Adaptive weighted suboptimal control for linear dynamic systems having a polynomial input

Introducing a cost term on the highest power of the nonlinear polynomial, we derive a simple direct adaptive control weighted suboptimal control algorithm which is very useful for the control of all stable nonminimum-phase and some unstable nonminimum-phase linear systems having a polynomial input. Both stochastic and deterministic situations are considered and the global convergence of the proposed algorithm has been established.