New Risk-Averse Control Paradigm for Stochastic Two-Time-Scale Systems and Performance Robustness

K. D. Pham ()
Additional contact information
K. D. Pham: Kirtland Air Force Base

Journal of Optimization Theory and Applications, 2010, vol. 146, issue 2, No 15, 537 pages

Abstract: Abstract This work is concerned with the optimal control of stochastic two-time-scale linear systems with performance measure in a finite-horizon integral-quadratic form. Nature, modeled by stationary Wiener processes whose mean and covariance statistics are known, malevolently affects the state dynamics and output observations of the control problem class. With particular focus on the system performance robustness, the use of higher-order statistics or cumulants associated with the performance measure of chi-squared random variable type makes it possible to restate the stochastic control problem as the solution of a deterministic one, which subsequently allows disregarding all sample-path realizations by Nature acting on the original problem. The distinguishing feature of the risk-averse control paradigm is that the performance index is multiobjective in nature, being composed of both risk-neutral integrals and risk-sensitive costs associated with the ubiquitous linear-quadratic-Gaussian (LQG) and rather recent risk-sensitive control problems. Another issue that makes this class of control particularly interesting is the fact that Nature has the ability to exercise all the higher-order characteristics of the uncertain chi-squared performance measure. The efficient controller, having access to Nature’s apriori statistical knowledge and employing dynamic output feedback, seeks to minimize the performance uncertainty that Nature can do over the set of mixed random realizations. Furthermore, the results herein potentially generalize the existing results for the single-objective H 2, H ∞, and risk-sensitive control problems to a substantially larger class of systems, wherein Nature selects mixed sample-path realizations that need not be Gaussian. That is, the entire probability density function of Nature’s choices is not necessarily known except for its first two statistics. Finally, the numerical simulations for a two-time-scale longitudinal dynamics of the F-8 jet aircraft demonstrate that the proposed control paradigm has competitive performance in the closed-loop system responses and offers multiple levels of robustness for the system performance.

Keywords: Two-time-scale stochastic system; Multiobjective cumulant-based control; Risk-averse controllers; Mayer form optimization (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-009-9629-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:146:y:2010:i:2:d:10.1007_s10957-009-9629-x

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-009-9629-x

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().