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M.i. Andriychuk - One of the best experts on this subject based on the ideXlab platform.
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Some Generalizations of the Synthesis Problem for Plane Arrays
2018 XXIIIrd International Seminar Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED), 2018Co-Authors: M.i. Andriychuk, Yarema F. KuleshnykAbstract:The usual variational statement of Synthesis Problem is generalized for accounting the additional requirements to the synthesized radiation pattern (RP) and field distribution in the appointed areas of a near zone. For this goal, the minimizing functional is supplemented by term providing the ability to minimize the values of field in these areas; the creating the deep minimums in the RP for the certain angular coordinates is realized too. The approach foresees the obtaining the explicit formula for the field values in a near zone. The results of computational modeling testify the ability to create zeros in the RP and to minimize significantly the values of field in a near zone of plane arrays.
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Two approaches to solving the antenna Synthesis Problems according to the amplitude radiation pattern
2017 XI International Conference on Antenna Theory and Techniques (ICATT), 2017Co-Authors: M.i. AndriychukAbstract:A nonlinear Synthesis Problem according to given amplitude radiation pattern for plane aperture is considered in two ways. An analytical formula for the optimal current is obtained in the first approach. This current generates the amplitude radiation pattern which is close to the given one with the prescribed accuracy. The second approach consists of variational statement of Synthesis Problem. The numerical results illustrate that each method has advantages in the certain range of frequencies.
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New solutions to Synthesis Problem of plane array with hexagonal geometry
2014 XIXth International Seminar Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED), 2014Co-Authors: M.i. Andriychuk, Victor P. TkachukAbstract:Variational approach is applied for solving the Synthesis Problem of plane hexagonal array according to the prescribed power radiation pattern (RP). The mean-square deviation of the prescribed and synthesized RPs in sum with squared norm of currents in the array elements is used as criterion of optimization. The investigation of solution to the respective nonlinear equation has been carried out. The numerical results testify the effectiveness of the approach proposed.
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Polynomial approach to linear antenna array Synthesis Problem according to power radiation pattern with restriction on its norm
2014 International Conference on Mathematical Methods in Electromagnetic Theory, 2014Co-Authors: M.i. Andriychuk, Olena O. Bulatsyk, Nikolai N. VoitovichAbstract:The Synthesis Problem for equidistant linear antenna array according to the prescribed power radiation pattern (RP) is generalized by taking into account an additional restriction on the norm of the synthesized RP. The variational approach supplemented by the Lagrange method of multipliers is applied for the formulation of Problem. The phase RP is uniquely represented by the complex polynomial of high degree. The modified Newton method is used for numerical solving the respective integral-transcendental equation system. The approach was numerically applied to an example of the antenna array Synthesis Problem.
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Comparing different approaches to linear antenna Synthesis Problems according to power radiation pattern
2014 XIXth International Seminar Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED), 2014Co-Authors: M.i. Andriychuk, Olena O. Bulatsyk, Nikolai N. VoitovichAbstract:The antenna Synthesis Problem according to the prescribed power radiation pattern with the equality norm condition is solved by the approach based on the concept of generating polynomials. The variational formulation, supplied by the Lagrange method of multipliers, is applied. The modified Newton method is used for numerical solving of the respective integro-transcendental equation systems. The approach was numerically tested on the example of the antenna Synthesis Problem, recently solved directly by the Newton method. Numerical results are compared and analyzed.
Matthew M. Peet - One of the best experts on this subject based on the ideXlab platform.
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A Convex Reformulation of the Controller Synthesis Problem for Infinite-Dimensional Systems using Linear Operator Inequalities (LOIs) with Application to MIMO Multi-Delay Systems
2018 Annual American Control Conference (ACC), 2018Co-Authors: Matthew M. PeetAbstract:In this paper, we propose a formal duality and operator-based framework for controller Synthesis of infinite-dimensional systems using convex optimization. Specifically, we propose a class of what we call Linear Operator Inequalities (LOIs) and give conditions under which LOIs are solvable and under which they can be used for controller Synthesis. Within this LOI framework, the first technical contribution of the paper is a new dual stability condition under which we can reformulate the controller Synthesis Problem as an LOI. The second technical contribution is LOIs for both primal and dual stability of systems with multiple delays. The third technical contribution is to show that both these LOIs are solvable. Finally, we use an LMI-based framework to solve these LOIs and demonstrate numerically that the primal and dual stability conditions are functionally equivalent for MIMO systems with multiple delays.
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A Convex Formulation of the H ∞ -Optimal Controller Synthesis Problem for Multi-Delay Systems.
arXiv: Systems and Control, 2018Co-Authors: Matthew M. PeetAbstract:Optimal controller Synthesis is a bilinear Problem and hence difficult to solve in a computationally efficient manner. We are able to resolve this bilinearity for systems with delay by first convexifying the Problem in infinite-dimensions - formulating the $H_\infty$ optimal state-feedback controller Synthesis Problem for distributed-parameter systems as a Linear Operator Inequality - a form of convex optimization with operator variables. Next, we use positive matrices to parameterize positive `complete quadratic' operators - allowing the controller Synthesis Problem to be solved using Semidefinite Programming (SDP). We then use the solution to this SDP to calculate the feedback gains and provide effective methods for real-time implementation. Finally, we use several test cases to verify that the resulting controllers are \textit{optimal} to several decimal places as measured by the minimal achievable closed-loop $H_\infty$ norm, and as compared against controllers designed using high-order Pad\'e approximations.
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A convex reformulation of the controller Synthesis Problem for MIMO single-delay systems with implementation in SOS
2017 American Control Conference (ACC), 2017Co-Authors: Matthew M. PeetAbstract:In this paper, we propose a new dual class of stability condition for MIMO single-delay systems which is based on the implicit existence of a Lyapunov-Krasovskii functional but does not explicitly construct such a functional. This new type of stability condition allows the controller Synthesis Problem to be formulated as a convex optimization Problem with little or no conservatism using a variable transformation. Furthermore, we show how to invert this variable transformation in order to obtain the stabilizing controller. The stability and controller Synthesis conditions are then enforced using the SOS framework exploiting recent advances in this field. Numerical testing verifies there is little to no conservatism in either the “dual” stability test or the controller Synthesis condition.
P.o. Savenko - One of the best experts on this subject based on the ideXlab platform.
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About branching of solutions of Synthesis Problem for a flat aperture according to the prescribed amplitude directivity pattern
2010 XVth International Seminar Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED), 2010Co-Authors: L. P. Protsakh, P.o. Savenko, M. D. TkachAbstract:The Synthesis Problem of flat aperture according to the prescribed amplitude directivity pattern (DP), which is reduced to investigation and numerical solution of a two-dimensional non-linear integral equation of the Hammerstein type, is considered. The transcendental equations for finding the branching lines of the solutions are obtained. A numerical method of their finding is proposed. For the case of rectangular aperture the investigations of finding the branching-off solutions are given.
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Numerical solution of nonlinear Synthesis Problem of flat aperture with use of smoothing functional
2008 13th International Seminar Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory, 2008Co-Authors: P.o. Savenko, M. D. TkachAbstract:One approach to the numerical solution of Synthesis Problem of antennas with flat radiating aperture according to the prescribed requirements to amplitude directivity pattern and presence of restrictions on norm of currents of excitation is stated. Nonuniqueness and branching of the solutions are characteristics of such class of Problems. Finding the optimum solutions is reduced to investigation and numerical solution of Hammestein type nonlinear two-dimensional integral equation. Numerical algorithms for finding the branching lines and branch off solutions of this equation are constructed and justified. Numerical examples are given.
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The properties of solutions of the Synthesis Problem for the waveguide array
DIPED - 2001. Proceedings of 6th International Seminar Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (IEEE Cat. , 2001Co-Authors: M. I. Andriychuk, P.o. SavenkoAbstract:The Synthesis Problem of waveguide array with due regard for the mutual coupling of the elements is considered. The variational statement of Problem consists in minimization of functional presenting the mean-square deviation of the prescribed and synthesized amplitude radiation patterns; the functional contains additional summand, which specifies limitation on a norm of the excitation coefficients of the array elements. The nonlinear equation, corresponding to a functional, is solved numerically by the method of successive approximations. The linear equation for investigation of branchpoints is obtained. The results of numerical calculations are discussed.
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About structure of solutions of nonlinear Synthesis Problem of linear antenna according to the prescribed power directivity pattern
DIPED - 2000. Proceedings of 5th International Seminar Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (IEEE Cat. , 2000Co-Authors: P.o. SavenkoAbstract:As an example of the Synthesis Problem of a linear antenna according to the prescribed power directivity pattern (DP), the results of research of the structure and properties of nonlinear integrated equation solutions, which is the Euler one of the goal functional, are presented. This functional includes both the requirement on the mean-square deviation, the given and synthesized DP by power, and the weighed restriction on the norm of the excitation sources in the form of the stabilizing functional. On the basis of the methods of branching theory of the nonlinear equations solutions it is shown that for the nonlinear Synthesis Problem the bifurcation of the solutions is characteristic. The equations for finding the bifurcation points are obtained. The quantity and characteristic properties difference from trivial solutions in the space of real continuous functions are determined.
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Numerical solution of Synthesis Problem of flat microstrip antenna array according to the prescribed power directivity pattern
DIPED - 2000. Proceedings of 5th International Seminar Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (IEEE Cat. , 2000Co-Authors: P.o. Savenko, M. D. TkachAbstract:The variational Synthesis Problem of a flat microstrip antenna array according to the prescribed directivity pattern by power is considered. The mutual influence of their elements is taken into account in an approximation of the given surface currents distribution on the radiators. The effective computing algorithm of finding the nonlinear Synthesis equations solutions of various types is proposed. These equations are Euler ones of the researched functional. The Synthesis numerical examples of the space directivity pattern are presented.
D. Braha - One of the best experts on this subject based on the ideXlab platform.
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On the complexity of the design Synthesis Problem
IEEE Transactions on Systems Man and Cybernetics - Part A: Systems and Humans, 1996Co-Authors: O. Maimon, D. BrahaAbstract:Presents and analyzes a formal model of a design process, emphasizing the Synthesis part. The design artifact description is identified as an algebraic structure. The desired function and constraints are mapped to the artifact description using an evolutionary process that can be visualized as a feedback loop of analysis, Synthesis and evaluation. A special case of the Synthesis activity, called the basic Synthesis Problem (BSP), is addressed. The BSP is shown to be NP-complete. As a consequence, tractability can be obtained by enforcing constraints on the artifact structure. As such, the authors present a model having an element of descriptive design theory that is also a framework for the future development of computational support systems and automatic design tools.
Wolfgang Reisig - One of the best experts on this subject based on the ideXlab platform.
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The Synthesis Problem of Petri nets
Acta Informatica, 1996Co-Authors: Jörg Desel, Wolfgang ReisigAbstract:The Synthesis Problem of concurrent systems is the Problem of synthesizing a concurrent system model from sequential observations. The paper studies the Synthesis Problem for elementary Petri nets and transition systems. A characterization of the class of transition systems which correspond to elementary Petri nets is proven. It is shown how to generate all elementary Petri nets corresponding to a given transition system. If there is any such elementary Petri net, it is proven that there always exists a small one which has only polynomially many elements in the size of the transition system.
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the Synthesis Problem of petri nets
Symposium on Theoretical Aspects of Computer Science, 1993Co-Authors: Jörg Desel, Wolfgang ReisigAbstract:The Problem of deriving concurrent operational models from sequentially observed behaviour is solved for elementary Petri nets. Labelled directed graphs are used to represent behaviour. A new characterization of graphs representing the behaviour of some elementary Petri net is given. It is shown how the set of all nets exhibiting the behaviour given by a graph can be constructed and that, if this set is not empty, it contains a net with a polynomial number of elements in the size of the graph.
