On the role of subspace zeros in retrospective cost adaptive control of non-square plants

References

• Astrom, K.J., Hagander, P., & Sternby, J. (1984). Zeros of sampled systems. IEEE Transactions on Automatic Control, 20, 31–38.
   Google Scholar
• Astrom, K.J., & Wittenmark, B. (1995). Adaptive control (2nd ed.). Reading, MA: Addison-Wesley.
   Google Scholar
• Bernstein, D.S. (2009). Matrix mathematics. Princeton, NJ: Princeton University Press.
   Google Scholar
• D’Amato, A.M., Sumer, E.D., & Bernstein, D.S. (2011). Frequency domain stability analysis of retrospective cost adaptive control for systems with unknown nonminimum-phase zeros. Proceedings of Conference on Decision and Control (pp. 1098–1103). Orlando, FL.
   Google Scholar
• D’Amato, A.M., Sumer, E.D., Mitchell, K.S., Morozov, A.V., Hoagg, J.B, & Bernstein, D.S. (2011). Adaptive output feedback control of the NASA GTM model with unknown nonminimum-phase zeros. Proceedings of AIAA Guidance, Navigation and Control Conference(AIAA-2011-6204). Portland, OR.
   Google Scholar
• Davison, E.J. (1983). Some properties of minimum phase and squared-down systems. IEEE Transactions on Automatic Control, 28, 221–222.
   Web of Science ®Google Scholar
• Davison, E.J., & Wang, S.H. (1974). Properties and calculation of transmission zeros of linear multivariable systems. Automatica, 10, 643–658.
   Web of Science ®Google Scholar
• Freudenberg, J.S., & Looze, D.P. (1985). Right half plane poles and zeros and design tradeoffs in feedback systems. IEEE Transactions on Automatic Control, 30, 555–565.
   Web of Science ®Google Scholar
• Goodwin, G.C., & Sin, K.S. (1984). Adaptive filtering prediction and control. Englewood Cliffs, NJ: Prentice-Hall.
   Google Scholar
• Hoagg, J.B. (2010). Retrospective cost adaptive control for nonminimum-phase discrete-time systems. Part 1: The ideal controller and error system. Part 2: The adaptive controller and stability analysis. Proceedings of the 49th Conference on Decision and Control (pp. 893–904). Atlanta, GA.
   Google Scholar
• Hoagg, J.B., & Bernstein, D.S. (2007). Nonminimum-phase zeros: Much to do about nothing. IEEE Control Systems Magazine, 27, 45–57.
   Web of Science ®Google Scholar
• Hoagg, J.B., Santillo, M.A., & Bernstein, D.S. (2008a). Discrete-time adaptive command following and disturbance rejection with unknown exogenous dynamics. IEEE Transactions on Automatic Control, 53, 912–928.
   Web of Science ®Google Scholar
• Hoagg, J.B., Santillo, M.A., & Bernstein, D.S. (2008b). Internal model control in the shift and delta domains. IEEE Transactions on Automatic Control, 53, 1066–1072.
   Web of Science ®Google Scholar
• Ioannou, P.A., & Sun, J. (1996). Robust adaptive control. Upper Saddle River, NJ: Prentice Hall.
   Google Scholar
• Karcanias, N., & Giannakopoulos, C. (1989). Necessary and sufficient conditions for zero assignment by constant squaring down. Linear Algebra and its Applications, 122–124, 415–446.
   Web of Science ®Google Scholar
• Karcanias, N., & Kouvaritakis, B. (1979). The output zeroing problem and its relationship to the invariant zero structure: A matrix pencil approach. International Journal of Control, 30, 395–415.
   Web of Science ®Google Scholar
• Kouvaritakis, B., & MacFarlane, A.G.J. (1976). Geometric approach to analysis and synthesis of system zeros. Part 1: Square systems. Part 2: Nonsquare systems. International Journal of Control, 23, 149–181.
   Web of Science ®Google Scholar
• Latawiec, K., Banka, S., & Tokarzewski, J. (2000). Control zeros and nonminimum phase LTI MIMO systems. Annual Reviews in Control, 24, 105–112.
   Google Scholar
• Lavretsky, E. (2011). Adaptation along prescribed directions. Proceedings of American Control Conference (pp. 1748–1752). San Francisco, CA.
   Google Scholar
• Leventides, J., & Karcanias, N. (2008). Structured squaring down and zero assignments. International Journal of Control, 81, 294–306.
   Web of Science ®Google Scholar
• MacFarlane, A.G.J., & Karcanias, N. (1976). Poles and zeros of linear multivariable systems: A survey of the algebraic, geometric and complex-variable theory. International Journal of Control, 24, 33–74.
   Web of Science ®Google Scholar
• Maciejowski, J.M. (1989). Multivariable feedback design. Wokingham: Addison-Wesley.
   Google Scholar
• Misra, P. (1992). A computational algorithm for squaring-up. Part I: Zero input-output matrix. Proceedings of the 31st Conference on Decision and Control (pp. 149–150). Tucson, AZ.
   Google Scholar
• Misra, P. (1993). Numerical algorithms for squaring-up non-square systems. Part II: General case. Proceedings of the American Control Conference (pp. 1573–1577). San Francisco, CA.
   Google Scholar
• Narendra, K.S., & Annaswamy, A.M. (1989). Stable adaptive systems. Englewood Cliffs, NJ: Prentice Hall.
   Google Scholar
• Rosenbrock, H.H. (1970). State-space and multivariable theory. New York, NY: Wiley.
   Google Scholar
• Saberi, A., & Sannuti, P. (1988). Squaring down by static and dynamic compensators. IEEE Transactions on Automatic Control, 45, 1655–1704.
   Google Scholar
• Saberi, A., & Sannuti, P. (1990). Squaring down of non-strictly proper systems. International Journal of Control, 51, 621–629.
   Web of Science ®Google Scholar
• Santillo, M.A., & Bernstein, D.S. (2010). Adaptive control based on retrospective cost optimization. AIAA Journal of Guidance, Control and Dynamics, 33, 289–304.
   Web of Science ®Google Scholar
• Schrader, C.B., & Sain, M.K. (1989). Research on system zeros: A survey. International Journal of Control, 50, 1407–1433.
   Web of Science ®Google Scholar
• Skogestad, S., & Postlethwaite, I. (2005). Multivariable feedback control: Analysis and design (2nd ed.). New York, NY: Wiley.
   Google Scholar
• Soderstrom, T., & Stoica, P. (1989). System identification. Englewood Cliffs, NJ: Prentice Hall.
   Google Scholar
• Sumer, E.D., & Bernstein, D.S. (2012). Retrospective cost adaptive control with error-dependent regularization for MIMO systems with uncertain nonminimum-phase transmission zeros. Proceedings of AIAA Guidance Navigation and Control Conference (AIAA-2012-4670-123). Minneapolis, MN.
   Google Scholar
• Sumer, E.D., D’Amato, A.M., & Bernstein, D.S. (2011). Robustness of retrospective cost adaptive control to Markov parameter uncertainty. In Proceedings of Conference on Decision and Control (pp. 6085–6090). Orlando, FL.
   Google Scholar
• Tokarzewski, J. (2002). A general solution to the output-zeroing problem for MIMO LTI systems. International Journal of Applied Mathematics and Computer Science, 12, 161–171.
   Google Scholar
• Tokarzewski, J. (2006). Finite zeros in discrete time control systems. Berlin: Springer-Verlag.
   Google Scholar
• Vardulakis, A.I.G. (1980). Zero placement and the ‘Squaring Down’ problem: A polynomial approach. International Journal of Control, 31, 821–832.
   Web of Science ®Google Scholar
• Venugopal, R., & Bernstein, D.S. (2000). Adaptive disturbance rejection using ARMARKOV system representations. IEEE Transactions on Control System Technology, 8, 257–269.
   Web of Science ®Google Scholar