Filter Design with Constraint Conditions

This article discusses the design of filters for linear systems with state constraints. In such cases, to ensure system stability and controllability, the filter must incorporate state constraint conditions. This paper introduces a novel approach that first transforms state constraints into output constraints, then designs a filter to satisfy these transformed output constraints. The method effectively addresses state constraint issues and has been widely applied in practical applications. From an implementation perspective, the transformation process typically involves mathematical operations like projection or constraint embedding algorithms, while the filter design may utilize constrained optimization techniques or modified Kalman filter implementations. Additionally, the article proposes potential improvements and application domains to further refine and extend this methodology, including possible code implementations using constrained least-squares solutions or barrier function methods in optimization routines.