Nonlinear observer design for state and disturbance estimation

A new systematic framework for nonlinear observer design that allows the concurrent estimation of the process state variables, together with key unknown process or sensor disturbances is proposed. The nonlinear observer design problem is addressed within a similar methodological framework as the one introduced for state estimation purposes only. From a mathematical standpoint, the problem under consideration is addressed through a system of first-order singular PDEs for which a rather general set of solvability conditions is derived. A nonlinear observer can then be designed with a state-dependent gain that can be computed from the solution of the system of singular PDEs. Under the aforementioned conditions, both state and disturbance estimation errors converge to zero with assignable rates. The convergence properties of the proposed nonlinear observer are tested through simulation studies in an illustrative example involving a biological reactor.