Abstract
In this paper, the problem of characterizing adaptive output feedback control laws for a general class of unknown MIMO linear systems is considered. Specifically, the presented control approach relies on three components, i.e., a predictor, a reference model and a controller. The predictor is designed to predict the system’s output with arbitrary accuracy, for any admissible control input. Subsequently, a full state feedback control law is designed to control the predictor output to approach the reference system, while the reference system tracks the desired trajectory. Ultimately, the control objective of driving the actual system output to track the desired trajectories is achieved by showing that the system output, the predictor output and the reference system trajectories all converge to each other.
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Atassi, A., Khalil, H.: A separation principle for the stabilization of a class of nonlinear systems. IEEE Trans. Autom. Control 44, 1672–1687 (1999)
Cao, C., Hovakimyan, N.: \(\cal{L}_1\) adaptive output feedback controller for systems with time-varying unknown parameters and bounded disturbances. In: Proceedings of American Control Conference, pp. 486–491 (2007a)
Cao, C., Hovakimyan, N.: \(\cal{L}_1\) adaptive output feedback controller to systems of unknown dimension. In: American Control Conference, 2007. ACC ’07, pp. 1191–1196, July (2007b)
Cao, C., Hovakimyan, N.: \(\cal{L}_1\) adaptive output feedback controller for non-strictly positive real reference systems with applications to aerospace examples. In: AIAA Guidance, Navigation, and Control Conference and Exhibit (2008)
Cao, C., Hovakimyan, N.: \(\cal{L}_1\) adaptive output feedback controller for non strictly positive real multi-input multi-output systems in the presence of unknown nonlinearities. In: American Control Conference, 2009. ACC ’09., pp. 5138–5143, June (2009)
Chen, M.-S., Kao, C.-Y.: Control of linear time-varying systems using forward Riccati equation. J. Dyn. Syst. Meas. Control 119(3), 536–540 (1997)
Hovakimyan, N., Cao, C.: L1 Adaptive Control Theory: Guaranteed Robustness with Fast Adaptation, vol. 21. Siam (2010)
Ioannou, P.A., Sun, J.: Robust Adaptive Control. Courier Corporation, (2012)
Khalil, H. K.: Nonlinear Systems. Upper Saddle River, Prentice Hall, NJ (2002)
Kharisov, E., Hovakimyan, N.: \(\cal{L}_1\) adaptive output feedback controller for minimum phase systems. In: American Control Conference (ACC), 2011, pp. 1182–1187, IEEE (2011)
Lee, H., Cichella, V., Hovakimyan, N.: L1 adaptive output feedback augmentation of model reference control. Am. Control Conf. (ACC) 2014, 697–702 (2014)
Leonessa, A., Haddad, W.M., Hayakawa, T., Morel, Y.: Adaptive control for nonlinear uncertain systems with actuator amplitude and rate saturation constraints. Int. J. Adapt. Control Signal Process. 23(1), 73–96 (2009)
Morel, Y., Leonessa, A.: Direct adaptive tracking control of quadrotor aerial vehicles. In: ASME 2006 International Mechanical Engineering Congress and Exposition, pp. 155–161, American Society of Mechanical Engineers (2006)
Morel, Y., Leonessa, A.: Nonlinear predictor-based output feedback control for a class of uncertain nonlinear systems. In: ASME 2010 Dynamic Systems and Control Conference, pp. 939–946, American Society of Mechanical Engineers (2010)
Nguyen, C.H., Leonessa, A.: Adaptive predictor-based output feedback control for a class of unknown MIMO linear systems. In: ASME 2014 Dynamic Systems and Control Conference, American Society of Mechanical Engineers (2014a)
Nguyen, C.H., Leonessa, A.: Adaptive predictor-based output feedback control for a class of unknown MIMO linear systems: experimental results, In: ASME 2014 Dynamic Systems and Control Conference, American Society of Mechanical Engineers (2014b)
Nguyen, C.H., Leonessa, A.: Adaptive predictor-based output feedback control for a class of unknown MIMO systems: experimental results. In: American Control Conference, pp. 3515–3521, July (2015)
Penrose, R.: A generalized inverse for matrices. In: Proceedings of Cambridge Philosophical Society, vol. 51, pp. 406–413, Cambridge Univ Press (1955)
Schafer, R.D.: An Introduction to Nonassociative Algebras, Dover Publications, New York (1966)
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Communicated by Eva Kanso.
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Nguyen, C.H., Leonessa, A. Adaptive Predictor-Based Output Feedback Control for a Class of Unknown MIMO Linear Systems. J Nonlinear Sci 27, 1257–1290 (2017). https://doi.org/10.1007/s00332-017-9368-3
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DOI: https://doi.org/10.1007/s00332-017-9368-3