Aposteriori polynomial fitting method for the general optimal control problem

When the general optimal control problem is considered for arbitrary initial conditions, one finally arrives to the well-known Hamilton-Jaeobi-Bellman (HJB) equation, which is quite difficult to solve. In fact, it is rarely feasible to solve HJB equation for a nonlienar system of any practical siginificance; and hence, the development of exact explicit optimal feedback control schemes is usually unattainable for nonlienar systems. Here, a new method is presented which relies on the performance index sensitivity with respect to the changes in the controller parameter vector. This method gives rise to a sub-optimal control strategy even for nonlienar system dynamics and nonquadratic performance index.