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Economic resource allocation in system simulation and control design

Abstract

This dissertation studies the optimal simulation problem and the economic system design problem. First, the optimal simulation problem is formulated to find a reduced order model implemented with finite precision computations that gives the best simulation accuracy. Then the economic system design problem is set up to design/select components given the system performance requirements such that the total cost (in an economic sense) is minimized. Both problems are motivated by the system design philosophy. That is, enlarging the design space by introducing more freedoms to achieve a higher level optimal solution. As the simulation accuracy depends on the simulation model order, realization, method of model reduction, as well as the wordlength of the computer, the simulation problem is studied as an integration of model reduction and its implementation. A variety of model reduction methods are investigated; then the q-Markov Covariance Equivalent Realization (q-Markov COVER, also known as QMC) and model reduction via feedback control design are used for the integration. To design simulations using data matching, we developed an algorithm which produces finite wordlength q-Markov COVERs that match a pre-specified set of input/output cross-correlation and output autocorrelation data, when the model is installed in a computational environment with specified bits assigned to the fixed-point or floating point simulation. These results allow the design of digital simulations or controller realizations with no error within the specified set of cross-correlation and autocorrelation data. A data- based closed-loop simulation framework is proposed as an application of this simulation method. To design simulations using norm minimization, it is shown that the parametrization of a lower-order simulation model with roundoff error consideration can be treated as a reduced order output feedback control design problem with measurement noise. The design conditions for the simulation model that can bound covariance errors, or deliver mixed H2/H∞ performance are expressed in terms of linear matrix inequalities (LMIs) and a coupling nonconvex constraint. A convexifying algorithm is applied to attain local optimality. As an application of economic design in simulation problems, we simultaneously find the simulation model of a stable linear system and allocate computational resources (wordlength) among the digital devices such that the computational cost is minimized without violating the required simulation accuracy. A more elegant application of the economic system design is to integrate sensor/actuator selection and control design. This problem is set up to seek a trade-off among three competitive factors: control performance, control effort and hardware cost. This enlarged design problem is converted to LMI optimizations which produce simultaneously the output hardware precision distribution and output feedback control. An iterative algorithm is proposed for the selecting of actuators/sensors in the structural control aiming to minimize the number and cost of sensor/actuator and this algorithm is applied to tensegrity structures

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