Recursive designs of robust and adaptive controllers for extensions of existing canonical forms and for their interconnections

• Applicant: Professor Dr. Sergey Dashkovskiy
• Subject Area: Mathematics
• Term: from 2011 to 2014
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 197928859

• Final Report Year: 2014

Final Report Abstract

In this project we have extended known backstepping designs of robust and adaptive controllers to more general classes of nonlinear systems. Namely our work address backstepping designs for the so-called generalizaed triangular form (GTF) systems. In particular GTF systems do not have a controllable linearization and do not possess the feedback linearization property even locally. Having obtained these results for systems of ordinary differential equations, we also extended them to the case of switched systems with unknown, arbitrary switchings. We considered the cases when these classes of systems have unknown parameters and/or external disturbances and/or dynamic uncertainties. In these cases we have solved the problems of adaptive stabilization and as a more general case input-to-state stabilization with respect to the external disturbances. For some special cases we developed constructive designs and made simulation study. In the case of dynamic uncertainties, we used the tools based on small-gain theorems. Since the small-gain theorems for switched systems with arbitrary switchings were unknown, we proved them for the case of large-scale interconnections.

Publications

• Global uniform input-to-state stabilization of large-scale interconnections of MIMO generalized triangular form switched systems. Mathematics of Control, Signals, and Systems, 24(2012) 1-2, pp. 135-168
  S. Dashkovskiy, S. Pavlichkov
  (See online at https://doi.org/10.1007/s00498-012-0078-y)
• Robust stabilization of the generalized triangular form nonlinear systems with disturbanees. IEEE Transactions on Automatic Control
  S. Dashkovskiy, S. Pavlichkov
  (See online at https://doi.org/10.1109/TAC.2013.2292453)
• Stabilization of generalized triangular form systems with dynamic uncertainties by means of small gain theorems. 9th IFAC Symposium on Nonlinear Control Systems, NOLCOS13, Toulouse, France September 4-6,2013, pp.32-37
  S. Dashkovskiy, S. Pavlichkov, Zhong-Ping Jiang
  
• Uniform Asymptotic Stabilization of Nonlinear Switched Systems with Arbitrary Switchings and with Dynamic Uncertainties by Means of Small Gain Theorems. 52nd IEEE Conference on Decision and Control, CDC'13, Florence, Italy, December 2013, pp. 5264-5269
  S. Dashkovskiy, S. Pavlichkov, Z.-P. Jiang