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An optimal feedback control has been obtained for linear-quadratic optimal control problems with constraints described by differential-algebraic equations. For that purpose, a new implicit Riccati equation (Riccati differential algebraic system) is provided, and its solvability is investigated. It is shown that one can do without those strong consistency… (More)
The work deals with linear-quadratic optimal control problems with constant coefficients when the state equation is unresolved with respect to the derivative. In the first two problems, the performance index is the sum of the integral of a quadratic form with respect to the control and quadratic forms with respect to the differences between the output… (More)
Optimal feedback control depending only on the system state is constructed for a control problem by the non-causal descrip-tor system for which optimal feedback control depending on state derivatives was considered in the paper (Müller, 1998). To this end, a non-symmetric solution of the algebraic operator Riccati equation is used.
performance index has been constructed as series of non-negative integer powers of a small parameter. The estimates have been obtained for the proximity of the asymptotic approximate solutions to the exact one. The nice property is proved, namely, the values of the minimized functional do not increase when higher-order approximations to the optimal control… (More)