Regions of guaranteed cost for LMI-based robust model predictive controllers for systems with uncertain input delay

Rossi, Fernanda Quelho; Waschburger, Ronaldo; Galvão, Roberto Kawakami Harrop

doi:10.1109/systol.2013.6693826

Cited by 2 publications

(6 citation statements)

References 22 publications

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“…where ( ) ∈ R denotes the plant state at time , Φ ∈ R × , Γ ∈ R × are known matrices, and ∈ N is an uncertain delay, which may take values in the range [0, ]. For simplicity, the formulation presented herein is derived for a single-input system (i.e., = 1), as in [28]. However, the extension to the multiple-input case does not pose substantial difficulties, involving mostly changes in notation [35].…”

Section: Handling Of Uncertain Input Delaysmentioning

confidence: 99%

“…Remark 2. This polytopic description of the input delay uncertainty was adopted in [26][27][28] as a direct extension of the original RMPC formulation of [12]. This approach can also be employed if the delay is lower-bounded by a known value > 0, in which case the vertices of the uncertainty polytope Ω corresponding to Λ 0 , Λ 1 , .…”

Section: Handling Of Uncertain Input Delaysmentioning

confidence: 99%

“…A simpler approach can also be adopted if the uncertainty is restricted to the input delay. In this case, the original RMPC formulation of [12] can be employed by using an augmented state vector including current values of the state and past values of the control input [26][27][28]. As can be seen, much research effort has been devoted to the control of time delay systems with RMPC techniques derived from [12].…”

Section: Introductionmentioning

confidence: 99%

“…The RMPC approach adopted in this paper follows the formulation proposed in [12]. Uncertainty in the input delay is handled by using an augmented state vector, as in [28]. Moreover, offset-free tracking of step changes in the setpoint is ensured by introducing an integrator associated with the process variable of interest (water level).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust Predictive Control of Water Level in an Experimental Pilot Plant with Uncertain Input Delay

Rossi¹,

Galvão

2014

Mathematical Problems in Engineering

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This paper is concerned with the predictive control of water level in an experimental pilot plant, in the presence of input constraints and uncertain time delays. Robustness is achieved by casting the delay uncertainty into a polytopic form and using a predictive control formulation based on linear matrix inequalities. Integral action is introduced into the controller to ensure offset-free tracking of step changes in the setpoint. Moreover, an integrator resetting procedure based on the concept of regions of guaranteed cost is proposed to improve the resulting transient response. The results show that the introduction of robustness into the predictive control formulation is indeed of value to avoid closed-loop instability in the presence of time delays. In addition, the integrator resetting procedure was found to provide substantial performance improvements in terms of overshoot and settling time.

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Section: Handling Of Uncertain Input Delaysmentioning

confidence: 99%

Section: Handling Of Uncertain Input Delaysmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust Predictive Control of Water Level in an Experimental Pilot Plant with Uncertain Input Delay

Rossi¹,

Galvão

2014

Mathematical Problems in Engineering

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“…GCCs are obtained by either Linear Matrix Inequalities (LMI) [19] or Algebraic Riccati Equations (ARE) [26] and the concept was extended to polytopic-bounded l2-norm RM-PCs problems based on LMIs [21], [23]. However, a semidefinite programming (SDP) problem must be solved for the guaranteed cost constrained optimization, which increases computational requirements in comparison to LPs, QPs and QCQPs.…”

Section: Introductionmentioning

confidence: 99%

Guaranteed cost approach for robust model predictive control of uncertain linear systems

Massera

Terra

Wolf

2017

2017 American Control Conference (ACC)

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In this paper we propose a constrained guaranteed cost robust model predictive controller (GCMPC) for uncertain discrete time systems. This controller was developed based on a quadratic cost functional and guarantee robustness with respect to quadratically bound uncertainties. Such a class of problems is currently intractable by Min-Max Robust Model Predictive Controllers without polytopic approximations of the uncertainties. The proposed technique is computationally more efficient then an enumeration-based approach and requires only a Quadratically Constrained Quadratic Problem (QCQP) optimization, whereas LMI-based GCMPC approaches require a Semi-Definite Programming (SDP) optimization.

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Regions of guaranteed cost for LMI-based robust model predictive controllers for systems with uncertain input delay

Cited by 2 publications

References 22 publications

Robust Predictive Control of Water Level in an Experimental Pilot Plant with Uncertain Input Delay

Robust Predictive Control of Water Level in an Experimental Pilot Plant with Uncertain Input Delay

Guaranteed cost approach for robust model predictive control of uncertain linear systems

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