This paper is concerned with the sampled-data based adaptive
linear quadratic (LQ) control of hybrid systems with both
unmeasurable Markov jump processes and stochastic noises.
By the least matching error estimation algorithm, parameter estimates
are presented. By a double-step (DS) sampling approach and the certainty
equivalence principle, a sampled-data based adaptive LQ control is
designed. The DS-approach is characterized by a comparatively large
estimation step for parameter estimation and a sufficient small control
step for control updating. Under mild conditions, the closed-loop system
is shown to be stable. It is found that the key factor determining the
performance index is the estimation step rather than the control step.
When the estimation step becomes too small, the system performance will
become worse. When the estimation step is fixed, the system performance
can indeed be improved by reducing the control step, but cannot reach
the optimal value. The index difference between the sampled-data based
adaptive LQ control and the conventional LQ optimal control is asymptotically
bounded by a constant depending on the estimation step and the priori
information of the parameter set.