Prediction-based observation of nonlinear systems non-affine in the unmeasured states

The presented work addresses the observation problem for a large class of nonlinear systems, including systems which are nonlinear in the unmeasured states. Assuming partial state measurements, the unmeasured states are reconstructed so that a prediction of the measured states converges to a neighborhood of the actual measurements. This prediction-based observer algorithm relies on carefully selected prediction-observation errors, designed using a backstepping technique. Lyapunov´s direct method is used to show Lyapunov stability and convergence of these errors to an arbitrarily small neighborhood of the origin. The technique is applied to two different nonlinear systems. Results of numerical simulations are presented for both cases and illustrate the efficacy of the algorithm. Experimental results are also provided for one of the examples.