Robust ℋ_∞ non-linear estimation

This work investigates the problem of ℋ_∞ estimation for uncertain continuous time non-linear systems with non-linear time-varying parameter uncertainty. A non-linear estimator is looked for so that a prescribed bound on the ratio between the energy of the estimation error and the energy of the noise inputs is achieved for any set of parameters in a prescribed bounded region. Conditions for the existence of such an estimator are not easy to find and we therefore formulate an auxiliary estimation problem for a related system which is obtained from the original one by converting the parameter uncertainty into exogenous bounded energy signals. It is shown that an ℋ_∞ non-linear estimator that solves the auxiliary problem, if one exists, guarantees, when applied to the original problem, the required performance for all possible parameters. This approach allows us to solve the robust non-linear ℋ_∞ estimation problem via recently developed ℋ_∞ non-linear filtering techniques. The results are demonstrated by a simple example.