Optimal Online Control of Dynamical Systems Under Uncertainty

Calculation of interval damping ratio under uncertain load in power system

“…Using the first-order Taylor series expansion at the current operating point (x (r) , u (r) ), the original problem (7)- (9) is transformed into the following linear programming (LP) problem [19][20]:…”

Optimal Measurement Feedback Control of Finite-time Continuous Linear Systems

“…In the following we review some results about open-loop optimal control subject to uncertain initial states which are needed in the later sections. Further details can be found in Gabasov et al (2007).…”

“…The solution of P 0 (τ, X) is an input u 0 (•; τ, X) ∈ U [τ,T ] steering every realization of the initial state x(τ ) ∈ X into the terminal set S. Furthermore, it minimizes the worst-case cost max x∈X h T 0 x(T ; τ, x, u(•)). In Gabasov et al (2007) it is shown that the optimal openloop control u 0 (•; τ, X) can be obtained by the solution of the following optimal control problem min…”

“…As shown in Gabasov et al (2007), this goal can be achieved on the base of "purified measurements" y p 0 (s) = y p (s) − Cx 0 (s; 0, u p (•)), s ∈π [0,τ ] , by the solution of m + 1 optimization problemŝ…”