Control vector structure for a minimal-time circuit optimization process

2015 ◽  
Author(s):  
A. Zemliak ◽  
F. Reyes ◽  
T. Markina
Keyword(s):  
Optimization Process ◽  
Circuit Optimization ◽  
Control Vector ◽  
Minimal Time ◽  
Vector Structure

Analysis of the structure of different optimization strategies

2020 ◽  
Vol 39 (3) ◽  
pp. 583-593
Author(s):  
Alexander Zemliak ◽  
Jorge Espinosa-Garcia
Keyword(s):  
Lyapunov Function ◽  
Dynamic System ◽  
Optimal Structure ◽  
Optimization Process ◽  
Main Element ◽  
Circuit Optimization ◽  
Control Vector ◽  
Processor Time ◽  
Content Type ◽  
Cpu Time

Purpose In this paper, on the basis of a previously developed approach to circuit optimization, the main element of which is the control vector that changes the form of the basic equations, the structure of the control vector is determined, which minimizes CPU time. Design/methodology/approach The circuit optimization process is defined as a controlled dynamic system with a special control vector. This vector serves as the main tool for generalizing the problem of circuit optimization and produces a huge number of different optimization strategies. The task of finding the best optimization strategy that minimizes processor time can be formulated. There is a need to find the optimal structure of the control vector that minimizes processor time. A special function, which is a combination of the Lyapunov function of the optimization process and its time derivative, was proposed to predict the optimal structure of the control vector. The found optimal positions of the switching points of the control vector give a large gain in CPU time in comparison with the traditional approach. Findings The optimal positions of the switching points of the components of the control vector were calculated. They minimize processor time. Numerical results are obtained for various circuits. Originality/value The Lyapunov function, which is one of the main characteristics of any dynamic system, is used to determine the optimal structure of the control vector, which minimizes the time of the circuit optimization process.

Generalized Methodology Application for System Design

2022 ◽  
Vol 21 ◽  
pp. 10-17
Author(s):  
Alexander Zemliak
Keyword(s):  
System Design ◽  
Design Process ◽  
Classical Problem ◽  
Computer Time ◽  
Time Algorithm ◽  
Structural Basis ◽  
Circuit Optimization ◽  
Design Strategies ◽  
Analogue Circuit ◽  
Minimal Time

The design process for analogue circuit design is formulated on the basis of the optimum control theory. The artificially introduced special control vector is defined for the redistribution of computational costs between network analysis and parametric optimization. This redistribution minimizes computer time. The problem of the minimal-time network design can be formulated in this case as a classical problem of the optimal control for some functional minimization. There is a principal difference between the new approach and before elaborated methodology. This difference is based on a higher level of the problem generalization. In this case the structural basis of design strategies is more complete and this circumstance gives possibility to obtain a great value of computer time gain. Numerical results demonstrate the effectiveness and prospects of a more generalized approach to circuit optimization. This approach generalizes the design process and generates an infinite number of the different design strategies that will serve as the structural basis for the minimal time algorithm construction. This paper is advocated to electronic systems built with transistors. The main equations for the system design process were elaborated.

scholarly journals Circuit Optimization Study According to the Maximum Principle

2021 ◽  
Vol 20 ◽  
pp. 362-371
Author(s):  
Alexander Zemliak
Keyword(s):  
Maximum Principle ◽  
Traditional Approach ◽  
Optimization Procedure ◽  
Circuit Optimization ◽  
Control Vector ◽  
Processor Time ◽  
The Maximum Principle ◽  
Cpu Time ◽  
Optimization Study ◽  
Time Minimization

The minimization of the processor time of designing can be formulated as a problem of time minimization for transitional process of dynamic system. A special control vector that changes the internal structure of the equations of optimization procedure serves as a principal tool for searching the best strategies with the minimal CPU time. In this case a well-known maximum principle of Pontryagin is the best theoretical approach for finding of the optimum structure of control vector. Practical approach for realization of the maximum principle is based on the analysis of behavior of a Hamiltonian for various strategies of optimization. The possibility of applying the maximum principle to the problem of optimization of electronic circuits is analyzed. It is shown that in spite of the fact that the problem of optimization is formulated as a nonlinear task, and the maximum principle in this case isn't a sufficient condition for obtaining a minimum of the functional, it is possible to obtain the decision in the form of local minima. The relative acceleration of the CPU time for the best strategy found by means of maximum principle compared with the traditional approach is equal two to three orders of magnitude.

A modified genetic algorithm for system optimization

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Alexander Zemliak
Keyword(s):  
Genetic Algorithm ◽  
Fitness Function ◽  
System Optimization ◽  
High Accuracy ◽  
Optimization Process ◽  
Processing Unit ◽  
Local Minima ◽  
Control Vector ◽  
Content Type ◽  
Cpu Time

Purpose In this paper, the previously developed idea of generalized optimization of circuits for deterministic methods has been extended to genetic algorithm (GA) to demonstrate new possibilities for solving an optimization problem that enhance accuracy and significantly reduce computing time. Design/methodology/approach The disadvantages of GAs are premature convergence to local minima and an increase in the computer operation time when setting a sufficiently high accuracy for obtaining the minimum. The idea of generalized optimization of circuits, previously developed for the methods of deterministic optimization, is built into the GA and allows one to implement various optimization strategies based on GA. The shape of the fitness function, as well as the length and structure of the chromosomes, is determined by a control vector artificially introduced within the framework of generalized optimization. This study found that changing the control vector that determines the method for calculating the fitness function makes it possible to bypass local minima and find the global minimum with high accuracy and a significant reduction in central processing unit (CPU) time. Findings The structure of the control vector is found, which makes it possible to reduce the CPU time by several orders of magnitude and increase the accuracy of the optimization process compared with the traditional approach for GAs. Originality/value It was demonstrated that incorporating the idea of generalized optimization into the body of a stochastic optimization method leads to qualitatively new properties of the optimization process, increasing the accuracy and minimizing the CPU time.

Sign in / Sign up

Export Citation Format

Share Document