Research: Active-Adaptive Control Theory:

Nonlinearly Parametrized Systems

An assumption that has been systematically adopted in the adaptive control design is that the unknown parameters enter linearly in the dynamic equations describing the plant. However, it is well known that there exist many practical examples whose corresponding models are nonlinearly parametrized: distillation columns, bioreactors, robot dynamics, friction compensation. Adaptive control theory for systems where parameters occur nonlinearly is currently being developed.

Parametric uncertainties in adaptive estimation and control have been dealt with, by and large, in the context of linear parametrizations. Algorithms based on the gradient descent method either lead to instability or inaccurate performance when the unknown parameters occur nonlinearly. Complex dynamic models are bound to include nonlinear parametrizations which necessitate the need for new adaptation algorithms that behave in a stable and accurate manner. Friction dynamics, magnetic bearings, chemical reactors, and bio-chemical processes are some examples where more than one physical parameter occurs nonlinearly in the underlying dynamic model. Nonlinear model structures such as neural networks, wavelets, Hammerstein models, and Uryson models routinely include nonlinear parametrization for reasons of parsimony. We have been developing an adaptive systems theory for problems in dynamic systems where parameters occur nonlinearly. Stability, control, convergence, and robustness of adaptive systems that arise in this context are being investigated. Results that have been derived thus far related to adaptive control of nonlinearly parametrized systems can be found in the publications listed below.

The following are some of the current projects:

Estimation in Systems with Sigmoidal Activation Functions
Global Stability of Frequency Estimation
A tool for convexification
Parameter convergence in systems with nonlinear parametrization

Sponsors:

U.S. Army Research Office

Recent Publications:

C. Cao and A.M. Annaswamy, “A hierarchical discretized-parameter polynomial adaptive estimator for nonlinearly parameterized systems,” American Control Conference, Boston, MA, 2004.

M.S. Netto, A.M. Annaswamy, S. Mammar and S. Glaser, “Adaptive control of systems with multilinear parameterization,” Conference on Decision and Control, December 2005.

F.P. Skantze, A. Kojic, A.P. Loh and A.M. Annaswamy, "Adaptive Estimation of Discrete-time Systems with Nonlinear Parametrization", Automatica, vol 36, No. 12, pp. 1879-1887, December 2000.

A. Kojic and A.M. Annaswamy, "Adaptive Control of Nonlinearly Parametrized Systems with a Triangular Structure," accepted for publication, Automatica, August 2000.

A. Kojic, A.M. Annaswamy, A.P. Loh, and R. Lozano, "Adaptive Control of A Class of Second Order Nonlinear Systems with Convex/Concave Parameterization," Systems and Control Letters, vol. 37, pp. 267-274, 1999.

A.P. Loh, A.M. Annaswamy, and F.P. Skantze, "Adaptation in the Presence of a General Nonlinear Parametrization: An Error Model Approach," IEEE Transactions on Automatic Control, pp. 1634-1652, vol. 44, September 1999.

A.M. Annaswamy, F.P. Skantze, and A.P. Loh, "Adaptive Control of Continuous-time Systems with Convex/Concave Parametrization," Automatica, vol. 14, No. 1, pp. 33-49, January 1998.