STOCHASTIC LINEAR-QUADRATIC ADAPTIVE-CONTROL FOR CONTINUOUS-TIME FIRST-ORDER SYSTEMS

In this paper, we discuss the linear quadratic (LQ) adaptive control p roblem for the following continuous-time first-order scalar stochastic system: dx(t) = ax(t)dt + bu(t)dt + cdw(t), with cost function min li m 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 equ al to 0, q(2)>0. Based on the self-convergence property of continuous- time weighted least-squares (CWLS) algorithm [9] and the similar param eter modification method [13], the stability of the closed-loop system is achieved without invoking any excitations. Here self-convergence m eans that the convergence is automatic in the sense that no excitation conditions on the signals or measurements is needed. It is a terminol ogy from [10]. The strong consistency of CWLS and the optimality of th e adaptive control are established by incorporating with diminishing e xcitations, (C) 1997 Elsevier Science B.V.