Optimal capacitor placement, considering power system loss reduction, voltage profile improvement, line reactive power decrease and power factor correction, is of particular importance in power system planning and control. The distribution system operator calculates the optimal place, number and capacity of capacitors based on two major purposes: active power loss reduction and return on invest...

Abst rac t -A concept of exact slow optimal control is defined for a general class of nonlinear singularly perturbed systems utilizing the slow manifold theory. Under a set of conditions an exact optimal feedback regulation restricted to the slow manifold is obtained. The result is applied to a class of nonlinear systems with nonlinear fast actuators. It is shown that by adding an extra compens...

where S = (St)t 0 is the maximum process associated with the one-dimensional time-homogeneous diffusion X = (Xt)t 0 , the function x 7! c(x) is positive and continuous, and the supremum is taken over all stopping times of X for which the integral has finite expectation. It is proved, under no extra conditions, that this problem has a solution, i.e. the payoff is finite and there is an optimal s...

We present a practical stability result for dynamical systems depending on a small parameter. This result is applied to a practical stability analysis of fast time-varying systems studied in averaging theory, and of highly oscillatory systems studied by Sussmann and Liu. Furthermore, the problem of practically stabilizing control affine systems with drift is discussed.

In this paper suucient second order optimality conditions are established for optimal control problems governed by a linear elliptic equation with nonlinear boundary condition, where pointwise constraints on the control are given. The second order condition requires the coercivity of the Lagrange{function on a suitable subspace together with rst order suucient conditions on a certain set of str...

We prove the existence of optimal control for nonlinear systems having implicit derivative with quadratic performance criteria.

In this paper, the optimal adaptive leader-follower consensus of linear continuous time multi-agent systems is considered. The error dynamics of each player depends on its neighbors’ information. Detailed analysis of online optimal leader-follower consensus under known and unknown dynamics is presented. The introduced reinforcement learning-based algorithms learn online the approximate solution...