Model validation and set membership state estimation for continuous-time nonlinear systems: Contraction metric approach

This paper studies the set membership state estimation(SMSE) and model validation for continuous-time nonlinear systems with uncertainties. These two problems are formulated as nonlinear optimal tracking problem with reversed time while such optimal problems cannot be solved analytically for nonlinear systems, as for linear systems. This paper proposes a novel approach based on contraction theory to obtain an upper bound of the cost functional of nonlinear tracking problem. Minimizing the upper bound leads to an approximate solution to the nonlinear tracking problem. This approach is applied to the SMSE and model validation problems and it leads to a sufficient condition for the existence of solutions to these two problems. Through minimizing the upper bound, approximate state estimation membership set is obtained. Also, the outline of how to use Sum-of-Square (SOS) programming to compute the solutions is discussed.