Statistical Control of Stochastic Systems Incorporating Integral Feedback: Performance Robustness Analysis
An innovative paradigm for statistical approximation is presented to evaluate performance measure statistics of a class of stochastic systems with integral control. This methodology, which makes use of both compactness from the logic of the state-space model description and quantitativity from the probabilistic knowledge of stochastic disturbances, now allows us to predict more accurately the effect of a chi-squared random variable on the performance uncertainty of the stochastic system with both state feedback and integral output feedback. It is shown that the computational method detailed herein is able to calculate the exact statistics of the performance measure of any orders which are then utilized in the design of an optimal statistical control solution to effectively address the unresolved challenge of closed-loop performance robustness without massive Monte Carlo simulations.
KeywordsStochastic System State Transition Matrix Stochastic Uncertainty Performance Uncertainty Performance Measure Statistic
This material is based upon work supported in part by the U.S. Air Force Research Laboratory-Space Vehicles Directorate and the U.S. Air Force Office of Scientific Research. Much appreciation from the author goes to Dr. Donna C. Senft, the branch chief of Spacecraft Components Technology, for serving as the reader of this work and providing helpful criticism.
- [PSL02a]K. D. Pham, M. K. Sain, and S. R. Liberty, Robust Cost-Cumulants Based Algorithm for Second and Third Generation Structural Control Benchmarks, Proceedings of the American Control Conference, pp. 3070–3075, Anchorage, Alaska, May 08–10, 2002.Google Scholar
- [PSL02b]K. D. Pham, M. K. Sain, and S. R. Liberty, Cost Cumulant Control: State-Feedback, Finite-Horizon Paradigm with Application to Seismic Protection, Special Issue of Journal of Optimization Theory and Applications, Edited by A. Miele, Kluwer Academic/Plenum Publishers, New York, Vol. 115, No. 3, pp. 685–710, December 2002.Google Scholar
- [PSL04]K. D. Pham, M. K. Sain, and S. R. Liberty, Infinite Horizon Robustly Stable Seismic Protection of Cable-Stayed Bridges Using Cost Cumulants, Proceedings of the American Control Conference, pp. 691–696, Boston, Massachusetts, June 30, 2004.Google Scholar
- [PSL05]K. D. Pham, M. K. Sain, and S. R. Liberty, Statistical Control for Smart Base-Isolated Buildings via Cost Cumulants and Output Feedback Paradigm, Proceedings of the American Control Conference, pp. 3090–3095, Portland, Oregon, June 8–10, 2005.Google Scholar
- [Pha05]K. D. Pham, Minimax Design of Statistics-Based Control with Noise Uncertainty for Highway Bridges, Proceedings of DETC 2005/2005 ASME 20th Biennial Conference on Mechanical Vibration and Noise: Active Control of Vibration and Acoustics I, DETC2005-84593, Long Beach, California, September 24–28, 2005.Google Scholar
- [PhR07]K. D. Pham and L. Robertson, Statistical Control Paradigm for Aerospace Structures Under Impulsive Disturbances, The 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA 2007-1755, Honolulu, Hawaii, April 23–26, 2007.Google Scholar