Abstract
This paper relates to minimax control design problems for a class of parabolic systems with nonregular boundary conditions and uncertain distributed perturbations under pointwise control and state constraints. The main attention is paid to the Dirichlet boundary control that offers the lowest regularity properties. Our variational analysis is based on well-posed multistep approximations and involves the solving of constrained optimal control problems for ODE and PDE systems. The design procedure essentially employs monotonicity properties of the parabolic dynamics and its asymptotics on the infinite horizon. Finally we justify a suboptimal three-positional structure of feedback boundary controllers and provide calculations of their optimal parameters that ensure the required system performance and robust stability under any admissible perturbations.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35359-3_40
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© 1999 IFIP International Federation for Information Processing
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Mordukhovich, B.S. (1999). Minimax Design of Constrained Parabolic Systems. In: Chen, S., Li, X., Yong, J., Zhou, X.Y. (eds) Control of Distributed Parameter and Stochastic Systems. IFIP Advances in Information and Communication Technology, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35359-3_14
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DOI: https://doi.org/10.1007/978-0-387-35359-3_14
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-4868-0
Online ISBN: 978-0-387-35359-3
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