Characteristics study of an electronic systems design strategy that includes the traditional strategy and the modified traditional strategy

Abstract

This work presents 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 theory 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), where is possible to use different kind of optimization procedures and different models, but in each step solution is not possible to change these; the modified traditional design strategy (MTDS) is also included, where the model of the system is part of optimization procedure but an objective function of optimization process is constructed such includes the traditional objective function and some penalty functions that feign the model of the system. A whole of special control functions are introduced artificially to generalize the methodology and producing several design trajectories for the same optimization process, where the first and final trajectories correspond to TDS and MTDS respective. The combination of a whole these trajectories produce an infinite number of design strategies, some of these are quasi-optimal in time and only one is optimal in time. The determinations of switching points for the optimal construction algorithm are found using optimal control theory, whit approximation methods and through the special Lyapunov function. These ideas are proposed using the method of gradient optimization and acceleration effect. The analysis of some non linear electronic circuits models shows that this strategy can reduce the total number of operations many times and accelerate the design process. Qualitative and numeric results of this iterative process are generated in a personal computer in a C++ language elaborated program whit a visual C++ graphic user interface. The examples presented show that the traditional design methodology is not time optimal, and the potential gain in compute time of the optimal design strategy whit respect to traditional design strategy increases in accordance with the size and complexity.