The control of nonminimum phase systems remains an important open problem in nonlinear control, finding relevance in the control of underactuated and flexible systems. One wishes to cause the output of a dynamical system to track a desired trajectory while maintaining internal stability of a nominally unstable system. I have developed an approach to output tracking for a class of nonminimum phase systems based upon the construction of a manifold embedded in state space. The manifold is such that if the state of the system is forced to remain in a neighborhood of the manifold, then approximate output tracking with bounded internal dyanmics is achieved. The controller also includes a dynamical part that provides a causal estimate of a state on the manifold which can be tracked by choice of input. This allows the scheme to be causal while avoiding the need to solve partial differential equations.
N. H. Getz,
"Internal Equilibrium Control of a Bicycle", 34th IEEE Conference
on Decision and Control, 13-15 December 1995, New Orleans.
N. H. Getz, "Tracking
with Balance", IFAC World Congress,
5 July, 1996, San Francisco
N. H. Getz, "Dynamic
Inversion of Nonlinear Maps with Applications to Nonlinear Control and Robotics", Ph.D. Dissertation, December, 1995, University of California
at Berkeley.
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N. H. Getz
and J. K.
Hedrick, "An
Internal Equilibrium Manifold Method of Tracking for Nonlinear Nonminimum
Phase Systems", Proceedings of the
1995 American Control Conference, 21-23 June 1995, Seattle