Application of the network equivalent concept for external system representation for power system transient analysis is well known. However, the challenge to utilize an equivalent network, approximated by a rational function, is to guarantee the passivity of the corresponding model. In this regard, special techniques are required to enforce the passivity of the equivalent model through a post processing approach that minimizes its impact on the original model characteristics. In this paper, the passivity is enforced by expressing the problem in terms of a convex optimization problem that guarantees the global OPTIMAL solution. The convex optimization problem is efficiently solved by recently developed numerical interior–point methods. This passivity enforcement is also global which indicates that the passivity enforcement in one region does not lead to passivity violation in other regions.

In this paper, minimum and near-minimum time OPTIMAL control laws are developed and compared for a rigid space platform with flexible links during an orientating maneuver with a large angle of rotation. The control commands are considered as typical bang-bang with multiple symmetrical switches, the time OPTIMAL control solution for the rigid-body mode is obtained as a bang bang function and applied to the flexible system after smoothening the control inputs to avoid stimulation of the flexible modes. This will also reflect practical limitations in exerting bang-bang actuator forces/torques due to delays and non-zero time constants of existing actuation elements. The smoothness of the input command is obtained by reshaping its profile based on consideration of additional derivative constraints. the OPTIMAL control problem is converted into parameter optimization problem. The steps of the solution procedure and numerical algorithm to obtain the time OPTIMAL control input are discussed next. The developed control law is applied to a given satellite during a slewing maneuver. The simulation results show that the control input with just a few switching times can significantly lessen the vibrating motion of the flexible appendage, which reveals the merits of the developed control law. The modified realistic OPTIMAL input compared to the bang-bang solution goes well with the practical limitations and alleviates the vibrating motion of the flexible appendage, which reveals the merits of the new developed control law.

The objective of this article is to derive the necessary OPTIMALity conditions, known as Pontryagin's minimum principle, for fuzzy OPTIMAL control problems based on the concepts of differentiability and integrability of a fuzzy mapping that may be parameterized by the left and right-hand functions of its a-level sets.

In this paper, we solve Hamilton-Jocobi-Bellman (HJB) equations arising in OPTIMAL control problems using Homotopy Perturbation Transform Method (HPTM). The proposed method is a combined form of the Laplace Transformation Method with the Homotopy Perturbation Method to produce a highly effective method to handle many problems. Applying the HPTM, solution procedure becomes easier, simpler and more straightforward. Some illustrative examples are given to demonstrate the simplicity and efficiency of the proposed method.