Basis functions design for the approximation of constrained linear quadratic regulator problems encountered in model predictive control

Muehlebach, Michael; D’Andrea, Raffaello

doi:10.1109/cdc.2017.8264593

Cited by 4 publications

(3 citation statements)

References 17 publications

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“…), (10) where ω denotes the frequency (rad/s). • In case the dynamics in (1) are linear time-invariant, the cost is quadratic, and constraints are absent (g = 0), the choice M = A + BK, where A and B refer to the system dynamics, and K to the infinite-horizon linear quadratic regulator gain, recovers the solutions to the infinite-horizon linear quadratic regulator problem (see [22] for the continuous-time analogue). Any superposition of the above choices is valid as well, and is obtained by a blockdiagonal choice of the matrix M .…”

Section: A Examplesmentioning

confidence: 99%

“…The input and state parametrizations that will be introduced in the following can be viewed as approximations to the underlying constrained linear quadratic regulator problem. This point of view has been explored in the technical report [16], where various approximation results (including convergence) are discussed. Preliminary results appeared in the conference papers [17] and [18].…”

Section: Introductionmentioning

confidence: 99%

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A Method for Reducing the Complexity of Model Predictive Control in Robotics Applications

Muehlebach

D’Andrea

2019

IEEE Robot. Autom. Lett.

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This article describes an approach for parametrizing input and state trajectories in model predictive control. The parametrization is designed to be invariant to time shifts, which enables warm-starting the successive optimization problems and reduces the computational complexity of the online optimization. It is shown that in certain cases (e.g. for linear time-invariant dynamics with input and state constraints) the parametrization leads to inherent stability and recursive feasibility guarantees without additional terminal set constraints. Due to the fact that the number of decision variables are greatly reduced through the parametrization, while the warmstarting capabilities are preserved, the approach is suitable for applications where the available computational resources (memory and CPU-power) are limited.

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Section: A Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Method for Reducing the Complexity of Model Predictive Control in Robotics Applications

Muehlebach

D’Andrea

2019

IEEE Robot. Autom. Lett.

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“…However, the use of a simple first order Laguerre function is still somewhat limited, and for higher-order systems, significant prediction inconsistency may still exist. While it is possible to increase the order of the Laguerre polynomial [15], this is not straightforward in general [16] and not in line with the simplicity concept which is an essential facet of PFC.…”

Section: Introductionmentioning

confidence: 99%

Improved Constraint Handling Approach for Predictive Functional Control Using an Implied Closed-Loop Prediction

Abdullah

Rossiter

Ghaffar³

2021

IIUMEJ

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Predictive Functional Control is a simple alternative to the traditional PID controller which has the capability to handle process constraints more systematically. Nevertheless, the most basic form of PFC has suffered from ill-posed prediction due to its simplicity in formulation and assumption of constant future input dynamics. Although some constraints can be satisfied, nevertheless the performance may be very conservative due to this issue. The main objective of this paper is to improve the constrained performance of a PFC controller with a minimum modification of the existing formulation. Specifically, a novel constraint handling approach for PFC is proposed based on an implied closed-loop prediction. Instead of assuming a constant input as deployed in the conventional open-loop prediction, the implied closed-loop input dynamics are utilised to detect future constraint violations. In addition, a future perturbation is introduced into the prediction structure as an extra degree of freedom for satisfying the constraints. Two simulation results confirm that the proposed approach gives far less conservative constraint handling and thus better control performance compared to the nominal PFC. Furthermore, this novel implementation also alleviates the well-known tuning difficulties and prediction inconsistency issues that are associated with conventional PFC when handling constraints. ABSTRAK: Kawalan Kefungsian Ramalan adalah alternatif mudah kepada kawalan tradisional PID yang mempunyai kekangan keupayaan bagi mengawal proses secara lebih tersusun. Namun, keadaan paling asas pada kesan PFC adalah daripada ramalan tak teraju-rapi yang disebabkan oleh formula ringkas dan anggapan dinamik input yang sama bagi masa depan. Walau kekangan ini dapat diatasi, namun prestasi akan berubah secara konservatif disebabkan oleh isu ini. Objektif utama kajian ini adalah bagi membaiki kekangan prestasi kawalan PFC dengan modifikasi minimum formula yang ada. Secara spesifik, pendekatan nobel kawalan PFC dicadangkan berdasarkan ramalan lingkaran-tertutup. Selain anggapan input tetap seperti yang dilakukan pada ramalan lingkaran-terbuka yang konservatif, dinamik input yang dibuat pada lingkaran-tertutup telah digunakan bagi mengesan kekangan masa depan yang bertentangan. Tambahan, gangguan yang bakal berlaku pada masa depan telah diperkenalkan ke dalam struktur ramalan sebagai tambahan darjah pada kebebasan bagi mengatasi kekangan. Dua dapatan simulasi kajian menyetujui pendekatan yang dicadangkan dan menyebabkan sangat kurang kekangan pengendalian pada sistem konservatif, oleh itu kawalan yang lebih bagus pada prestasi berbanding pada PFC nominal. Selain itu, pendekatan nobel ini juga menghilangkan kesukaran pelarasan yang dikenali ramai dan ramalan isu tidak konsisten yang terdapat pada PFC konvensional apabila mengendali kekangan.

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Using Laguerre functions to improve the tuning and performance of predictive functional control

Abdullah

Rossiter

2019

International Journal of Control

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This paper proposes an alternative parameterisation of the degrees of freedom in a predictive functional control (PFC) law. Using recent insights on the potential of Laguerre functions in traditional MPC (Rossiter et al., 2010;Wang, 2009), it is demonstrated that these functions can also be exploited to give a good effect in PFC. An appropriate design with tuning methodology is developed and this is then demonstrated with a number of numerical examples.

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Basis functions design for the approximation of constrained linear quadratic regulator problems encountered in model predictive control

Cited by 4 publications

References 17 publications

A Method for Reducing the Complexity of Model Predictive Control in Robotics Applications

A Method for Reducing the Complexity of Model Predictive Control in Robotics Applications

Improved Constraint Handling Approach for Predictive Functional Control Using an Implied Closed-Loop Prediction

Using Laguerre functions to improve the tuning and performance of predictive functional control

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