Indirect adaptive suboptimal control for linear dynamic systems having polynomial nonlinearities

An indirect adaptation algorithm to adaptively implement a control weighted one-step-ahead suboptimal control law previously derived for the control of stochastic linear dynamic systems having polynomial nonlinearities is presented. Since identification is separated from the calculation of controller design and a single adaptation algorithm is used, the indirect scheme provides more flexibility and has the advantage that few estimated parameters and less memory space are required in the case when the system time delay d and/or degree p of the polynomial are large. It has been shown that the proposed indirect scheme has the same global convergence property as the direct scheme given by Zhang and Lang (see ibid., vol.AC-32, no.8 (1987))