Finite-Time Observers for Parameters and State Variables of Nonlinear Systems

We provide a new class of finite-time observers for continuous-time nonlinear systems that are affine in the unmeasured state variable and that also contain unknown constant parameters. Our method provides exact values of the state variables and of the constant parameters, in a fixed finite time that is independent of the initial values. We also provide analogs where there is a known delay in the measurements, and for discrete-time systems. Our approach does not rely on an adaptive controller, and is suitable for computing exact values of constant weights in artificial neural network representations of additive uncertainties in the dynamics. Our example illustrates the ease with which our assumptions can be verified in practice.