Alexander Zemliak

Comparison of Lyapunov function behavior for different strategies of optimization

The problem of designing of analog network for a minimal computer time has been formulated as the functional minimization problem of the control theory. The design process in this case is formulated as the controllable dynamic system. The optimal sequence of the control vector switch points was determined as a principal characteristic of the minimal-time system design algorithm. The conception of the Lyapunov function was proposed to analyze the behavior of the process of designing. The special function that is a combination of the Lyapunov function and its time derivative was proposed to predict the design time of any strategy by means of the analysis of initial time interval of the process of network optimization. This approach gives us the possibility to select the quasi optimal strategy of network optimization by analyzing the initial part of the total design process only.

Study of structure of the control vector for the best optimization strategy

The generalized methodology for the electronic networks optimization was elaborated by means of the optimal control theory approach. In this case the problem of the electronic system design is formulated as a classical problem of functional minimization of the optimal control theory. The minimal time system design algorithm was defined as a controllable dynamic process with an optimal control vector. By this methodology the aim of the system design process with minimal computer time is presented as a transition process of some dynamic system that has the minimal transition time. The optimal position of the control vector switch points was determined as a principal characteristic of the minimal-time system design algorithm.

Control vector structure for a minimal-time circuit optimization process

The circuit optimization process is formulated as a dynamic controllable system. A special control vector is defined to redistribute the compute expense between a network analysis and a parametric optimization. The problem of a minimal-time circuit optimization was formulated as a classical problem of the optimal control for minimization of one functional. The conception of the Lyapunov function of dynamic system is used to analyze the principal characteristics of the design process. The analysis of the Lyapunov function and its time derivative gives us a possibility to predict the optimal control vector structure for constructing a minimal-time circuit design algorithm.

Control vector structure for circuit optimization

The methodology for the electronic networks optimization was elaborated by means of the optimal control theory approach. In this case the problem of the electronic system design is formulated as a classical problem of functional minimization of the optimal control theory. The minimal time system design algorithm was defined as a controllable dynamic process with an optimal control vector. By this methodology the aim of the system design process with minimal computer time is presented as a transition process of some dynamic system that has the minimal transition time. The optimal position of the control vector switch points was determined as a principal characteristic of the minimal-time algorithm. The Lyapunov function of the optimization process was proposed to define optimal structure of control vector.

Structure of quasi optimal algorithm for analogue circuit optimization

The methodology of designing of analog circuits, based on applications of control theory is the basis for constructing of optimum or quasi optimal algorithm of optimization. By a major criterion here, allowing to exposing the necessary structure of algorithm, there is a behavior of function of Lyapunov, which was defined for the process of optimization. Characteristics of function of Lyapunov and its derivative have been analyzed for searching of optimum structure of control vector and optimal algorithm. A flow diagram of quasi optimal algorithm was built on basic of generalized methodology. The properties of this algorithm demonstrate a great acceleration of the process in comparing to the traditional approach.

On stability of optimization process for analog circuits

The optimization process for analog network is formulated as a dynamic controllable system. The problem of minimal-time network optimization can be formulated as a classical problem of optimal control for some functional minimization. A conception of Lyapunov function of dynamic controllable system is used to analyze the principal characteristics of the optimization process. The analysis of stability of different strategies of optimization gives a correlation between behavior of Lyapunov function and CPU time.

On structure of quasi optimal algorithm of analogue circuit designing

The methodology of designing of analog circuits, being based on applications of control theory is basis for constructing of optimum or quasi optimal algorithm of designing. By a major criterion here, allowing to exposing the necessary structure of algorithm, there is a behavior of function of Lyapunov, which was defining for the process of optimization of circuit. Characteristics of function of Lyapunov and its derivative had been analyzed for searching of optimum structure of control vector and optimal algorithm. The flow diagram of quasi optimal algorithm was built on basic of generalized methodology. The properties of this algorithm demonstrate a great acceleration of the process in comparing to traditional approach.

Analysis of Lyapunov function for different strategies of network optimization using parallel computing

The problem of analog system design for a minimal computer time has been formulated as the functional minimization problem of the control theory. The design process in this case is formulated as the controllable dynamic system. The conception of the Lyapunov function of dynamic controllable system is used to analyze the principal characteristics of the design process. The different forms of the Lyapunov function were proposed to analyze the behavior of a design process. The special function that is a combination of the Lyapunov function and its time derivative was proposed to compare the different design strategies that compose the structural basis of generalized methodology. This comparison has been implemented by parallel computing.

Generalized optimization methodology of second level for system design

The new general methodology for the analog system optimization was elaborated by means of the optimum control theory formulation in order to improve the characteristics of the system design process. A special control vector is defined to redistribute the compute expensive between a network analysis and a parametric optimization. This approach generalizes the design process and generates a set of the different optimization strategies that serves as the structural basis to the optimal design strategy construction. The principal difference between this new methodology and before elaborated theory is the more general approach on the definition of the system parameters and more broadened structural basis. The main equations for the system optimization process were elaborated. These equations include the special control functions that generalize the total system optimization process. Numerical results that include as passive and active nonlinear networks demonstrate the efficiency and perspective of the proposed approach.

Lyapunov function analysis for different strategies of circuit optimization

The problem of optimization of analog circuit for a minimal computer time has been formulated as the functional minimization problem of the control theory. The process of circuit optimization is formulated as the controllable dynamic system. The conception of the Lyapunov function was proposed to analyze the behavior of the process of circuit optimization. The special function that is a combination of the Lyapunov function and its time derivative was proposed to predict the design time of any strategy. This approach gives us the possibility to select the best strategy from the complete structural basis analyzing the initial part of the total optimization process only.