Tatiana M. Markina

Behaviour of Lyapunov’s function for different strategies of circuit optimisation

The process of analogue circuit optimisation is mathematically defined as a controllable dynamic system. In this context the minimisation of the processor time of designing can be formulated as a problem of time minimisation for transitional process of dynamic system. In order to analyse the properties of such a system, it is proposed to use the concept of Lyapunov function of dynamic system. Using this function and its time derivative, the special functions have been built that allow us to predict the total processor time for circuit optimisation by analysing the initial interval of the optimisation process. Numerical results indicate the possibility of predicting the processor time of different strategies for circuit optimisation.

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.

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.

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.

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.

Dynamic characteristics of different system design strategies

The design process for analog network design is formulated as a dynamic controllable system. A special control vector is defined to redistribute the compute expensive between a network analysis and a parametric optimization. The problem of the minimal-time network design can be formulated as a classical problem of the optimal control for some functional minimization. A conception of a Lyapunov function of dynamic controllable system is used to analyze the principal characteristics of the design process. The analysis of some derivative functions of the Lyapunov function gives us a possibility to compare the design time of different design strategies and predict the design strategy with a minimal design time.

Stability Analysis of Different Design Strategies for Analogue Network Design

The design process for analog network design is formulated as a dynamic controllable system. A special control vector is defined to redistribute the compute expensive between a network analysis and a parametric optimization. This redistribution permits the minimization of a 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. The conception of the Lyapunov function of dynamic controllable system is used to analyze the principal characteristics of the design process. The analysis of the Lyapunov function and its time derivative gives a possibility to compare the different design strategies.

Characteristics of stability of different design strategies for analogue circuit design

The design process for analog network design is formulated as a dynamic controllable system. A special control vector is defined to redistribute the compute expensive between a network analysis and a parametric optimization. This redistribution permits the minimization of a 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. The conception of the Lyapunov function of dynamic controllable system is used to analyze the principal characteristics of the design process. The analysis of the Lyapunov function and its time derivative gives a possibility to compare the different design strategies.