May, B. Scott (1997) Probabilistic robust control: theory and applications. California Institute of Technology . (Unpublished) http://resolver.caltech.edu/CaltechEERL:1997.EERL9708

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Abstract
In this work, the development of a probabilistic approach to robust control is motivated by structural control applications in civil engineering. Often in civil structural applications, a system's performance is specified in terms of its reliability. In addition, the model and input uncertainty for the system may be described most appropriately using probabilistic or "soft" bounds on the model and input sets. The probabilistic robust control methodology contrasts with existing W... /A robust control methodologies that do not use probability information for the model and input uncertainty sets, yielding only the guaranteed (i.e., "worstcase") system performance, and no information about the system's probable performance which would be of interest to civil engineers. The design objective for the probabilistic robust controller is to maximize the reliability of the uncertain structure/controller system for a probabilisticallydescribed uncertain excitation. The robust performance is computed for a set of possible models by weighting the conditional performance probability for a particular model by the probability of that model, then integrating over the set of possible models. This integration is accomplished efficiently using an asymptotic approximation. The probable performance can be optimized numerically over the class of allowable controllers to find the optimal controller. Also, if structural response data becomes available from a controlled structure, its probable performance can easily be updated using Bayes's Theorem to update the probability distribution over the set of possible models. An updated optimal controller can then be produced, if desired, by following the original procedure. Thus, the probabilistic framework integrates system identification and robust control in a natural manner. The probabilistic robust control methodology is applied to two systems in this thesis. The first is a highfidelity computer model of a benchmark structural control laboratory experiment. For this application, uncertainty in the input model only is considered. The probabilistic control design minimizes the failure probability of the benchmark system while remaining robust with respect to the input model uncertainty. The performance of an optimal loworder controller compares favorably with higherorder controllers for the same benchmark system which are based on other approaches. The second application is to the Caltech Flexible Structure, which is a lightweight aluminum truss structure actuated by three voice coil actuators. A controller is designed to minimize the failure probability for a nominal model of this system. Furthermore, the method for updating the modelbased performance calculation given new response data from the system is illustrated.
Item Type:  Report or Paper (Technical Report)  

Additional Information:  Ph.D, 1998  
Group:  Earthquake Engineering Research Laboratory  
Funders: 
 
Record Number:  CaltechEERL:1997.EERL9708  
Persistent URL:  http://resolver.caltech.edu/CaltechEERL:1997.EERL9708  
Usage Policy:  You are granted permission for individual, educational, research and noncommercial reproduction, distribution, display and performance of this work in any format.  
ID Code:  26275  
Collection:  CaltechEERL  
Deposited By:  Imported from CaltechEERL  
Deposited On:  17 Aug 2001  
Last Modified:  07 Mar 2014 00:16 
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