Comparative study of non-linear state-observation techniques.

*(English)*Zbl 0627.93012Authors’ abstract: This paper contains a comparative study of four techniques for observing the states of non-linear systems. The first technique examined is inspired by D. Bestle and M. Zeitz [ibid. 38, 419-431 (1983; Zbl 0521.93012)] and A. J. Krener and W. Respondek [SIAM J. Control Optimization 23, 197-216 (1985; Zbl 0569.93035)]. In this method a non-linear transformation is found that brings the system into a canonical form, from where observer design is facilitated.

The second technique is attributable to F. E. Thau [Int. J. Control 17, 471-479 (1973; Zbl 0249.93006)]. In this method, the error between the system’s true state and the output of the observer is shown to be asymptotically convergent to zero provided that an additional assumption is valid.

The third technique is due to W. T. Baumann and W. J. Rugh [IEEE Trans. Autom. Control AC-31, 40-46 (1986; Zbl 0582.93031)]. In this method, extended or pseudolinearization of the error differential equation about a family of equilibrium points results in an observer design such that the eigenvalues of the linearized error equation are locally invariant. Finally, techniques from variable-structure systems are utilized to design an observer that yields an exponentially decaying error like Thau’s observer, but, unlike Thau’s, does not incorporate the non-linearities of the system into the observer design. An example illustrating the performance of the four techniques is included.

The second technique is attributable to F. E. Thau [Int. J. Control 17, 471-479 (1973; Zbl 0249.93006)]. In this method, the error between the system’s true state and the output of the observer is shown to be asymptotically convergent to zero provided that an additional assumption is valid.

The third technique is due to W. T. Baumann and W. J. Rugh [IEEE Trans. Autom. Control AC-31, 40-46 (1986; Zbl 0582.93031)]. In this method, extended or pseudolinearization of the error differential equation about a family of equilibrium points results in an observer design such that the eigenvalues of the linearized error equation are locally invariant. Finally, techniques from variable-structure systems are utilized to design an observer that yields an exponentially decaying error like Thau’s observer, but, unlike Thau’s, does not incorporate the non-linearities of the system into the observer design. An example illustrating the performance of the four techniques is included.

Reviewer: J.Hammer

##### MSC:

93B07 | Observability |

93C10 | Nonlinear systems in control theory |

93C35 | Multivariable systems, multidimensional control systems |

93C15 | Control/observation systems governed by ordinary differential equations |