# Unlocking of predicate: application to non-anticipating selections

## TL;DR

The paper introduces a novel method called 'unlocking of predicate' to construct non-anticipating selections in control theory, enabling better analysis and construction of solutions under uncertainty.

## Contribution

It formalizes the predicate unlocking operation, providing rules and properties for constructing unlocking mappings, and applies this to non-anticipating mappings in control theory.

## Key findings

- Constructed unlocking mappings for non-anticipating predicate
- Derived the greatest non-anticipating selection using unlocking mappings
- Provided a formal framework for predicate unlocking in control problems

## Abstract

We consider an approach to constructing a non-anticipating selection of a multivalued mapping; such a problem arises in control theory under conditions of uncertainty. The approach is called "unlocking of predicate" and consists in the reduction of finding the truth set of a predicate to searching fixed points of some mappings. Unlocking of predicate gives an extra opportunity to analyze the truth set and to build its elements with desired properties. In this article, we outline how to build "unlocking mappings" for some general types of predicates: we give a formal definition of the predicate unlocking operation, the rules for the construction and calculation of "unlocking mappings" and their basic properties. As an illustration, we routinely construct two unlocking mappings for the predicate "be non-anticipating mapping" and then on this base we provide the expression for the greatest non-anticipating selection of a given multifunction.