A computational technique for the design of a specific optimal controller

For a linear plant, the optimization of a performance index of integral type, which is quadratic in states and control, results in a control law. This ideal controller, however, must often be replaced by an approximate controller; e.g., due to inaccessible state variables. The input-output relation of such a controller may be specified within some parameters in advance. A specific optimal controller (SOC) is obtained when the parameters are chosen in an optimal manner so as to minimize a performance criterion; for example, the degradation of a performance index. Since these parameters depend on the initial state, the SOC is designed in regard to the worst initial state resulting in the maximum deterioration, which is then minimized by the best parameters. A computational procedure for this design is proposed. An algorithm is constructed and applied to this min-max problem.