The Experts below are selected from a list of 252 Experts worldwide ranked by ideXlab platform
Heikki Hyotyniemi - One of the best experts on this subject based on the ideXlab platform.
-
on Unsolvability of nonlinear system stability
European Control Conference, 1997Co-Authors: Heikki HyotyniemiAbstract:Any algebraically computable function can be expressed as a nonlinear discrete-time system of the form s(k + 1) = f(As(k)), where f(·) is a simple ‘cut’ operation. This result is utilized to demonstrate that there cannot exist any general decision procedure for analysing the stability of systems of the above form.
Marian Boykan Pour-el - One of the best experts on this subject based on the ideXlab platform.
-
CCA - The Degree of Unsolvability of a Real Number
Computability and Complexity in Analysis, 2001Co-Authors: Anthony J. Dunlop, Marian Boykan Pour-elAbstract:Each real number x can be assigned a degree of Unsolvability by using, for example, the degree of Unsolvability of its binary or decimal expansion, or of its Dedekind cut, or of some other representation of x. We show that the degree of Unsolvability assigned to x in any such way is the same regardless of the representation used. This gives to each real number a unique degree of Unsolvability. If x is of computably enumerable degree, there is a computable sequence of rationals which converges to x with a modulus of convergence having the same degree of Unsolvability as x itself. In contrast, if x is computable relative to the halting set but is not of computably enumerable degree, this is not true. Specifically, if {rn} is any computable sequence of rationals converging to such a real number x, the modulus of convergence of {rn} must have degree of Unsolvability strictly higher than that of x. Thus there is an inherent gap between the degree of Unsolvability of such an x and the degree of Unsolvability of the modulus of convergence of an approximating computable sequence of rationals; this gap is bridged (in the sense of the "join operator" of degree theory) by a set of natural numbers which measures the twists and turns of the computable sequence {rn}.
-
The degree of Unsolvability of a real number
Lecture Notes in Computer Science, 2001Co-Authors: Anthony J. Dunlop, Marian Boykan Pour-elAbstract:Each real number x can be assigned a degree of Unsolvability by using, for example, the degree of Unsolvability of its binary or decimal expansion, or of its Dedekind cut, or of some other representation of x. We show that the degree of Unsolvability assigned to x in any such way is the same regardless of the representation used. This gives to each real number a unique degree of Unsolvability. If x is of computably enumerable degree, there is a computable sequence of rationals which converges to x with a modulus of convergence having the same degree of Unsolvability as x itself. In contrast, if x is computable relative to the halting set but is not of computably enumerable degree, this is not true. Specifically, if {r n } is any computable sequence of rationals converging to such a real number x, the modulus of convergence of {r n } must have degree of Unsolvability strictly higher than that of x. Thus there is an inherent gap between the degree of Unsolvability of such an x and the degree of Unsolvability of the modulus of convergence of an approximating computable sequence of rationals; this gap is bridged (in the sense of the join operator of degree theory) by a set of natural numbers which measures the twists and turns of the computable sequence {r n }.
Thomas J. Overbye - One of the best experts on this subject based on the ideXlab platform.
-
A power flow measure for unsolvable cases
IEEE Transactions on Power Systems, 1994Co-Authors: Thomas J. OverbyeAbstract:As power systems become more heavily loaded, there will be an increase in the number of situations where the power flow equations have no real solution, particularly in contingency analysis and planning applications. Since these cases can represent the most severe threats to viable system operation, it is important that a computationally efficient technique be developed to both quantify the degree of Unsolvability, and to provide optimal recommendations of the parameters to change to return to a solvable solution. Such an algorithm is developed in the paper. The distance in parameter space between the desired operating point and the closest solvable operating point provides a measure of the degree of Unsolvability, with the difference between these two points providing the optimal system parameter changes. The algorithm is based upon a Newton-Raphson power flow algorithm, which provides both computational efficiency and compatibility with existing security analysis techniques. The method is demonstrated on systems of up to 118 buses. >
Li Chun-wen - One of the best experts on this subject based on the ideXlab platform.
-
Constructive inverse system method for general nonlinear systems
Control theory & applications, 2003Co-Authors: Li Chun-wenAbstract:The Unsolvability of implicit equations existing in the inversion algorithm in the inverse system method (ISM) is considered, and a constructive inversion algorithm is presented for general nonlinear systems so as to avoid solving implicit equations via elimination method. Based on the algorithm, the corresponding modification of ISM is discussed, and the constructive ISM is proposed through dynamical compensation. These improvements enable ISM to be constructively applicable in principle to arbitrary nonlinear system that is smooth enough.
Anthony J. Dunlop - One of the best experts on this subject based on the ideXlab platform.
-
CCA - The Degree of Unsolvability of a Real Number
Computability and Complexity in Analysis, 2001Co-Authors: Anthony J. Dunlop, Marian Boykan Pour-elAbstract:Each real number x can be assigned a degree of Unsolvability by using, for example, the degree of Unsolvability of its binary or decimal expansion, or of its Dedekind cut, or of some other representation of x. We show that the degree of Unsolvability assigned to x in any such way is the same regardless of the representation used. This gives to each real number a unique degree of Unsolvability. If x is of computably enumerable degree, there is a computable sequence of rationals which converges to x with a modulus of convergence having the same degree of Unsolvability as x itself. In contrast, if x is computable relative to the halting set but is not of computably enumerable degree, this is not true. Specifically, if {rn} is any computable sequence of rationals converging to such a real number x, the modulus of convergence of {rn} must have degree of Unsolvability strictly higher than that of x. Thus there is an inherent gap between the degree of Unsolvability of such an x and the degree of Unsolvability of the modulus of convergence of an approximating computable sequence of rationals; this gap is bridged (in the sense of the "join operator" of degree theory) by a set of natural numbers which measures the twists and turns of the computable sequence {rn}.
-
The degree of Unsolvability of a real number
Lecture Notes in Computer Science, 2001Co-Authors: Anthony J. Dunlop, Marian Boykan Pour-elAbstract:Each real number x can be assigned a degree of Unsolvability by using, for example, the degree of Unsolvability of its binary or decimal expansion, or of its Dedekind cut, or of some other representation of x. We show that the degree of Unsolvability assigned to x in any such way is the same regardless of the representation used. This gives to each real number a unique degree of Unsolvability. If x is of computably enumerable degree, there is a computable sequence of rationals which converges to x with a modulus of convergence having the same degree of Unsolvability as x itself. In contrast, if x is computable relative to the halting set but is not of computably enumerable degree, this is not true. Specifically, if {r n } is any computable sequence of rationals converging to such a real number x, the modulus of convergence of {r n } must have degree of Unsolvability strictly higher than that of x. Thus there is an inherent gap between the degree of Unsolvability of such an x and the degree of Unsolvability of the modulus of convergence of an approximating computable sequence of rationals; this gap is bridged (in the sense of the join operator of degree theory) by a set of natural numbers which measures the twists and turns of the computable sequence {r n }.
