Locally optimal feedforward/state feedback control of nonlinear systems with uncertain parameters

In this paper a new formulation of the locally optimal feedback strategy (LOFS) is given which completes the well-known optimal control solution of the feedforward problem for nonlinear systems. Instead of aiming at optimality for each point around the state space trajectory as in the classical approach, the LOFS is the optimal state feedback around the nominal point in a space of uncertain problem parameters. It is defined by the minimization of a scalar criterion of the second order performance index sensitivity matrix for the nominal parameters. A gradient search based algorithm to find the optimal feedback is outlined together with two computationally faster suboptimal versions. First numerical results are presented.