A nonsmooth Newton method for the design of state feedback stabilizers under structure constraints |
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| Authors: | Mohamed Yagoubi Redouane Chaibi |
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| Institution: | 1. IMT Atlantique, LS2N, CNRS UMR-6004, Nantes, France;2. Sidi-Mohamed Ben-Abdellah University, Fès, Morocco;1. Department of Physical Therapy and Rehabilitation Science, School of Medicine, University of Maryland, Baltimore, Maryland 21201, United States;2. Department of Biongineering, School of Engineering, University of Maryland, College Park, Maryland 20742, United States;3. Institute of Robotics and Mechatronics, German Aerospace Center (DLR), Wessling, Bavaria 82234, Germany;1. ENEA – Frascati RC, Via Enrico Fermi 45, 00044 Frascati, Rome, Italy;2. Centro de Investigación y de Estudios Avanzados – CINVESTAV del I.P.N., Unidad Guadalajara, Av. del Bosque 1145, Col. El Bajío, Zapopan 45010, Jalisco, México;3. Department of Information Engineering, Computer Science and Mathematics (DISIM), University of L’Aquila, Via Vetoio, Loc. Coppito, 67100 L’Aquila, Italy;4. Center of Excellence DEWS, University of L’Aquila, Via Vetoio, Loc. Coppito, 67100 L’Aquila, Italy;1. School of Electronics Engineering, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Republic of Korea;2. School of Architecture and Civil Engineering, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Republic of Korea;1. Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin 150001, China;2. State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China;1. School of Computer and Information Engineering, Henan University, Kaifeng 475004, China;2. Miami College of Henan University, Henan University, Kaifeng 475004, China;3. Henan Key Laboratory of Big Data Analysis and Processing, Henan University, Kaifeng 475004, China |
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| Abstract: | The paper proposes a method for structured state-feedback controllers design for linear time-invariant systems. A necessary and sufficient condition for structured state-feedback stabilizability of linear systems, making an appeal to the linear-quadratic (LQ) regulator theory, is first proposed. The latter is presented in the form of a nonlinear matrix equation. Then, it is recast as a nonsmooth unconstrained equation using projection onto the positive semi-definite matrices cone. Thereby, a nonsmooth Newton’s iterative algorithm, based on the Clarke generalized Jacobian of said projection, is proposed. This method has a guaranteed local convergence. Finally, numerical examples illustrate the effectiveness of the proposed method. |
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