Stable LPV Realization of Parametric Transfer Functions and Its Application to Gain-Scheduling Control Design

Blanchini, Franco; Casagrande, Daniele; Miani, Stefano; Viaro, Umberto

doi:10.1109/tac.2010.2044259

Cited by 57 publications

(61 citation statements)

References 32 publications

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“…We are now ready to present a slightly modified 2 version of Theorem 3.1 from [5], which will be used to construct our adaptive controller. Theorem 1.…”

Section: The Gain Scheduling Resultsmentioning

confidence: 99%

“…This will be achieved primarily through extending the work on gain scheduling in [5]. We will only consider a scalar parameter uncertainty, but assumption (ii) will be relaxed.…”

Section: Purposementioning

confidence: 99%

“…Once the necessary state and parameter estimates are calculated in the estimation phase, an appropriately scaled control signal is applied in the second phase. The estimation procedure similar to the one suggested in [21] will be used and the obtained estimates will be plugged into the perfect information control law from [5]. We will require an upper bound on the magnitude of the derivative of the parameter to make the estimation possible.…”

Section: Purposementioning

confidence: 99%

“…The control of LPV systems has attracted much interest and several approaches have been developed recently. Of special significance is the invariant set approach presented in [2], [3], [4], [6], [5], where it is shown that polyhedral Lyapunov functions and associated geometrically intuitive methods can be used for controller synthesis.…”

mentioning

confidence: 99%

“…In [5] it is shown that if certain conditions are satisfied, then an observer based controller can be constructed such that the closed loop system is stable under arbitrarily fast timevariations in the parameter. This is true under a number of assumptions including the following: (i) the set of possible parameter values is compact and (ii) the parameters are measurable.…”

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confidence: 99%

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Nonlinear periodic adaptive control for linear time-varying plants

Rudko

Miller

2016

2016 American Control Conference (ACC)

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In adaptive control the goal is to deal with systems that have unknown and/or timevarying parameters. Adaptive control techniques have been developed since 1950's and most results were proven in the cases when the time-variations were non-existent or slow. However the results pertaining to systems with fast time-variations are still limited, in particular, when it comes to plants with unstable zero dynamics.In this work we adopt the controller design technique from the area of gain scheduling, where the time-varying parameter is assumed to be measurable. We propose the design of a nonlinear periodic controller, where in each period the state and parameter values are estimated and an appropriate stabilizing control signal is applied. It is shown that the closed loop system is stable under fast parameter variations with persistent jumps: the trajectory of the closed loop state in response to the initial condition is bounded by a decaying exponential plus a gain times the size of the noise. Our approach imposes several constraints on the plant; however, we show that there exists at least one interesting class of systems, which includes plants with unstable zero dynamics, that can be stabilized by our controller.iii

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“…We are now ready to present a slightly modified 2 version of Theorem 3.1 from [5], which will be used to construct our adaptive controller. Theorem 1.…”

Section: The Gain Scheduling Resultsmentioning

confidence: 99%

“…This will be achieved primarily through extending the work on gain scheduling in [5]. We will only consider a scalar parameter uncertainty, but assumption (ii) will be relaxed.…”

Section: Purposementioning

confidence: 99%

Section: Purposementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Nonlinear periodic adaptive control for linear time-varying plants

Rudko

Miller

2016

2016 American Control Conference (ACC)

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Robust Path Tracking Control

2021

Autonomous Road Vehicle Path Planning and Tracking Control

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Gain‐Scheduled Control via Switching of LTI Controllers and State Reset

Masubuchi¹,

Ishii²,

Ohta³

et al. 2015

Asian Journal of Control

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This paper proposes a synthesis method of gain-scheduled control systems that switch linear time-invariant controllers according to hysteresis of the scheduling parameter. Stability and L 2 -gain analysis and synthesis methods for switched systems are applied to the switched gain-scheduled control synthesis using reset of the controller state, where also the reset law is computed via linear matrix inequalities (LMIs). In addition to optimization of an upper bound of L 2 -gain, we reduce jumps of control input via an auxiliary optimization. Numerical examples are presented to illustrate the switched gain-scheduled controller.

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Stable LPV Realization of Parametric Transfer Functions and Its Application to Gain-Scheduling Control Design

Cited by 57 publications

References 32 publications

Nonlinear periodic adaptive control for linear time-varying plants

Nonlinear periodic adaptive control for linear time-varying plants

Robust Path Tracking Control

Gain‐Scheduled Control via Switching of LTI Controllers and State Reset

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