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Solution of a Singular H¥ Control Problem: A Regularization ApproachTopics: Decision Support Systems; Evolutionary Computation and Control; Optimization Algorithms

Keyword(s):H¥ Control Problem, Singular Problem, Regularization, H¥ Partial Cheap Control Problem, Riccati Matrix Algebraic Equation, Asymptotic Design of Controller.

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Abstract: We consider an infinite horizon H¥ control problem for linear systems with additive uncertainties (disturbances).
The case of a singular weight matrix for the control cost in the cost functional is treated. In such a
case, a part of the control coordinates is singular, meaning that the H¥ control problem itself is singular. We
solve this problem by a regularization. Namely, we associate the original singular problem with a new H¥
control problem for the same equation of dynamics. The cost functional in the new problem is the sum of the
original cost functional and an infinite horizon integral of the squares of the singular control coordinates with
a small positive weight. This new H¥ control problem is regular, and it is a partial cheap control problem.
Based on an asymptotic analysis of this H¥ partial cheap control problem, a controller solving the original
singular H¥ control problem is designed. Illustrative example is presented.

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Glizer, V. and Kelis, . (2017). Solution of a Singular H¥ Control Problem: A Regularization Approach.In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-758-263-9, ISSN 2184-2809, pages 25-36. DOI: 10.5220/0006397600250036

@conference{icinco17, author={Valery Y. Glizer. and Oleg Kelis.}, title={Solution of a Singular H¥ Control Problem: A Regularization Approach}, booktitle={Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,}, year={2017}, pages={25-36}, publisher={SciTePress}, organization={INSTICC}, doi={10.5220/0006397600250036}, isbn={978-989-758-263-9}, }

TY - CONF

JO - Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, TI - Solution of a Singular H¥ Control Problem: A Regularization Approach SN - 978-989-758-263-9 AU - Glizer, V. AU - Kelis, . PY - 2017 SP - 25 EP - 36 DO - 10.5220/0006397600250036