Decentral nonlinear observer design using a block-triangular form

Abstract

The observer design for nonlinear multiple-output systems is shown to be considerably simpli® ed in a decentral approach. The method requires a block-triangular system representation which either can be detected in the system di erential equations or may be obtained by a state transformation. The transformation is investigated in detail, and necessary and su cient conditions for its existence are discussed. Moreover, the method is illustrated by the ball-and-beam example.

Variants of nonlinear normal form observer design

“…This approach is similar to the extended Kalman filter and requires only the observability rank condition (9.9). The third variant concerns the block-triangular (normal.form) observer [16,17,18,19], where the presence of multiple outputs is used to decompose the original system in subsystems that have to be connected in a cascade. This structure allows a decentral (normal form) observer design.…”

“…Block-triangular observers [16,17,18,19] are designed in a decentral approach, i.e. they are designed by considering subsystems.…”

“…5~=f(x), y=h(x), xeMc1R n, yeYC.l~ p, p>l. (9.39) A survey of the literature on decentral observer design can be found in [19].…”

“…The first step of the decentral approach is to decompose the system (9.39) into single output observable subsystems [16,17,18,19]. (9 9 can be connected mutually by their states (see Figure la), or they can be connected in a cascade or block-triangular .form (see Figure lb), respectively 9 A mutual connection by the outputs (Figure lc) is a special case of a block-triangular form.…”

“…(9 9 can be connected mutually by their states (see Figure la), or they can be connected in a cascade or block-triangular .form (see Figure lb), respectively 9 A mutual connection by the outputs (Figure lc) is a special case of a block-triangular form. [16,17,18,19].…”