Study of Structure of Control Vector for the Problem of Analog Circuit Optimization

The generalized methodology for electronic networks optimization was elaborated by means of the optimal control theory approach. A special control vector is defined to redistribute the compute expense between a network analysis and a parametric optimization. In this case the problem of the electronic system optimization is formulated as a classical problem of functional minimization of the optimal control theory. The optimization algorithm with a minimal computer time was defined as a controllable dynamic process with an optimal control vector. By this methodology the aim of the optimization process with a 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 algorithm with a minimal computer time for network optimization. The conception of the Lyapunov function of dynamic controllable system is used to analyze the principal characteristics of the process of network optimization. The special function that is a combination of Lyapunov function of the design process and its time derivative was proposed to predict the optimal control vector to construct the best algorithm for circuit optimization. Key-Words: Time-optimal design algorithm, circuit optimization, control theory formulation, Lyapunov function, switch points.