Comparison of set-valued dynamical system state estimates

Abstract

The article deals with set-valued state estimation for linear dynamical systems. Set-valued estimation consists of a construction of feasible sets, which are guaranteed to contain all state vectors. The known set-valued state estimation algorithms include performing set operations like Minkowski sum and set intersection, those are computationally complex. Feasible set approximation with canonical forms, i.e. ellipsoids, parallelotopes, zonotopes, is used to reduce computational complexity although it causes loss of estimation accuracy. The algorithm of feasible set polyhedral approximation without performing set operations is suggested. The algorithm produces set-valued estimate as a polyhedra of any shape. The algorithm consists of solving a row of linear programming problems and can be easily programmed. The article shows the comparison of set-valued estimates constructed with polyhedral approximation algorithm with ellipsoidal estimates and confidence areas based on Kalman filter estimates.