Adaptive neural observer with forward co-state propagation

An adaptive nonlinear observer using input and output measurements is described by using techniques of optimization theory, the calculus of variations and gradient descent dynamics. A series of formulations of general parameterized nonlinear observers of continuous-time and discrete-time are given, including a co-state (sensitivity) dynamics equation that propagates forward in time and serves as a filtered version of the measured error signal. Several Matlab simulation examples in the continuous-time and discrete-time cases are given to illustrate the approach.