The AAstrom-Wittenmark self-tuning regulator revisited and ELS-based adaptive trackers

Although considerable progress has been made in stochastic adaptive control, the problem concerning the convergence of the original self-tuning regulator proposed by K.J. AAstrom and B. Wittenmark (1973) is still open. Since it is attractive in theory and important in applications, this problem is examined and a rigorous proof of its stability and optimality is given. Related problems such as convergence of the extended-least-squares (ELS)-based adaptive tracker are also considered. >

[1]  Björn Wittenmark,et al.  On Self Tuning Regulators , 1973 .

[2]  G. Stewart Introduction to matrix computations , 1973 .

[3]  W. Stout Almost sure convergence , 1974 .

[4]  P. Ramadge,et al.  Discrete Time Stochastic Adaptive Control , 1981 .

[5]  T. Lai,et al.  Least Squares Estimates in Stochastic Regression Models with Applications to Identification and Control of Dynamic Systems , 1982 .

[6]  P. Caines,et al.  Adaptive control with recursive identification for stochastic linear systems: Multivariable case , 1982, 1982 21st IEEE Conference on Decision and Control.

[7]  Graham C. Goodwin,et al.  Stochastic adaptive control using a modified least squares algorithm , 1982, Autom..

[8]  Han-Fu Chen Recursive System Identification and Adaptive Control by Use of the Modified Least Squares Algorithm , 1984 .

[9]  Sean P. Meyn,et al.  The zero divisor problem of multivariable stochastic adaptive control , 1985 .

[10]  P. Kumar,et al.  Adaptive control with the stochastic approximation algorithm: Geometry and convergence , 1985 .

[11]  T. Lai,et al.  Extended least squares and their applications to adaptive control and prediction in linear systems , 1986 .

[12]  Han-Fu Chen,et al.  Convergence rate of least-squares identification and adaptive control for stochastic systems† , 1986 .

[13]  P. R. Kumar,et al.  Self-tuning trackers , 1987 .

[14]  Lei Guo,et al.  Asymptotically optimal adaptive control with consistent parameter estimates , 1987 .

[15]  Lei Guo,et al.  Least-squares identification for ARMAX models without the positive real condition , 1989 .

[16]  P. Kumar,et al.  Convergence of adaptive control schemes using least-squares parameter estimates , 1990 .

[17]  Lei Guo On adaptive stabilization of time-varying stochastic systems , 1990 .