For a sufficiently wide class of the linear hybrid systems, an algorithm of optimal feedback control was proposed. Consideration was given to the hybrid control systems with autonomous switching, as well as the corresponding problems of the hybrid linear-quadratic optimal control based on the recently suggested principle of maximum. Interrelations between the hybrid principle of maximum and the method of dynamic programming for the systems of this class were discussed. The classical formalism was extended, the corresponding Riccati equations were obtained, and discontinuity of the "hybrid" Riccati matrix was proved. The computational aspects of the established theoretical results were considered.
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