This paper introduces a new strategy, called "cyclic switching," to deal with the well-known certainty equivalence control synthesis problem which arises in the design of identifier-based adaptive controllers because of the existence of points in parameter space where the design model /spl Sigma//sub D/, upon which certainty equivalence synthesis is based, loses stabilizability. Unlike most previously suggested methods for handling this problem, the technique proposed here can be employed with or without process excitation. For the technique to work it is not necessary for there to be a mechanism for moving tuned parameters away from values at which /spl Sigma//sub D/ loses stabilizability, and no such mechanism is used.

Identification of linear time-invariant multivariable systems can best be understood as comprising three separate problems: selection of system model structure, filter design, and parameter estimation itself. Approaching the first using matchable-observable models originally developed in the adaptive control literature and the second via direct or derivative-free optimization, effective least-squares algorithms can be used for parameter estimation. The accuracy, robustness and moderate computational demands of the methods proposed are demonstrated via simulations with randomly generated models and applied to identification using real process data. The results obtained are comparable or superior to the best results obtained using standard implementations of the algorithms described in the literature.

The quadratic distance function on a Riemannian manifold can be expressed in terms of the position vector, which in turn can be constructed using geodesic normal coordinates through consideration of the exponential map. The formulas for the derivative of the distance are useful to study Lyapunov stability of dynamical systems, and to build cost functions for optimal control and estimation.