In this work, we propose algorithms for optimizing the choice of feedback in the modal control problem in multidimensional linear systems with the criterion of minimizing the norm of the feedback matrix. The proposed approaches to solving this problem are based on representing the original system in an orthonormal basis. In particular, representing controllability in a block form lets us divide a high dimensional optimization problem into optimization subproblems of lower dimension. We pay special attention to finding the initial value of the feedback matrix with suboptimal search procedures. We give recommendations on constructing numerical search procedures for suboptimal solutions with gradient-based methods. The efficiency of the developed algorithms is demonstrated with numerical examples.
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