Causal Gain-scheduled output feedback controllers using parameter-dependent Lyapunov Functions
This paper addresses the design problem of Gain-Scheduled Output Feedback (GSOF) controllers, in which causality with respect to (w.r.t) scheduling parameters in the GSOF controllers is kept, for continuous-/discrete-time Linear Parameter-Varying (LPV) systems using Parameter-Dependent Lyapunov Func...
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| Vydané v: | Automatica (Oxford) Ročník 129; s. 109569 |
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| Jazyk: | English |
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01.07.2021
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| ISSN: | 0005-1098, 1873-2836 |
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| Abstract | This paper addresses the design problem of Gain-Scheduled Output Feedback (GSOF) controllers, in which causality with respect to (w.r.t) scheduling parameters in the GSOF controllers is kept, for continuous-/discrete-time Linear Parameter-Varying (LPV) systems using Parameter-Dependent Lyapunov Functions (PDLFs). In general, continuous-time GSOF controllers designed by conventional methods, i.e. so-called change-of-variables using PDLFs, depend on the derivatives of scheduling parameters, and discrete-time GSOF controllers designed by conventional methods or extended Linear Matrix Inequality (LMI) technique using parameter-dependent auxiliary matrices both depend on the one-step-ahead scheduling parameters. These mean that the designed GSOF controllers are not implementable to practical systems due to the non-causality w.r.t. scheduling parameters. On this issue, we propose a formulation which circumvents the causality problem by replacing the term that introduces the causality issue with another term via the reverse use of the Elimination lemma which is also known as “S-variable” approach. A toy example and a practical example (lateral-directional motion control around wing level flight of JAXA’s research airplane MuPAL-α) are included to demonstrate the effectiveness compared to the existing methods. |
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| AbstractList | This paper addresses the design problem of Gain-Scheduled Output Feedback (GSOF) controllers, in which causality with respect to (w.r.t) scheduling parameters in the GSOF controllers is kept, for continuous-/discrete-time Linear Parameter-Varying (LPV) systems using Parameter-Dependent Lyapunov Functions (PDLFs). In general, continuous-time GSOF controllers designed by conventional methods, i.e. so-called change-of-variables using PDLFs, depend on the derivatives of scheduling parameters, and discrete-time GSOF controllers designed by conventional methods or extended Linear Matrix Inequality (LMI) technique using parameter-dependent auxiliary matrices both depend on the one-step-ahead scheduling parameters. These mean that the designed GSOF controllers are not implementable to practical systems due to the non-causality w.r.t. scheduling parameters. On this issue, we propose a formulation which circumvents the causality problem by replacing the term that introduces the causality issue with another term via the reverse use of the Elimination lemma which is also known as ''S-variable'' approach. A toy example and a practical example (lateral-directional motion control around wing level flight of JAXA's research airplane MuPAL-α) are included to demonstrate the effectiveness compared to the existing methods. This paper addresses the design problem of Gain-Scheduled Output Feedback (GSOF) controllers, in which causality with respect to (w.r.t) scheduling parameters in the GSOF controllers is kept, for continuous-/discrete-time Linear Parameter-Varying (LPV) systems using Parameter-Dependent Lyapunov Functions (PDLFs). In general, continuous-time GSOF controllers designed by conventional methods, i.e. so-called change-of-variables using PDLFs, depend on the derivatives of scheduling parameters, and discrete-time GSOF controllers designed by conventional methods or extended Linear Matrix Inequality (LMI) technique using parameter-dependent auxiliary matrices both depend on the one-step-ahead scheduling parameters. These mean that the designed GSOF controllers are not implementable to practical systems due to the non-causality w.r.t. scheduling parameters. On this issue, we propose a formulation which circumvents the causality problem by replacing the term that introduces the causality issue with another term via the reverse use of the Elimination lemma which is also known as “S-variable” approach. A toy example and a practical example (lateral-directional motion control around wing level flight of JAXA’s research airplane MuPAL-α) are included to demonstrate the effectiveness compared to the existing methods. |
| ArticleNumber | 109569 |
| Author | Sato, Masayuki Peaucelle, Dimitri |
| Author_xml | – sequence: 1 givenname: Masayuki surname: Sato fullname: Sato, Masayuki email: sato.masayuki@jaxa.jp organization: Japan Aerospace Exploration Agency, 6-13-1 Osawa, Mitaka, Tokyo, Japan – sequence: 2 givenname: Dimitri surname: Peaucelle fullname: Peaucelle, Dimitri email: dimitri.peaucelle@laas.fr organization: LAAS-CNRS and Université de Toulouse, F-31031 Toulouse cedex 4, France |
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| CitedBy_id | crossref_primary_10_1016_j_jfranklin_2025_107928 crossref_primary_10_1080_00207721_2023_2245948 crossref_primary_10_1016_j_ejcon_2023_100925 |
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| Keywords | Gain-scheduled output feedback controller Elimination lemma LPV systems Causality S-variable approach |
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| SubjectTerms | Automatic Control Engineering Causality Computer Science Elimination lemma Gain-scheduled output feedback controller LPV systems S-variable approach |
| Title | Causal Gain-scheduled output feedback controllers using parameter-dependent Lyapunov Functions |
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