instance in robust control theory. Using our general results, we can solve not only Isaacs equations, but also equations for other sophisticated control problems, for instance models with state dependent constraints on the control set.