Adaptive control of linear dynamic processes by a modified method of least squares

The paper is concerned with control of discrete-time stochastic linear dynamic process whose parameters are known. For a wide range of control strategies a single-parametric family of adaptation algorithms is proposed which result from a modification of the method of least squares. The output and control of the system are shown to be strongly adaptive; in other words, the asymptotic, in time, tendency of the process output $y_t$ and control $u_t$ to the ideal processes $y_t^*$ and $u_t^*$ obtained with the known process parameters is proved. These conditions are fairly simply structured and easily verified in applications.