Stochastic linear quadratic adaptive control for continuous-time first-order systems

In this paper, we discuss the linear quadratic (LQ) adaptive control problem for the following continuous-time first-order scalar stochastic system: dx(t) = ax(t)dt + bu(t)dt + cdw(t), with cost function min lim sup J(t)(u), u is an element of u t-->infinity where J(t)(u) = 1/t (0) integral(t) (q(1)x(s)(2) + q(2)u(s)(2))ds, q(1) greater than or equal to 0, q(2)>0. Based on the self-convergence property of continuous-time weighted least-squares (CWLS) algorithm [9] and the similar parameter modification method [13], the stability of the closed-loop system is achieved without invoking any excitations. Here self-convergence means that the convergence is automatic in the sense that no excitation conditions on the signals or measurements is needed. It is a terminology from [10]. The strong consistency of CWLS and the optimality of the adaptive control are established by incorporating with diminishing excitations, (C) 1997 Elsevier Science B.V.