Optimal Synthesis Problem Research Articles

Optimal Synthesis of a Satellite Attitude Control System under Constraints on Control Torques and Velocities of Reaction Wheels

The problem of optimal synthesis of a nonlinear system’s control law parameters of satellite attitude control under constraints is considered. The maximum stability degree of a system is considered as an optimality criterion. The reaction wheels’ control moments and angular velocities achievable within the drives’ physical characteristics are considered as constraints. A linear model of the system converted from the original nonlinear model was used to solve the problem. The decomposition method, based on the transition from real time to relative time, is used to separate the tasks of optimality criterion maximization and constraints consideration. A method of synthesizing the optimal form of system transient process according to the maximum stability degree criterion is developed. An analytical method for determining the optimal values of control law parameters is proposed, based on the structural features of the linear differential equations system. A method that takes into account constraints on control moments and angular velocities of reaction wheels, based on transition scale from relative time to real time and its calculation algorithm, ensuring that conditions of all constraints are met, is developed. An example of solving the problem of optimal system synthesis is considered. The results demonstrate the effectiveness and simplicity of the proposed methods and algorithm for targeted selection of a system’s technical characteristics, taking into account constraints on reaction wheels’ maximum angular velocities and control moments values.

Toward Optimal Synthesis of Discrete-Time Hopfield Neural Network.

In this research brief, the relationship between eigenvectors (with {+1, -1} components) of a synaptic weight matrix W and the stable/anti-stable states of discrete-time Hopfield associative memory (HAM) is established. Also, the synthesis of W with desired stable/anti-stable states using spectral representation of W in even/odd dimension is discussed when the threshold vector is a non-zero vector. Freedom in choice of eigenvalues is capitalized to improve the noise immunity of the Hopfield neural network (HNN). Also, the problem of optimal synthesis of Hopfield Associative memory is formulated.

H∞‐optimal observer design for systems with multiple delays in states, inputs and outputs: A PIE approach

AbstractThis article investigates the ‐optimal estimation problem of a class of linear system with delays in states, disturbance input, and outputs. The estimator uses an extended Luenberger estimator format which estimates both the present and history states. The estimator is designed using an equivalent Partial Integral Equation (PIE) representation of the coupled nominal system. The advantage of the resulting PIE representation is compact and delay free—obviating the need for commonly used bounding technique such as integral inequalities which typically introduces conservatism into the resulting optimization problem. The ‐optimal estimator synthesis problem is then reformulated as a Linear Partial Inequality (LPI)—a form of convex optimization using operator variables and inequlities. Such LPI‐based optimization problems can be solved using semidefinite programming via the PIETOOLS toolbox in Matlab. Compared with previous work, the proposed method simplifies the analysis and computation process and resulting in observers which are non‐conservtism to 4 decimal places when compared with Pad‐based ODE observer design methodologies. Numerical examples and simulation results are given to illustrate the effectiveness and scalability of the proposed approach.

Synthesis of optimal covert sensor–actuator attackers for discrete-event systems

This work introduces an approach for the synthesis of optimal covert sensor–actuator attackers in the context of discrete-event systems (DES). Building upon existing works on optimal supervisor synthesis, on one hand, and the base model construction in the transformation of covert sensor–actuator attacker synthesis to supervisor synthesis, on the other hand, we show how the optimal covert sensor–actuator attacker synthesis problem could be transformed to the optimal supervisor synthesis problem, thus generalizing its logic counterpart. We consider several different types of optimization objectives, such as (1) minimization of attack energy cost, and (2) minimization of time cost to cause damage infliction; for the latter one, asynchronous event firings and concurrent event firings at the plant are both considered. We provide the necessary and sufficient conditions for the existence of an optimal attacker for both the energy minimization case and damage infliction time minimization case. Thus, this work may potentially provide a unified approach for the optimal synthesis of covert sensor–actuator attackers in different setups.

A Benders decomposition framework for the optimization of disjunctive superstructures with ordered discrete decisions

AbstractThis study introduces the logic‐based discrete‐Benders decomposition (LD‐BD) for Generalized Disjunctive Programming (GDP) superstructure problems with ordered Boolean variables. The key idea is to obtain Benders cuts that use neighborhood information of a reformulated version of Boolean variables. These Benders cuts are iteratively refined, which guarantees convergence to a local optimum. A mathematical case study, the optimization of a network with Continuous Stirred‐Tank Reactors (CSTRs) in series, and a large‐scale problem involving the design of a distillation column are considered to demonstrate the features of LD‐BD. The results from these case studies have shown that the LD‐BD method exhibited good performance by finding attractive locally optimal solutions relative to existing logic‐based solvers for GDP problems. Based on these tests, the LD‐BD method is a promising strategy to solve optimal synthesis problems with ordered discrete decisions emerging in chemical engineering applications.

Optimal synthesis of a planar mechanism using Matlab: Example of slider crank in a rowing motion

<abstract> <p>This paper illustrates the conducted effort to introduce the methodology of optimal synthesis of mechanisms through an engineering problem under Matlab. This project is part of a first course on poly-articulated mechanisms and robotics at the graduate level. The course combines both the theoretical and implementation under Matlab aspects to achieve its goals. The example of the rowing machine is considered to introduce the crank-slider mechanism and the kinematic analysis using complex numbers. The mechanism is associated with a spring to ensure the device simulating the resistance in the rowing bench simulator. The optimal synthesis problem is formulated for the desired effort to perform and solved using the Sequential Quadratic Programming method. All developments are implemented under Matlab.</p> </abstract>

Comparative Study on the Synthesis of Path-Generating Four-Bar Linkages Using Metaheuristic Optimization Algorithms

Four-bar linkages are one of the most widely used mechanisms in industries. This paper presents a comparative study on the accuracy and efficiency of the optimum synthesis of path-generating four-bar linkages using five metaheuristic optimization algorithms. The utilized metaheuristic methods included two swarm intelligence-based algorithms, i.e., particle swarm optimization and hybrid particle swarm optimization, and three evolutionary-based algorithms, i.e., differential evolution, ensemble of parameters and mutation strategies in differential evolution, and linearly ensemble of parameters and mutation strategies in differential evolution. The objective function to be minimized is the sum of squares of the distance between the generated points and the precision points of a coupler point. The optimal design of four-bar linkages must meet the Grashof’s criteria and exhibit sequential constraints that can prevent the occurrence of order defect. This study investigated five representative cases of the dimensional synthesis of four-bar path generators with and without prescribed timing and compared the optimal solutions of the utilized five metaheuristic methods to those of previously reported algorithms in literature. The improved metaheuristic methods exhibited superior optimal solution and enhanced reliability compared to the original methods. Moreover, three improved metaheuristic methods were not only easy implemented, but also more efficient for solving the optimal synthesis problems, particularly for high dimensional problems.

Neural metamodelling of fields: Towards a new deal in computational electromagnetics

In computational electromagnetism there are manyfold advantages when using machine learning methods, because no mathematical formulation is required to solve the direct problem for given input geometry. Moreover, thanks to the inherent bidirectionality of a convolutional neural network, it can be trained to identify the geometry giving rise to the prescribed output field. All this puts the ground for the neural meta-modeling of fields, in spite of different levels of cost and accuracy. In the paper it is shown how CNNs can be trained to solve problems of optimal shape synthesis, with training data sets based on finite-element analyses of electric and magnetic fields. In particular, a concept of multi-fidelity model makes it possible to control both prediction accuracy and computational cost. The shape design of a MEMS design and the TEAM workshop problem 35 are considered as the case studies.

An efficient combined local and global search strategy for optimization of parallel kinematic mechanisms with joint limits and collision constraints

The optimization of parallel kinematic manipulators (PKM) involve several constraints that are difficult to formalize, thus making optimal synthesis problem highly challenging. The presence of passive joint limits as well as the singularities and self-collisions lead to a complicated relation between the input and output parameters. In this article, a novel optimization methodology is proposed by combining a local search, Nelder–Mead algorithm, with global search methodologies such as low discrepancy distribution for faster and more efficient exploration of the optimization space. The effect of the dimension of the optimization problem and the different constraints are discussed to highlight the complexities of closed-loop kinematic chain optimization. The work also presents the approaches used to consider constraints for passive joint boundaries as well as singularities to avoid internal collisions in such mechanisms. The proposed algorithm can also optimize the length of the prismatic actuators and the constraints can be added in modular fashion, allowing to understand the impact of given criteria on the final result. The application of the presented approach is used to optimize two PKMs of different degrees of freedom.

Sparse Control Synthesis for Uncertain Responsive Loads With Stochastic Stability Guarantees

Recent studies have demonstrated the potential of flexible loads in providing frequency response services. However, uncertainty and variability in various weather-related and end-use behavioral factors often affect the demand-side control performance. This work addresses this problem with the design of a demand-side control to achieve frequency response under load uncertainties. Our approach involves modeling the load uncertainties via stochastic processes that appear as both multiplicative and additive to the system states in closed-loop power system dynamics. Extending the recently developed mean square exponential stability (MSES) results for stochastic systems, we formulate multi-objective linear matrix inequality (LMI)-based optimal control synthesis problems to not only guarantee stochastic stability, but also promote sparsity, enhance closed-loop transient performance, and maximize allowable uncertainties. The fundamental trade-off between the maximum allowable ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">critical</i> ) uncertainty levels and the optimal stochastic stabilizing control efforts is established. Moreover, the sparse control synthesis problem is generalized to the realistic power systems scenario in which only partial-state measurements are available. Detailed numerical studies are carried out on IEEE 39-bus system to demonstrate the closed-loop stochastic stabilizing performance of the sparse controllers in enhancing frequency response under load uncertainties; as well as illustrate the fundamental trade-off between the allowable uncertainties and optimal control efforts.

Об абсолютном скольжении асинхронного двигателя

Рассмотрена возможность оптимального частотного управления асинхронным электродвигателем путем формирования относительного значения частоты питающего напряжения как суммы относительной частоты вращения ротора двигателя и его абсолютного скольжения. При этом аналитическая форма записи абсолютного скольжения получена как решение задачи оптимального синтеза системы управления электродвигателем с целью минимизации целевого интегрального функционала качества, заданного в общем виде. Выявлено, что абсолютное скольжение может быть представлена в виде алгебраической суммы его слагаемых. Рассмотрен конкретный пример минимизации квадратичного функционала качества с индикатрисой в виде квадрата разности требуемого и текущего значений электромагнитного моментов электродвигателя. Показано, что абсолютное скольжение представлено суммой двух слагаемых, условно названных статической и динамической составляющими. Приведены расчеты, показывающие влияние каждой составляющей на качество управления. Делаются выводы о целесообразности учета динамической составляющей в зависимости от режима работы электродвигателя.

ОБ ИСПОЛЬЗОВАНИИ ЭВРИСТИЧЕСКИХ АЛГОРИТМОВ В ЗАДАЧАХ ОПТИМАЛЬНОГО ПАРАМЕТРИЧЕСКОГО СИНТЕЗА

The problem of optimal synthesis of engineering systems is considered, with due account for the ran-dom changes in their production and operational parameters. A number of ways and means of creating effective heuristic algorithms for multidimensional search optimization are proposed to solve the emerging problems. The paper focuses on the bat algorithm and the creation of its parallel modifica-tion.

Задача оптимального синтеза двоичных 4-D-нелинейных модулярных динамических систем

Задача оптимального синтеза двоичных 4-D-нелинейных модулярных динамических систем

Near-Optimal Reactive Synthesis Incorporating Runtime Information.

We consider the problem of optimal reactive synthesis - compute a strategy that satisfies a mission specification in a dynamic environment, and optimizes a performance metric. We incorporate task-critical information, that is only available at runtime, into the strategy synthesis in order to improve performance. Existing approaches to utilising such time-varying information require online re-synthesis, which is not computationally feasible in real-time applications. In this paper, we pre-synthesize a set of strategies corresponding to candidate instantiations (pre-specified representative information scenarios). We then propose a novel switching mechanism to dynamically switch between the strategies at runtime while guaranteeing all safety and liveness goals are met. We also characterize bounds on the performance suboptimality. We demonstrate our approach on two examples - robotic motion planning where the likelihood of the position of the robot's goal is updated in real-time, and an air traffic management problem for urban air mobility.

On bandwidth maximization of fixed-geometry arrays through convex programming

ABSTRACTWe propose a new approach to solve the problem of optimal power synthesis of array antennas, so that maximum possible bandwidth can be granted to fixed sidelobe-level performances. The proposed approach can be applied to any kind of fixed-geometry array that radiates pencil beams and to linear equispaced arrays that generate shaped patterns. The designing problem is cast as a sequence of Convex Programming optimizations. Numerous numerical experiments, including full-wave synthesis of realistic antennas, were carried out and their results discussed here to assess the array antennas’ capability of achieving ultra-wideband performances.

МЕТОД ОПТИМАЛЬНОГО СИНТЕЗУ ІНФОРМАЦІЙНО-ВИМІРЮВАЛЬНИХ СИСТЕМ

У статті акцентовано увагу на існуючу проблему оптимального синтезу (побудови) інформаційно-вимірювальних систем (ІВС). Показано шляхи вирішення цієї проблеми за рахунок використання кривих обміну за Гуткіним Л.С. За допомогою яких можливо пояснити, які ІВС оптимальніші за своїми параметрами, як погоджувати показники якості вимірювань параметрів, як здолати потребу у великій апріорній невизначеності, не зменшуючи точності вимірювань, як пояснити суперечність деяких відомих теорій, як погоджувати апріорний діапазон з фізичним діапазоном, як використати отримані апріорні дані, як впливає на точність вимірювань змінний рівень сигналу, як впливає точність налаштування на точність вимірювань, як можна скоротити час пошуку сигналу, як впливає на автоматичне супроводження характер процесу, що стежить, тощо. Запропонований метод оптимального синтезу ІВС справедливий для ІВС будь-якого типу за сигналами, що використовуються, та різних параметрів, що вимірюються.

Metaheuristic optimization of building structures with different level of safety

A methodology for solving the optimal synthesis problems of bearing and enclosing structures is proposed, including for steel frames, column reinforced concrete foundations, heat-transmission shell using genetic iterative diagrams and triangulation procedures. The approaches to finding solutions for buildings of normal and increased levels of responsibility are considered. A three-stage diagram is proposed that includes, at the first stage, the synthesis of the topology of the steel frame, at the second stage, the optimization of its shape and parameters of the rods, and at the third stage, the consideration of possible emergency situations. For buildings with a normal level of responsibility in the particular case, the use of the first two stages is allowed. The structure of the frames is synthesized by using the algorithm of plane triangulation of a set of points, which are meant as structural joints. The design parameters are selected using an improved genetic algorithm adapted for solving problems of this type. An example of the synthesis of the building structure of a weighted vehicle is considered, illustrating the performance and high efficiency of the approach under consideration.

Algorithm of the Generalized Method of Potentials for the Problem of Optimal Linear Synthesis of a Communication Network

A new efficient algorithm for solving the linear separable problem of the synthesis of a communication network called the generalized method of potentials is considered and justified. It is a generalization of the known method of potentials for solving the standard transportation problem. The finiteness of the proposed algorithm is proved.

Formation of base data list and content for determining of the ways for military teams procurement with armament

Maintenance of samples of weapons is carried out at the stages of their life cycle and is carried out on the basis of coordination of actions of the customer and the consumer with a wide range of organizations from the main developer to the co-executors, which does not exclude the occurrence of conflict situations. This leads to the problem of implementing the optimal synthesis of such a complex system and does not allow to direct efforts to achieve the extremum of the target function of the system as a whole. Therefore, the emergence of such a problem and the existing conflicts in the process of determining the means of providing arms to military formations is considered as a complex organizational system, and the difficulties of direct solution of the problem of optimal synthesis in this case are related to: the interconnections of a complex system (between systems of the lower level and elements of the system); limited programming abilities; the construction of a mathematical model, etc.; and cause the need to find solutions to this problem.&#x0D; The methods developed at present allow analytically to calculate the technical perfection of the weapons samples that are considered for providing military formations, as investigated when choosing for procurement or development. Such tasks are deterministic, but, considering costs at all stages of the life cycle, there may be stochastic (probable ones) that can be solved by expert methods. At present, the list and content of the source data when choosing ways of providing weapons are not defined at all stages. Thus, having them strictly non-formalized, the statement of the problem of synthesis is carried out under conditions of uncertainty, which in most cases is solved by heuristic methods, which in turn allows elements of subjectivity.&#x0D; Having determined the list and content of the initial data, it is possible to pre-implement the calculations in cost form (strictly mathematical) in the form of expenses, having carried out the projection of expenditures at the stage of the weapon’s life cycle, and such a list to be chosen according to the criterion of the problem of synthesis, while defining the criteria of the restrictions, and to use these data for assessing the quality of this type of weapons and the cost of the stages of their life cycle. Also, in case of incomplete receipt of such data in cost form, with their partial, such an assessment will allow to determine between the corresponding methods when solving the problem of choosing ways of providing arms in the medium term. Even if this method is not analytical, then the relevant statistics will help to reduce the degree of uncertainty and subjectivism when choosing ways to provide armed skills by expert means.

DEVELOPMENT OF EXCITATION STRUCTURE RBF-METAMODELS OF MOVING CONCENTRIC EDDY CURRENT PROBE

Introduction. The work is devoted to metamodels creation of surface circular concentric eddy current probe. Formulation of the problem. In the problem of surface circular concentric eddy current probe synthesis in the general formulation, apriori given desired eddy currents density distribution in the control zone was used. The realization of the optimal synthesis problem involves a multiple solution to the analysis problem for each current structure of numerical calculations excitation, which are very costly in terms of computational and time costs, which makes it impossible to solve the synthesis problem in the classical formulation. By solving the critical resource intensiveness problem, there is the surrogate optimization technology using of that uses the surface circular concentric eddy current probe metamodel, which is much simpler in realization and is an approximation of the exact electrodynamic model. Goal. Creation of surface circular concentric eddy current probe RBF-metamodels, which can be used to calculate eddy currents density distribution in the control zone and suitable for use in optimal synthesis problems. Method. To develop an approximation model, a mathematical apparatus for artificial neural networks, namely, RBF–networks, has been used, whose accuracy has been increased with the help of the neural networks committee. Correction of errors in the committee was reduced by applying the bagging procedure. During the network training the regularization technique is used, which avoids re-learning the neural network. The computer experiment plan was performed using the Sobol LPt–sequences. The obtained multivariable regression model quality evaluation was performed by checking the response surface reproducibility correctness in the entire region of variables variation. Results. The modelling of eddy currents density distribution calculations on exact electrodynamic mathematical models in the experimental plan points are carried out. For the immovable and moving surface circular concentric eddy current probe, RBF–metamodels were constructed with varying spatial coordinates and radius. Scientific novelty. Software was developed for eddy currents density distribution calculation in the surface circular concentric eddy current probe control zone taking into account the speed effect on exact electrodynamic mathematical models and for forming experiment plan points using the Sobol LPt–sequences. The geometric surface circular concentric eddy current probe excitation structures models with homogeneous sensitivity for their optimal synthesis taking into account the speed effect are proposed. Improved computing technology for constructing metamodels. The RBF-metamodels of the surface circular concentric eddy current probe are built and based on the speed effect. Practical significance. The work results can be used in the surface circular concentric eddy current probe synthesis with an apriori given eddy currents density distribution in the control zone.