Stabilization of a nonlinear multivariable discrete-time time-invariant plant with uncertainty on a linear pseudoinverse model
This paper addresses the problem of the robust stabilization of a nonlinear multivariable time-invariant plant on a semi-infinite discrete time interval under arbitrary nonmeasurable bounded additive disturbances. A guaranteed value of the quality criterion is given by the functional representing the weighted sum of the limiting norms of the control vectors and output variables. To generate control actions, a controller containing a linear generalized inverse model and discrete-time integrators is introduced into the feedback loop. Sufficient conditions for the robust stability of the control system, as well as the conditions for the ultimate boundedness of all its signals (dissipativity conditions), are formulated. A corresponding simulation example is presented.
Unable to display preview. Download preview PDF.
- 1.L. M. Lyubchyk, “Disturbance rejection in linear discrete multivariable systems: inverse model approach,” in Proceedings of the 18th IFAC World Congress, Milano, Italy, 2011, pp. 7921–7926.Google Scholar
- 2.G. E. Pukhov and K. D. Zhuk, Synthesis of Interconnected Control Systems with the Method of Inverse Operators (Naukova Dumka, Kiev, 1966) [in Russian].Google Scholar
- 3.K. D. Zhuk, T. G. Pyatenko, and V. I. Skurikhin, “Problems of synthesis of controlling models in interconnected automatic systems,” in Proceedings of the Seminar on Mathematical Simulation Methods and Electrical Chain Theory, Kiev, 1964, pp. 3–17.Google Scholar
- 7.V. M. Kuntsevich, Control under Uncertainty: Guaranteed Results in Control and Identification Problems (Naukova Dumka, Kiev, 2006) [in Russian].Google Scholar
- 8.V. N. Afanas’ev, Control of Uncertain Dynamical Objects (Fizmatlit, Moscow, 2008) [in Russian].Google Scholar
- 10.V. F. Sokolov, Robust Control under Limited Perturbations (Komi Nauch. Tsentr UrO RAN, Syktyvkar, 2011) [in Russian].Google Scholar
- 13.V. A. Katkovnik and A. A. Pervozvanskii, “Methods of extremum search and problems of the synthesis of multidimensional control systems,” in Adaptive Automatic Systems, Ed. by G. A. Medvedev (Sovetskoe Radio, Moscow, 1972), pp. 17–42 [in Russian].Google Scholar
- 14.L. S. Zhiteckii, V. N. Azarskov, K. Yu. Solovchuk, and O. A. Sushchenko, “Discrete-time robust steady-state control of nonlinear multivariable systems: a unified approach,” in Proceedings of the 19th IFAC World Congress, Cape Town, South Africa, 2014, pp. 8140–8145.Google Scholar
- 15.G. E. Pukhov and Ts. S. Khatiashvili, Models of Technological Processes (Tekhnika, Kiev, 1974) [in Russian].Google Scholar