FMS of Centralized and Distributed Affine Nonlinear Systems and Observer Design Based on FMCF

The high-order full-measured form of affine nonlinear systems is established within both centralized and distributed frameworks. First, the observability canonical forms of single-output and multi-output affine nonlinear systems are derived separately, with a proof that any system equivalent to these canonical forms is also equivalent to a high-order full-measured system (FMS). Subsequently, the centralized framework is extended to the distributed case, laying the foundation for the design of distributed observers for affine nonlinear systems based on the full-measured canonical form (FMCF). Then, taking multi-elastic shaft single-linkage manipulators as a distributed system example, illustrating the procedure for obtaining FMCF parameters in distributed systems. Finally, an observer design method based on FMCF is proposed, ensuring that the observation error dynamics form a linear time-invariant system. The effectiveness of the proposed approach is verified through simulations on a strongly nonlinear Duffing-Van der Pol oscillator under harmonic excitation.