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This paper aims to propose a new approach on the problem of circuit optimisation by using the generalised optimisation methodology presented earlier. This approach is focused on the application of the maximum principle of Pontryagin for searching the best structure of a control vector providing the minimum central processing unit (CPU) time.

The process of circuit optimisation is defined mathematically as a controllable dynamical system with a control vector that changes the internal structure of the equations of the optimisation procedure. In this case, a well-known maximum principle of Pontryagin is the best theoretical approach for finding of the optimum structure of control vector. A practical approach for the realisation of the maximum principle is based on the analysis of the behaviour of a Hamiltonian for various strategies of optimisation and provides the possibility to find the optimum points of switching for the control vector.

It is shown that in spite of the fact that the maximum principle is not a sufficient condition for obtaining the global minimum for the non-linear problem, the decision can be obtained in the form of local minima. These local minima provide rather a low value of the CPU time. Numerical results were obtained for both a two-dimensional case and an N-dimensional case.

The possibility of the use of the maximum principle of Pontryagin to a problem of circuit optimisation is analysed systematically for the first time. The important result is the theoretical justification of formerly discovered effect of acceleration of the process of circuit optimisation.

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.

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.

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.

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.

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.

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.

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.

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.

This work seeks to present the theoretical study considerations and the characteristics of a general design methodology in optimal time for electronic systems using numerical methods and optimal control theory. Through this, the design problem of a system is formulated in terms of optimal control in minimal time.

This general design methodology includes the traditional design strategy (TDS), and the modified traditional design strategy (MTDS), where the model of the system is part of the optimization procedure but an objective function of the optimization process is constructed such as includes the traditional objective function and some penalty functions that feign the model of the system. Many special control functions are introduced artificially to generalize the methodology and produce several design trajectories for the same optimization process – the first and final trajectories correspond to TDS and MTDS, respectively. The combination of these trajectories produce an infinite number of design strategies, some of these are quasi‐optimal in time and only one is optimal in time.

Qualitative and numeric results of this iterative process are generated in a personal computer in a C++ language elaborated with a visual C++ graphic user interface. An algorithm is constructed to form an optimal in time design strategy switching from a MTDS subset to a TDS subset. Results of measured times are analyzed, showing that there is a control input U, such that the objective function is minimized in a minimum time.

These ideas are proposed using method of gradient optimization and special acceleration effect.

The purpose of this paper is to define the process of analog circuit optimization on the basis of the control theory application. This approach produces many different strategies of optimization and determines the problem of searching of the best strategy in sense of minimal computer time. The determining of the best strategy of optimization and a searching of possible structure of this strategy with a minimal computer time is a principal aim of this work.

Different kinds of strategies for circuit optimization have been evaluated from the point of view of operations’ number. The generalized methodology for the optimization of analog circuit was formulated by means of the optimum control theory. The main equations for this methodology were elaborated. These equations include the special control functions that are introduced artificially. This approach generalizes the problem and generates an infinite number of different strategies of optimization. A problem of construction of the best algorithm of optimization is defined as a typical problem of the control theory. Numerical results show the possibility of application of this approach for optimization of electronic circuits and demonstrate the efficiency and perspective of the proposed methodology.

Examples show that the better optimization strategies that are appeared in limits of developed approach have a significant time gain with respect to the traditional strategy. The time gain increases when the size and the complexity of the optimized circuit are increasing. An additional acceleration effect was used to improve the properties of presented optimization process.

The obtained results show the perspectives of new approach for circuit optimization. A large set of various strategies of circuit optimization serves as a basis for searching the better strategies with a minimum computer time. The gain in processor time for the best strategy reaches till several thousands in comparison with traditional approach.

In this paper, we propose further development of the generalized methodology for analogue circuit optimization. This methodology is based on optimal control theory. This approach generates many different circuit optimization strategies. We lead the problem of minimizing the CPU time needed for circuit optimization to the classical problem of minimizing a functional in optimal control theory.

The process of analogue circuit optimization is defined mathematically as a controllable dynamical system. In this context, we can formulate the problem of minimizing the CPU time as the minimization problem of a transitional process of a dynamical system. To analyse the properties of such a system, we propose to use the concept of the Lyapunov function of a dynamical system. This function allows us to analyse the stability of the optimization trajectories and to predict the CPU time for circuit optimization by analysing the characteristics of the initial part of the process.

We present numerical results that show that we can compare the CPU time for different circuit optimization strategies by analysing the behaviour of a special function. We establish that, for any optimization strategy, there is a correlation between the behaviour of this function and the CPU time that corresponds to that strategy.

The analysis shows that Lyapunov function of optimization process and its time derivative can be informative sources for searching a strategy, which has minimal processor time expense. This permits to predict the best optimization strategy by analyzing only initial part of the optimization process.