Newton, observers and nonlinear discrete-time control

Development of exact asymptotic observers for nonlinear discrete-time systems is addressed. It is argued that instead of trying to imitate the linear observer theory, the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations. In particular, it is shown that Newton's algorithm, properly interpreted, yields an asymptotic observer for a large class of discrete-time systems. The utility of the observer for closed-loop, observer-based, feedback control is also established. Some non-local aspects of the results are also discussed.<<ETX>>

[1]  W. Wolovich,et al.  A computational technique for inverse kinematics , 1984, The 23rd IEEE Conference on Decision and Control.

[2]  A. Krener,et al.  Nonlinear observers with linearizable error dynamics , 1985 .

[3]  H. Nijmeijer.  Observability of autonomous discrete time non-linear systems: a geometric approach , 1982 .

[4]  B. Francis,et al.  Stability Theory for Linear Time-Invariant Plants with Periodic Digital Controllers , 1988, 1988 American Control Conference.

[5]  M. Hirsch,et al.  On Algorithms for Solving f(x)=0 , 1979 .

[6]  W. Denham,et al.  Sequential estimation when measurement function nonlinearity is comparable to measurement error. , 1966 .

[7]  D. Aeyels.  GENERIC OBSERVABILITY OF DIFFERENTIABLE SYSTEMS , 1981 .

[8]  Arthur Krener,et al.  Higher order linear approximations to nonlinear control systems , 1987, 26th IEEE Conference on Decision and Control.

[9]  D. Aeyels.  On the number of samples necessary to achieve observability , 1981 .

[10]  S. Nicosia,et al.  Robot control by using only joint position measurements , 1990 .

[11]  Eduardo D. Sontag,et al.  A concept of local observability , 1984 .

[12]  Martin Corless,et al.  COMPARATIVE STUDY OF NONLINEAR STATE OBSERVATION TECHNIQUE , 1987 .

[13]  Jessy W. Grizzle,et al.  On observers for smooth nonlinear digital systems , 1990 .

[14]  S. Glad.  Observability and nonlinear dead beat observers , 1983, The 22nd IEEE Conference on Decision and Control.

[15]  W. Boothby.  An introduction to differentiable manifolds and Riemannian geometry , 1975 .

[16]  S. Żak,et al.  Comparative study of non-linear state-observation techniques , 1987 .

[17]  A. Schaft.  On nonlinear observers , 1985 .

[18]  Jessy W. Grizzle,et al.  Observer error linearization for sampled-data systems , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[19]  Christopher I. Byrnes,et al.  Steady state response, separation principle and the output regulation of nonlinear systems , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[20]  Arthur J. Krener,et al.  Linearization by output injection and nonlinear observers , 1983 .

[21]  P. Kokotovic,et al.  Feedback linearization of sampled-data systems , 1988 .

[22]  J. Carr.  Applications of Centre Manifold Theory , 1981 .

[23]  Mark W. Spong,et al.  A discrete-time observer for flexible-joint manipulators , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[24]  D. Luenberger.  Observers for multivariable systems , 1966 .