Abstract
Adaptive control-based schemes have been implemented to date in a variety of different ap-plications. However, the ability to obtain a predictable transient closed-loop performance in adaptive systems is still a challenging problem from a verification and validation point of view. To face this problem we have recently introduced an analysis and design framework for adaptive control systems in the presence of bounded uncertainty and bounded adaptive control (the boundedness can be enforced, for instance, by a parameter projection mechanism) showing that the transitory performance of a MRAC system can be expressed, analyzed, and optimized via a convex optimization formulation based on Linear Matrix Inequality (LMI) requirements. A key feature of this framework is that it is possible to tune the adaptive control parameters rigorously so that the tracking error of the closed-loop system evolves within an a priori specified region of the error space whose size can be minimized by selecting a suitable cost function. One drawback of this approach is the possible conservatism of the results. In fact, as with any robust control problem, the design philosophy is to guarantee the performance for all the set of allowed uncertainties. The consequence of this fact is that the robust LMIs constraints derived in this context may lead to conservative conditions due to unavoidable matrix majorations requested in the derivation of the robust LMI conditions. To overcome these limitations in this study we propose a novel stochastic analysis and design framework for MRAC systems where the uncertain parameters along with the adaptive control signal are considered as random variables. This brings the important advantage that the (stochastic) LMI conditions that define the performance requirements can be immediately derived from Lyapunov analysis without the need of matrix majorations and of the introduction of auxiliary variables. In turn, this leads to the fact that the stochastic LMI conditions are less conservative. In this paper we compared the robust worst-case framework with the novel stochastic framework. The (previous) robust and the (novel) probabilistic convex optimization approaches were both applied for the optimized design of minimum size tracking error invariant sets for a MRAC control systems in the presence of matched and of input uncertainty acting on the actuator dynamics. The comparative study was performed using the short period longitudinal dynamics of an F-16 aircraft model.
Recommended Citation
M. L. Fravolini et al., "Comparison of Robust and Probabilistic LMI-Based Design of Adaptive Flight Controllers with Uncertain Input Dynamics," 2016 AIAA Guidance, Navigation, and Control Conference, American Institute of Aeronautics and Astronautics, Jan 2016.
The definitive version is available at https://doi.org/10.2514/6.2016-1381
Department(s)
Mechanical and Aerospace Engineering
Publication Status
Full Access
International Standard Book Number (ISBN)
978-162410389-6
Document Type
Article - Conference proceedings
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 American Institute of Aeronautics and Astronautics, All rights reserved.
Publication Date
01 Jan 2016
