Enhancing interval observers for state estimation using constraints

Abstract: This work considers the problem of calculating an interval-valued state estimate for a nonlinear system subject to bounded inputs and measurement errors. Such state estimators are often called interval observers. Interval observers can be constructed using methods from reachability theory. Recent advances in the construction of interval enclosures of reachable sets for nonlinear systems inspire the present work. These advances can incorporate constraints on the states to produce tighter interval enclosures. When applied to the state estimation problem, bounded-error measurements may be used as state constraints in these new theories. The result is a method that is easily implementable and which generally produces better, tighter interval state estimates. Furthermore, a novel linear programming-based method is proposed for calculating the observer gain, which must be tuned in practice. In contrast with previous approaches, this method does not rely on special system structure. The new approaches are demonstrated with numerical examples.