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Adaptive Control, Filtering, and Signal Processing pp 165–198Cite as

Estimation-Based Schemes for Adaptive Nonlinear State-Feedback Control*

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 74))

Abstract

We present a new approach to adaptive nonlinear control based on a complete controller-identifier separation which has long been a goal in adaptive system design. Our controllers guarantee certain input/state stability properties with respect to the parameter error % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe % pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam % aaeaqbaaGcbiqaca0fcuaH4oqCgaacaaaa!3CEC! \[ \tilde \theta \] and its derivative % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe % pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam % aaeaqbaaGcbiqaca0fcuaH4oqCgaacgaGaaaaa!3CF4! \[ \dot \tilde \theta \] as inputs. The parameter identifiers, in turn, guarantee % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe % pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam % aaeaqbaaGcbiGacWefca0fcuaH4oqCgaacaiabgIGioprr1ngBPrwt % HrhAXaqehuuDJXwAKbstHrhAG8KBLbacgaGae8NeHWKaeyOhIukaaa!4AD4! \[ \tilde \theta \in \mathcal{L}\infty \] , and either % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe % pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam % aaeaqbaaGcbiGacWefca0fcuaH4oqCgaacgaGaaiabgIGioprr1ngB % PrwtHrhAXaqehuuDJXwAKbstHrhAG8KBLbacgaGae8NeHWKaeyOhIu % kaaa!4ADC! \[ \dot \tilde \theta \in \mathcal{L}\infty \] or % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe % pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam % aaeaqbaaGcbiGacWefca0fcuaH4oqCgaacgaGaaiabgIGioprr1ngB % PrwtHrhAXaqehuuDJXwAKbstHrhAG8KBLbacgaGae8NeHW0aaSbaaS % qaaiabikdaYaqabaaaaa!4A89! \[ \dot \tilde \theta \in \mathcal{L}_2 \] or both. This estimation-based approach encompases two families of schemes: swapping-based and observer-based. Swapping-based schemes allow the use of a wide variety of update laws — gradient and least-squares, normalized and unnormalized. Observer-based schemes use parameter identifiers of lower dynamic order. All these schemes achieve systematic improvement of transient performance.

This work was supported in part by the National Science Foundation under Grant ECS-9203491 and in part by the Air Force Office of Scientific Research under Grant F-49620-92-J-0495.

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA, 93106

    Miroslav Krstić & Petar V. Kokotović

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  1. Miroslav Krstić
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  2. Petar V. Kokotović
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Editor information

Editors and Affiliations

  1. Department of Automatic Control, Lund Institute of Technology, Lund, Sweden

    K. J. Åström

  2. Department of Electrical Engineering and Computer Science, The University of Newcastle, Rankin Drive, Newcastle, NSW, 2308, Australia

    G. C. Goodwin

  3. Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 1308 West Main Street, Urbana, IL, 61801-2307, USA

    P. R. Kumar

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Krstić, M., Kokotović, P.V. (1995). Estimation-Based Schemes for Adaptive Nonlinear State-Feedback Control*. In: Åström, K.J., Goodwin, G.C., Kumar, P.R. (eds) Adaptive Control, Filtering, and Signal Processing. The IMA Volumes in Mathematics and its Applications, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8568-2_7

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  • DOI: https://doi.org/10.1007/978-1-4419-8568-2_7

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