Robust control of nonlinear systems without matching condition

Within the framework of Lin et al., we study robust control of nonlinear systems. Instead of directly solving a robust control problem of stabilizing a nonlinear system with uncertainties, we translate the robust control problem into an optimal control problem with a cost function carefully selected to compensate the uncertainties. This approach is applicable to general nonlinear systems, even if the matching condition fails to hold. Since an optimal control problem is generally easier to solve than a robust control problem, this indirect approach provides an effective alternative to direct approaches studied in the literature. In particular, if the known dynamics of the system is linear and the uncertainty is bounded by linear functions, then the robust control problem can be translated into a linear quadratic regulator (LQR) problem, whose solution is well known. An example using this approach is worked out in details as an illustration