A Nash Game Approach to Mixed H2/H∞ Control for Input-Affine Nonlinear Systems

With the aim of designing controllers to simultaneously ensure robustness and optimality properties, the mixed H 2 / H ∞ control problem is considered. A class of input-affine nonlinear systems is considered and the problem is formulated as a nonzero-sum differential game, similar to what has been done in the 1990s by Limebeer et al. for linear systems. A heuristic algorithm for obtaining solutions for the coupled algebraic Riccati equations which are characteristic of the linear quadratic problem is provided together with a systematic method for constructing approximate solutions for the general, nonlinear problem. A few numerical examples are provided.