Mårtensson, Bengt Adaptive stabilization without high-gain. (English) Zbl 0651.93042 Modelling and adaptive control, Proc. IIASA Conf., Sopron/Hung. 1986, Lect. Notes Control Inf. Sci. 105, 226-238 (1988). [For the entire collection see Zbl 0643.00032.] The main result of this paper is the complete characterization of necessary and sufficient a priori knowledge needed for adaptive stabilization (namely knowledge of the order of any stabilizing controller for an unknown set of plants. The concept of switching function controller is introduced and some properties stated. The Turing machine of universal controllers is presented to solve the problem of adaptive stabilization. The only a priori used information is that there exists an integr \(\ell\), which is known, such that there exists a fixed linear time-invariant controller of order \(\ell\) that stabilizes the system. An explicit algorithm for this is given. Reviewer: M.de la Sen Cited in 13 Documents MSC: 93C40 Adaptive control/observation systems 93D15 Stabilization of systems by feedback 68Q05 Models of computation (Turing machines, etc.) (MSC2010) 93C10 Nonlinear systems in control theory 93D20 Asymptotic stability in control theory 93B40 Computational methods in systems theory (MSC2010) Keywords:adaptive stabilization; switching function controller; Turing machine of universal controllers; algorithm Citations:Zbl 0643.00032 PDFBibTeX XML