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This paper presents new methods for set-valued state estimation of nonlineardiscrete-time systems with unknown-but-bounded uncertainties. A single timestep involves propagating an enclosure of the system states through thenonlinear dynamics (prediction), and then enclosing the intersection of thisset with a bounded-error measurement (update). When these enclosures arerepresented by simple sets such as intervals, ellipsoids, parallelotopes, andzonotopes, certain set operations can be very conservative. Yet, using generalconvex polytopes is much more computationally demanding. To address this, thispaper presents two new methods, a mean value extension and a first-order Taylorextension, for efficiently propagating constrained zonotopes through nonlinearmappings. These extend existing methods for zonotopes in a consistent way.Examples show that these extensions yield tighter prediction enclosures thanzonotopic estimation methods, while largely retaining the computationalbenefits of zonotopes. Moreover, they enable tighter update enclosures becauseconstrained zonotopes can represent intersections much more accurately thanzonotopes.

Guaranteed methods based on constrained zonotopes for set-valued state estimation of nonlinear discrete-time systems