The Optimal Control Problem by Singular Linear System with Lumped Parameters


In this paper the linear quadratic optimal control problem is considered by singular linear system with lumped parameters. Using the transformation of similarity of singular matrix, the initial system is presented in the form of two subsystems. The Lagrange multiplier method is applied to the transformed system. Relying on this approach we obtain new forms of Euler–Lagrange equations. Furthermore, sufficient conditions are established. By fulfilling these conditions, the optimal control can be unified. Also, we propose the derivation of matrix differential Riccati equations for the above mentioned subsystems. We prove the symmetric property of matrix valued solutions of Riccati equations. By solving these equations, we obtain the formula for calculating the minimal value of optimality criteria.

Publication year: 
С. 67—72. Бібліогр.: 7 назв.

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