Dense admissible sets

1998 ◽  
pp. 216-225 ◽  
Author(s):  
Daniel M. Gordon ◽  
Gene Rodemich
Keyword(s):  
Admissible Sets

scholarly journals Transient stability analysis of power grids with admissible and maximal robust positively invariant sets

2020 ◽  
Vol 68 (12) ◽  
pp. 1011-1021
Author(s):  
Tim Aschenbruck ◽  
Willem Esterhuizen ◽  
Stefan Streif
Keyword(s):  
Power Systems ◽  
Transient Stability ◽  
Energy Transition ◽  
Power Grids ◽  
Invariant Sets ◽  
Admissible Sets ◽  
Major Fault ◽  
Bounded Disturbances ◽  
One Machine ◽  
Positively Invariant Sets

AbstractThe energy transition is causing many stability-related challenges for power systems. Transient stability refers to the ability of a power grid’s bus angles to retain synchronism after the occurrence of a major fault. In this paper a set-based approach is presented to assess the transient stability of power systems. The approach is based on the theory of barriers, to obtain an exact description of the boundaries of admissible sets and maximal robust positively invariant sets, respectively. We decompose a power system into generator and load components, replace couplings with bounded disturbances and obtain the sets for each component separately. From this we deduce transient stability properties for the entire system. We demonstrate the results of our approach through an example of one machine connected to one load and a multi-machine system.

scholarly journals FIRST-ORDER METHODS FOR GENERALIZED OPTIMAL CONTROL PROBLEMS FOR SYSTEMS WITH DISTRIBUTED PARAMETERS

2020 ◽  
pp. 18-44
Author(s):  
S. V. Denisov ◽  
V. V. Semenov
Keyword(s):  
Optimal Control Problems ◽  
A Priori Estimates ◽  
A Priori ◽  
Control Problems ◽  
First Order ◽  
Admissible Sets ◽  
Distributed Parameters ◽  
Priori Estimates ◽  
Systems With Distributed Parameters ◽  
First Order Methods

The problems of optimization of linear distributed systems with generalized control and first-order methods for their solution are considered. The main focus is on proving the convergence of methods. It is assumed that the operator describing the model satisfies a priori estimates in negative norms. For control problems with convex and preconvex admissible sets, the convergence of several first-order algorithms with errors in iterative subproblems is proved.

Characterizing strongly admissible sets

2020 ◽  
Vol 11 (3) ◽  
pp. 239-255
Author(s):  
Paul E. Dunne
Keyword(s):  
Principal Result ◽  
Admissible Sets ◽  
Grounded Semantics ◽  
Unique Status

The concept of strong admissibility plays an important role in dialectical proof procedures for grounded semantics allowing, as it does, concise proofs that an argument belongs to the grounded extension without having necessarily to construct this extension in full. One consequence of this property is that strong admissibility (in contrast to grounded semantics) ceases to be a unique status semantics. In fact it is straightforward to construct examples for which the number of distinct strongly admissible sets is exponential in the number of arguments. We are interested in characterizing properties of collections of strongly admissible sets in the sense that any system describing the strongly admissible sets of an argument framework must satisfy particular criteria. In terms of previous studies, our concern is the signature and with conditions ensuring realizability. The principal result is to demonstrate that a system of sets describes the strongly admissible sets of some framework if and only if that system has the property of being decomposable.

Some Lowenheim-Skolem results for admissible sets

1972 ◽  
Vol 12 (4) ◽  
pp. 427-432 ◽  
Author(s):  
Mark Nadel
Keyword(s):  
Admissible Sets

Infinitary logic and admissible sets

1969 ◽  
Vol 34 (2) ◽  
pp. 226-252 ◽  
Author(s):  
Jon Barwise
Keyword(s):  
Second Order ◽  
Order Logic ◽  
Predicate Calculus ◽  
Generalized Quantifiers ◽  
Infinitary Logic ◽  
First Order ◽  
Admissible Sets ◽  
Classical Language ◽  
Second Order Logic ◽  
Order Predicate Calculus

In recent years much effort has gone into the study of languages which strengthen the classical first-order predicate calculus in various ways. This effort has been motivated by the desire to find a language which is(I) strong enough to express interesting properties not expressible by the classical language, but(II) still simple enough to yield interesting general results. Languages investigated include second-order logic, weak second-order logic, ω-logic, languages with generalized quantifiers, and infinitary logic.

scholarly journals Model theory on admissible sets

1973 ◽  
Vol 5 (4) ◽  
pp. 257-289 ◽  
Author(s):  
Nigel Cutland
Keyword(s):  
Model Theory ◽  
Admissible Sets
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