Minimax problem of parametric optimization of a linear system with an initial perturbation

A linear system with control parameters in the right part and an indeterminate initial perturbation is considered. The objective function is formulated as a positive linear combination of quadratic terms on a set of phase trajectories. A minimax problem is set in accordance with the principle of guaranteed results. The regularization of the problem is carried out: explicit conditions for the parameters of the linear combination are obtained, which provide the concave-convex structure of the objective function. This property opens up the possibility of an effective numerical solution of the minimax problem.