Stochastic Adaptive Control via Consistent Parameter Estimation

The paper introduces novel techniques for achieving global convergence results and improving transient performance in stochastic adaptive control. For example, there is introduced switching between a least squares and an extended least squares parameter estimation algorithm according to an ill-conditioning measure, and there is appropriate selection of external persistently exciting signals, thereby speeding convergence of parameter estimates and improving performance. The convergence analysis is developed for stochastic adaptive control of linear discrete-time systems, such as are represented by auto-regressive, moving average, exogonous input models. The signal models are assumed to have fixed but unknown parameters which are estimated by “standard” least squares or extended least squares recursions. The theory is applicable to a wide class of control schemes with the property that when there is consistent deterministic plant parameter estimation, closed loop stability is achieved. Specific attention is paid to adaptive pole-assignment. The theory builds on a key result in a companion paper concerning persistence of excitation for time invariant completely reachable plants with bounded piecewise constant state feedback.