Multicriteria optimal control in dynamical systems

Linear dynamical controllable systems with subsystems are considered. The behavior of each subsystem is characterized by a quadratic integral criterion. The problem of multicriteria optimal control in such systems is formulated and solved. The solution obtained is based on the principle of proportional damages, which ensures the following properties: the control law is synthesized in linear form as in monocriterion optimization problems; the solution is invariant to the view of metrics which characterizes the distance between vector-criteria current values and their ideal values; and optimal values of criteria of quality have relative losses (damages) inversely proportional to the weight coefficients.<>