Optimal Disturbance Rejection for Nonlinear Control Systems

The problem of optimal disturbance rejection for a general class of multiinput/multioutput (MIMO) nonlinear systems, achieved over a set of stabilizing compensator operators, is formulated in a Banach space setting. Conditions on the operators are imposed based on the inputs as well as the outputs. An existence theorem for optimal solutions is established under some realistic and verifiable conditions. For solving the optimization problem, a generalized recursive nonlinear programming algorithm is posed, and a simple example of nonlinear optimal feedback design is given to show that the problem may be reduced to a standard min-max optimization, and is hence solvable. © 1989 IEEE