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Time-Varying Optimization and Its Application to Power System Operation

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Figure 1.1: The distances to the optimal trajectory ∥and the objective value differencesxb(t)−x∗(t)∥ and ∥xr(t)−x∗(t)∥, c(xb(t), t) − c(x∗(t), t) and c(xr(t), t) − c(x∗(t), t)of the two optimization schemes.
Figure 2.1: Illustration of condition (2.25). This condition is essentially on: (i)time-variability of a KKT point, (ii) extent of the contraction, and (iii) maximumerror in each iteration
Table 3.1: Averaged tracking errors of the first-order method and the second-ordermethod applied to the problem (3.34).
Figure 4.1: Diagram of the control of a time-varying system. The system’s input-state relation is given by F , which is influenced by some time-varying components.
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