System design problem formulation by control theory

Proceedings of the Joint INDS'11 &Amp; ISTET'11

Silva

2011

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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.

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Juárez

Proceedings of the Joint INDS'11 &Amp; ISTET'11

Silva

2011

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“…The idea to use the control theory, which was introduced in [14], is developed now for the design of the systems that are described by the nonlinear algebraic equation model. This methodology generalizes the design problem and can reduce the total necessary computer design time.…”

Section: Introductionmentioning

confidence: 99%

“…Different examples of the electronic circuit design have been analyzed using the proposed methodology. In contrast to [14][15][16] the present paper defines the new design problem formulation in continuous form.…”

Section: Introductionmentioning

confidence: 99%

On time-optimal procedure for analog system design

Rı́os

Miranda

et al. 2004

JART

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The process of any analog system design has been formulated on the basis of the control theory application. This approach produces many different design strategies inside the same optimization procedure and allows determining the problem of the optimal design strategy existence from the computer time point of view. Different kinds of system design strategies have been evaluated from the operations number. The general methodology for the analog system design was formulated by means of the optimum control theory. The main equations for this design methodology were elaborated. These equations include the special control functions that are introduced artificially. This approach generalizes the design process and generates an infinite number of the different design strategies. The problem of the optimum design algorithm construction is defined as the minimum-time problem of the control theory. Numerical results of some electronic circuit design demonstrate the efficiency and perspective of the proposed methodology. These examples show that the computer time gain of the optimal design strategy with respect to the traditional design strategy increases when the size and complexity of the system increase. An additional acceleration effect of the design process has been discovered by the analysis of various design strategies with the different initial points. This effect is displayed for all analyzed circuits and it reduces additionally the total computer time for the system design.

“…There is only one control function u 1 in this case because there is only one dependent parameter 2 x .…”

Section: Two-dimensional Problemmentioning

confidence: 99%

On start point selection for the time-optimal system design algorithm

2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353)

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-On the basis of generalized theory of system design the behavior of the different design trajectories in the design phase space was analyzed. The problem of the initial point selection for the time-optimal algorithm construction was connected with the discovering of an additional acceleration effect of design process. This acceleration effect has been discovered by the analysis of various design strategies with different initial points. This effect can be understood well on the basis of the elaborated design methodology by means of the different design trajectory analysis. It is displayed for all analyzed circuits and it reduces additionally the total computer time for the system design. Numerical results of some passive and active nonlinear electronic circuit design demonstrate the perspective of the proposed approach.