Discrete-time stability with perturbations: application to model predictive control

Scokaert, P.O.M.; Rawlings, James B.; Meadows, Edward S.

doi:10.1016/s0005-1098(96)00213-0

Cited by 168 publications

(98 citation statements)

References 14 publications

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“…However no significant progress with respect to the output feedback case has been made. The existing solutions are either of local nature (Scokaert et al, 1997;Magni et al, 1998) or difficult to implement (Michalska and Mayne, 1995). In this paper we have outlined, that using results from (Atassi and Khalil, 1999), "semi-global" stability results on a bounded region of attraction and recovery of performance can be achieved utilizing NMPC and a suited high gain observer for a class of systems.…”

Section: Discussionmentioning

confidence: 99%

“…In (Michalska and Mayne, 1995) a moving horizon observer is designed, that together with the NMPC scheme proposed in (Michalska and Mayne, 1993) is shown to lead to (semi-global) closed loop stability if no model-plant mismatch and disturbances are present. In (Magni et al, 1998), see also (Scokaert et al, 1997), local asymptotic stability for observer based discretetime nonlinear MPC is obtained for "weakly detectable" systems. However, these results are only of local nature, i.e.…”

Section: Introductionmentioning

confidence: 99%

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On output feedback nonlinear model predictive control using high gain observers for a class of systems

Imsland

Findeisen

Bullinger³

et al. 2001

IFAC Proceedings Volumes

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In recent years, nonlinear model predictive control schemes have been derived that guarantee stability of the closed loop under the assumption of full state information. However, only limited advances have been made with respect to output feedback in connection to nonlinear predictive control. Most of the existing approaches for output feedback nonlinear model predictive control do only guarantee local stability. Here we consider the combination of stabilizing instantaneous NMPC schemes with high gain observers. For a special MIMO system class we show that the closed loop is asymptotically stable, and that the output feedback NMPC scheme recovers the performance of the state feedback in the sense that the region of attraction and the trajectories of the state feedback scheme are recovered for a high gain observer with large enough gain and thus leading to semi-global/non-local results.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On output feedback nonlinear model predictive control using high gain observers for a class of systems

Imsland

Findeisen

Bullinger³

et al. 2001

IFAC Proceedings Volumes

View full text Add to dashboard Cite

show abstract

“…The same methodology is also adopted to perform the state estimation, namely the Receding Horizon Estimation e.g. Scokaert, et al, 1997), (Alessandri, et al, 2003). Though less popular than the Extended Kalman Filter (EKF), the RHE inherits most of the benefits from the MPC algorithm, and mainly adopted by the applications where hard constraints are applied to the estimator.…”

Section: Model Predictive Control (Mpc) 23mentioning

confidence: 99%

1-Bit processing based model predictive control for fractionated satellite missions

Bai

2014

Acta Astronautica

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In this thesis, a 1-bit processing based Model Predictive Control (OBMPC) structure is proposed for a fractionated satellite attitude control mission. Despite the appealing advantages of the MPC algorithm towards constrained MIMO control applications, implementing the MPC algorithm onboard a small satellite is certainly challenging due to the limited onboard resources. The proposed design is based on the 1-bit processing concept, which takes advantage of the affine relation between the 1-bit state feedback and multi-bit parameters to implement a multiplier free MPC controller.As multipliers are the major power consumer in online optimization, the OBMPC structure is proven to be more efficient in comparison to the conventional MPC implementation in term of power and circuit complexity. The system is in digital control nature, affected by quantization noise introduced by Δ∑ modulators. The stability issues and practical design criteria are also discussed in this work.Some other aspects are considered in this work to complete the control system. Firstly, the implementation of the OBMPC system relies on the 1-bit state feedbacks. Hence, 1-bit sensing components are needed to implement the OBMPC system. While the ∆∑ modulator based Microelectromechanical systems (MEMS) gyroscope is considered in this work, it is possible to implement this concept into other sensing components.Secondly, as the proposed attitude mission is based on the wireless inter-satellite link (ISL), a state estimator is required. However, conventional state estimators will once again introduce multi-bit signals, and compromise the simple, direct implementation of the OBMPC controller. Therefore, the 1-bit state estimator is also designed in this work to satisfy the requirements of the proposed fractionated attitude control mission.The simulation for the OBMPC is based on a 2U CubeSat model in a fractionated satellite structure, in which the payload and actuators are separated from the controller and controlled via the ISL. Matlab simulations and FPGA implementation based performance analysis shows that the OBMPC is feasible for fractionated satellite missions and is advantageous over the conventional MPC controllers. V VI

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“…These concepts can be extended to determine a variability index in order to establish a quantitative concept of stability (β-stability), as it was highlighted by (Srinivasan & Bonvin, 2007). To formulate this extension, the MPC stability conditions (rather than convergence conditions) must be defined, following the stability results presented in ( (Scokaert et al, 1997)). An extension of this remark is shown below.…”

Section: Decreasing Properties Of the Closed-loop Cost For A Single Runmentioning

confidence: 99%

Iterative Learning - MPC: an Alternative Strategy

Adam¹,

González²

2012

Frontiers in Advanced Control Systems

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Discrete-time stability with perturbations: application to model predictive control

Cited by 168 publications

References 14 publications

On output feedback nonlinear model predictive control using high gain observers for a class of systems

On output feedback nonlinear model predictive control using high gain observers for a class of systems

1-Bit processing based model predictive control for fractionated satellite missions

Iterative Learning - MPC: an Alternative Strategy

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