Abstract
As an application of an optimization technique, a gradient-projection method is employed to derive an adaptive algorithm for updating the parameters of an inverse which is designed to cancel the effects of actuator uncertainties in a control system. The actuator uncertainty is parametrized by a set of unknown parameters which belong to a parameter region. A desirable inverse is implemented with adaptive estimates of the actuator parameters. Minimizing an estimation error, a gradient algorithm is used to update such parameter estimates. To ensure that the parameter estimates also belong to the parameter region, the adaptive update law is designed with parameter projection. With such an adaptive inverse, desired control system performance can be achieved despite the presence of the actuator uncertainties.
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References
TAO, G., and KOKOTOVIĆ, P. V., Adaptive Control of Systems with Actuator and Sensor Nonlinearities, John Wiley and Sons, New York, New York, (1996).
TAO, G., and TIAN, M., Discrete-Time Adaptive Control of Systems with Multi-Segment Piecewise-Linear Nonlinearities, Proceedings of the American Control Conference, Seattle, Washington, pp. 3019–3024, 1995.
NARENDRA, K. S., and ANNASWAMY, A. M., Stable Adaptive Systems, Prentice-Hall, Englewood Cliffs, New Jersey, 1989.
IOANNOU, P. A., and SUN, J., Stable and Robust Adaptive Control, Prentice-Hall, Englewood Cliffs, New Jersey, 1995.
RAO, S. S., Optimization: Theory and Applications, Wiley Eastern, New Delhi, India, 1984.
IOANNOU, P. A., and KOKOTOVIĆ, P. V., Instability Analysis and Improvement of Robustness of Adaptive Control, Automatica, Vol. 20, pp. 583–594, 1984.
PRALY, L., Robust Model Reference Adaptive Controllers, Part 1: Stability Analysis, Proceedings of the 23rd IEEE Conference on Decision and Control, Las Vegas, Nevada, pp. 1009–1014, 1984.
NAIK, S. M., KUMAR, P. R., and YDSTIE, B. E., Robust Continuous-Time Adaptive Control by Parameter Projection, Foundations of Adaptive Control, Edited by P. V. Kokotović, Springer Verlag, Berlin, Germany, pp. 153–199, 1991.
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Tao, G. Adaptive Inverse Control Using a Gradient-Projection Optimization Technique. Journal of Optimization Theory and Applications 95, 677–691 (1997). https://doi.org/10.1023/A:1022682124301
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DOI: https://doi.org/10.1023/A:1022682124301