General Synthesis Problem Research Articles

Machine Learning Feedback Control Approach Based on Symbolic Regression for Robotic Systems

A control system of an autonomous robot produces a control signal based on feedback. This type of control implies the control of an object according to its state that is mathematically the control synthesis problem. Today there are no universal analytical methods for solving the general synthesis problem, and it is solved by certain particular approaches depending on the type of control object. In this paper, we propose a universal numerical approach to solving the problem of optimal control with feedback using machine learning methods based on symbolic regression. The approach is universal and can be applied to various objects. However, the use of machine learning methods imposes two aspects. First, when using them, it is necessary to reduce the requirements for optimality. In machine learning, optimization algorithms are used, but strictly optimal solutions are not sought. Secondly, in machine learning, analytical proofs of the received properties of solutions are not required. In machine methods, a set of tests is carried out and it is shown that this is sufficient to achieve the required properties. Thus, in this article, we initially introduce the fundamentals of machine learning control, introduce the basic concepts, properties and machine criteria for application of this technique. Then, with regard to the introduced notations, the feedback optimal control problem is considered and reformulated in order to add to the problem statement that such a property adjusts both the requirements of stability and optimality. Next, a description of the proposed approach is presented, theoretical formulations are given, and its efficiency is demonstrated on the computational examples in mobile robot control tasks.

Синтез управління стабілізацією геостаціонарного супутника у точці стояння

Розроблено методи та алгоритми балістичного забезпечення управління стабілізацією довготи точки стояння геостаціонарного супутника (ГСС). Еволюція поточних координат ГСС моделювалася диференціальними рівняннями руху матеріальної точки у центральному гравітаційному полі з урахуванням обмежених структурно-параметричних збурень відомої інтенсивності, викликаних загальним впливом Сонця, Місяця, відмінністю гравітаційного поля Землі від центрального тощо. Конкретне математичне моделювання цих збурень не розглядалося, використовувалися лише властивості їх загальної обмеженості за нормою. Для синтезу управління застосовувався відомий в теорії керування орієнтацією (кутовим положенням космічного апарата) аналог — метод декомпозиції загальної задачі синтезу на кінематичну і динамічну. Для їх вирішення використовувалися відомі узагальнення прямого методу Ляпунова дослідження стійкості розвʼязків диференціальних рівнянь на дослідження стійкості замкнених обмежених множин (конкретно багатовимірних еліпсоїдів) у їх фазових просторах. Поряд із методом синтезу управління стабілізацією довготи точки стояння ГСС запропоновано методи еліпсоїдального оцінювання, викликані впливом згаданих збурень помилок стабілізації, що встановилися. Методи засновані на побудові зовнішніх еліпсоїдальних оцінок множин досяжнос­ті та граничних множин у фазових просторах динамічних систем з обмеженими структурно-параметричними збуреннями. Запропоновано також метод отримання гарантованих інтервальних оцінок помилок стабілізації, що встановилися, по кожній з координат. Ефективність запропонованих методів керування ілюструється результатами компʼютер­ного моделювання.

Control Training

The paper devotes to a new conception ”Machine learning control”. The mathematical formulation of this term is presented. It is shown, that a numerical method for solution of the control general synthesis problem belongs to the machine learning control. In common case the machine learning control is a search some control function. There are two approaches to this problem. First approach consists of definition of the function with accuracy to some unknown parameters. A search of these parameters is a machine learning. Artificial neural network technology belongs to the first approach. The second approach consists of search mathematical expression of control function by computer. This is a search of function structure and parameters together. Now so far there is only one way to realize this approach. It is symbolic regression. The paper describes symbolic regression technology in common case and some examples of symbolic regression applications for the control synthesis problem are presented.

Shaped Beam Synthesis of Arbitrary Arrays via Linear Programming

A simple procedure for the synthesis of shaped beams with arbitrary arrays is presented. The steps that reduce this general synthesis problem to a linear programming one, which is then called iteratively, are detailed. Since linear program solvers are largely and freely available, the additional effort to solve the shaping beam synthesis problem is limited. Numerical applications and comparisons to results found in the literature are performed to show the efficiency of the proposed procedure. To illustrate its versatility, the shaped-beam pattern synthesis is also presented for a conformal array.

Observation and modeling of polarized light from scarab beetles

The light reflected from scarab beetles illuminated with unpolarized white light is analyzed ellipsometrically and displayed as the sum of an elliptically polarized spectrum I(p) and an unpolarized spectrum I(u). A chirped stack of chiral resonators, each with a characteristic Bragg wavelength and partial realignment of birefringent material to a fixed axis, is proposed as a model for simulation of both reflection and polarization spectra. Possible mechanisms that effectively eliminate impedance mismatch at the air-elytron interface and allow some beetles to exhibit nearly perfect circularly polarized reflections are discussed. Results are presented for three representative beetles, Ischiosopha bifasciata, which is shown to be a narrowband left-circular polarizer; Chrysophora chrysochlora, a broadband left-circular polarizer; and Chrysina woodi, an elliptical polarizer. The methods that are developed are applicable to the more general problem of synthesis of reflectors with prescribed reflection and polarization spectra.

Synthesis approach to the determination of optimal waste blends under uncertainty

AbstractThe generalized approach to the problem of synthesis under uncertainty is to formulate it as a stochastic optimization problem that involves optimization of a probabilistic function obtained by sampling over uncertain variables. The computational burden of this approach can be extreme and depends on the sample size used for characterizing the parametric uncertainties. A new and efficient approach for stochastic process synthesis is presented. The goals are achieved through an improved understanding of the sampling phenomena based on the concepts derived from fractal geometry. A new algorithm for stochastic optimization based on these concepts to accelerate the process of synthesis under uncertainty is presented. Apart from the benchmark HDA synthesis problem, a real‐world problem of synthesizing optimal waste blends is analyzed to test the applicability of this novel approach in addressing the general problem of synthesis under uncertainty. The solution of this real‐world large‐scale synthesis problem is presented under uncertainty through the application of the new stochastic annealing algorithm, which takes into consideration novel sampling methods used in probabilistic analysis of process models.

LMI-based controller synthesis: a unified formulation and solution

This paper proposes a unified approach to linear controller synthesis that employs various LMI conditions to represent control specifications. We define a comprehensive class of LMIs and consider a general synthesis problem described by any LMI of the class. We show a procedure that reduces the synthesis problem, which is a BMI problem, to solving a certain LMI. The derived LMI condition is equivalent to the original BMI condition and also gives a convex parametrization of all the controllers that solve the synthesis problem. The class contains many of widely-known LMIs (for H∞ norm, H2 norm, etc.), and hence the solution of this paper unifies design methods that have been proposed depending on each LMI. Further, the class also provides LMIs for multi-objective performance measures, which enable a new formulation of controller design through convex optimization. © 1998 John Wiley & Sons, Ltd.

Temporal structuring of acoustic segments in speech communication

The following problems were studied on the domain of the temporal structuring of speech utterance: the determination of algorithms of synthesis of the rhythmic patterns of the utterance, the problem which is often referred to as preprogramming of the temporal organization of the speech signal being part of a more general problem of synthesis (generation) of prosodic patterns of the utterance; the determination of signals used in the information exchange between linguistic and neuro-physiological levels of speech analysis and synthesis; the rules determining the conversion of transformation of the rhythmic patterns of the utterance into real-time intervals between articulatory positions and movements. The character of a durational correlation which has been revealed in this experiment (with the use of the special correlation coefficient ρ and the test of the H0-hypothesis) made it possible to define three types of temporal correlation: microcorrelation (for subsound and sound levels), mesocorrelation (for syllabic level), and macrocorrelation (for the level of phrase rhythmic structures—phonetic words). The integral temporal organization of speech utterance is determined on the one hand by a lower level effect—coarticulation, and on the other hand by a higher level effect—the rhythmic patterns of a phrase.

Stochastic optimization based algorithms for process synthesis under uncertainty

In this paper, a stochastic programming framework is presented to address process synthesis problems under uncertainty. The framework is based on a two-state stochastic MINLP formulation for the maximization of a function comprising the expected value of the profit, operating and fixed costs of the plant. Three alternative integration schemes are proposed for the evaluation of the expectancy, and their computational performance is studied through general synthesis problems. Results from different implementations on advance computer architectures are also reported to analyze the parallelization of the algorithm. The effects of the number of integration points, the size of the problem, and the number of uncertain parameters on the computational performance are also discussed.

Stochastic programming in process synthesis: A two-stage model with MINLP recourse for multiperiod heat-integrated distillation sequences

This paper presents a two-stage stochastic programming approach with MINLP recourse for the synthesis problem of heat integrated distillation sequences that can handle prespecified changes in the composition and/or flowrate of the multicomponent feed to the separation system for a finite number of periods of operation. A new synthesis strategy is proposed that combines the aspects of a superstructure approach with a partitioning of the design variables into two classes: structural and periodic. Structural design variables comprise the fixed elements of a design that are common to all operating conditions, while the periodic design variables are adjustable quantities that can be changed for optimal operation in each period. The synthesis strategy identifies the optimal separation sequence and selection of heat exchanger units that can accommodate the different periods of operation. In addition, for each selected unit, the approach provides simultaneous optimization of the column press ure, reflux ratio, number of trays, diameter and heat integration/exchange matches. The column pressure, reflux, number of trays and diameter are treated explicitly as continuous variables in the model. The mathematical formulation that results is a large-scale mixed-integer nonlinear programming (MINLP) problem. The structure of the problem can be exploited by viewing the multiperiod design problem as a two-stage stochastic programming problem with the feed composition and flowrate as the uncertain parameters. The different periods of operation provide the discretization of the uncertainty and the multiple scenarios of operation have (MINLP) recourse. A nested solution procedure is detailed that combines the Generalized Benders Decomposition and the Outer Approximation/Equality Relaxation algorithms. Emphasis is given to the application of this type of approach to the general synthesis problem and its potential for extension to design problems under uncertainty and/or flexibility requirements. Application of the approach is illustrated through an example problem.

Frequency-manipulated speech using a simulated constant-Q filter bank analyzer

A constant-Q spectrum analyzer was implemented digitally, using the Fourier-Mellon transform, to synthesize spectrally manipulated speech signals for audible and visual display and especially to produce frequency-transposed speech as an aid for the deaf. The work reported here was to assess the quality and intelligibility of sounds consisting of low-pass-filtered speech plus one "sine" wave, representing the high-frequency information, superimposed upon it. One-eighth-octave filters were used for analysis, and the one having the highest output was chosen to be transposed down in frequency. The general problem of synthesis where the high-frequency information comes at a higher rate than the low-frequency information will be discussed. A comparison of the visual patterns produced with linear- and logarithmic-frequency analysis will be shown and inferences drawn as to the extraction of transient speech information. Interference between the transposed second formant and the untransposed first formant will be illustrated. Preliminary tests of the intelligibility of diagnostic rhyming words incorporated in common phrases will be reported.

Modal Control Procedures for the Synthesis of Damping Actions in Multimachine Electric Power Systems

This paper deals with the synthesis of control actions in multimachine electric power systems, through modal (pole placement) techniques. The analysis is carried out with reference to a simplified linearized model, strictly oriented to the representation of the electromechanical oscillations. Particular reference is made to the synthesis of local additional feedbacks on machine excitation controls, or turbine controls, in order to achieve a desired improvement of oscillation dampings. After some comparison with other possible synthesis procedures, an iterative procedure is outlined, based on the inverse resolution of the characteristic equation for each assigned characteristic root; successful numerical applications are recalled. The considerations developed in the paper may look suitable also for the formulation and solution of more general synthesis problems.

Application of Structural Analysis of Algebraic Equations to the General Synthesis of a Process System

In this paper, pressuming that both the necessary kind and number of unit process have been given a priori, the general synthesis problem is dealt with introducing the concept of a terminal element expression. This expression is derived for each unit process by carrying out a structural analysis of the units model equations. The terminal expression, shows which variables in the model equations can be freely assigned arbitrary values.System structures are generated combinatorially by connecting the input and output terminals of the unit processes. The terminal elements then facilitate the mathematical solution of the structures. Identical structures are classified into equivalence classes so only topologically different structures obtained.An example of the synthesis of a multi-effect evaporator system is presented.

Synthesis of optimal processing system by an integrated approach

A general synthesis problem is defined as that of determining an optimal system structure by extracting it from an enlarged system structure generated by splitting streams into alternative routes. When the optimized splitting ratio is close to 0 or 1, one of the alternative streams can be eliminated to give the optimal synthesis. Box's Complex method, is used to solve an actual example amenable to the integrated approach.

A method of solving some unstable problems of optimal control synthesis

A PROBLEM in the theory of optimal processes with a rapid increase in the phase and conjugate variables is investigated. A method of reducing the unstable problem studied to an optimal control problem with restricted values of the phase coordinates and conjugate variables is proposed. The computational aspects of the method are discussed. As is well-known the general synthesis problem of optimal control in the presence of random perturbations has so far not been solved, and at the present time intensive research is going on into various particular classes of problems for which the solutions have been brought to a successful conclusion. In particular, in [1], Chapter VI, it was shown how the use of canonical expansions and statistical linearization makes it possible to reduce an extensive class of special non-linear synthesis problems to an optimal control problem; the canonical representation enables the characteristics of the random process to be described in a convenient form, and statistical linearization reduces the consideration of non-linear systems of extremely general form to the analysis of systems which, although they are non-linear, possess a number of characteristic features, simplifying their study. The practical use of the method explained in [1] encounters some difficulties. In the first place it must be mentioned that the optimal control problem obtained has considerably greater dimension than the original synthesis problem. In addition, another difficulty is encountered connected with the instability of the solutions of the systems of equations for the phase coordinates and the conjugate variables. In [2] and [3] a method is explained which enables the difficulties connected with the existence of rapidly increasing solutions of the conjugate system to be avoided. In this paper we consider an approach helping to overcome the difficulties connected with the rapid growth of the solutions of the systems of equations for the phase coordinates and the conjugate variables, and facilitating the use of the standard iterative method of [4] for the solution of unstable problems.

Some equivalences between equally and unequally spaced arrays

General analytical expressions are presented for unequally spaced arrays. These relations allow for the analysis of the nonuniformly spaced array in terms of its equivalent uniformly spaced array. The inherent broad-band qualities of the nonuniformly spaced array are discussed. Some equivalence is made between the amplitude and spatial variation in the uniformly and nonuniformly spaced array. The general synthesis problem is discussed. An array with monotonically increasing interelement spacings is presented as an example of the theory.

A General Method for Time Domain Network Synthesis

This paper presents one approach to the general problem of synthesis in the time domain. Given an arbitrary time function as the speci- fied input to an electrical network and another such time function as the desired output, it shows how to go about designing the net- work. These arbitrary time functions may be prescribed either graphically, analytically, or merely as sequences of values at stated intervals of time. The first step is to write the input and output time functions in time-sequence form. Then synthetic division of the output time se- quence by the input time sequence yields the sequence of areas under the impulse curve. The power series expansion of the Laplace trans- form is obtained from this sequence. A rational-function approxima- tion to this power series may then be calculated and, as a result of the special constraints used, the inverse Laplace transform of this ra- tional function will be a close approximation throughout the time domain to the required impulse response. The paper contributes to network theory a simple and straight for- ward synthesis method for the time domain, which is economical of computational time and effort. Examples are included to illustrate the method.

On The Number of Symmetry Types of Boolean Functions of n Variables

In recent years Boolean Algebra has come to play a prominent role in the analysis and synthesis of switching circuits [1; 4]. One general synthesis problem in which this algebra has proved useful is the following. Let there be given n input leads each of which can assume one of two possible states. It is desired to construct a network with these n input leads and a single output lead also capable of assuming either of two states. Furthermore, the state of the output lead for each of the 2n states of the input leads is prescribed.

The Synthesis of Two-Terminal Switching Circuits

THE theory of switching circuits may be divided into two major divisions, analysis and synthesis. The problem of analysis, determining the manner of operation of a given switching circuit, is comparatively simple. The inverse problem of finding a circuit satisfying certain given operating conditions, and in particular the best circuit is, in general, more difficult and more important from the practical standpoint. A basic part of the general synthesis problem is the design of a two-terminal network with given operating characteristics, and we shall consider some aspects of this problem.