A Computable Plant-Optimizer Region of Attraction Estimate for Time-distributed Linear Model Predictive Control

Leung, Jordan; Liao‐McPherson, Dominic; Kolmanovsky, Ilya

doi:10.23919/acc50511.2021.9482879

Cited by 11 publications

(12 citation statements)

References 15 publications

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“…. The lemma is a slightly modified version of [12, Lemma 7] with time-varying ℓ k -s. The proof follows directly from the one found in [12]. The following shows the existence of a Lyapunov function for the augmented state s k .…”

Section: B Suboptimal Mpcmentioning

confidence: 81%

“…The asymptotic stability of the time-distributed optimization MPC (TD-MPC) scheme is studied in [8] for discrete-time non-linear models with state and input constraints, and an explicit form for a Lyapunov function is derived in [11] for the same setting. Discrete-time linear models with a quadratic cost objective (LQMPC) are studied in [9] and a region of attraction (ROA) estimate is derived in [12].…”

Section: Introductionmentioning

confidence: 99%

“…Firstly, we propose scheduling the number of iterative optimization steps, ℓ k , in advance, and allowing them to be time-varying based on the available computational budget. Building on [11], [12] we derive an explicit form for the rate of decay of the exponentially stable suboptimal dynamics under certain conditions on ℓ k -s. Secondly, we study the transient performance of this scheme by quantifying its incurred suboptimality, which we define as the additional incurred closed-loop cost due to the approximate solution of the optimization problem. Finally, using our new analysis, we propose a diminishing horizon suboptimal MPC algorithm, called Dim-SuMPC, and quantify its finite-time performance.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the Regret of H_∞ Control

Karapetyan¹,

Iannelli²,

Lygeros³

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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The H∞ synthesis approach is a cornerstone robust control design technique, but is known to be conservative in some cases. The objective of this paper is to quantify the additional cost the controller incurs planning for the worst-case scenario, by adopting an approach inspired by regret from online learning. We define the disturbance-reality gap as the difference between the predicted worst-case disturbance signal and the actual realization. The regret is shown to scale with the norm of this gap, which turns out to have a similar structure to that of the certainty equivalent controller with inaccurate predictions, obtained here in terms of the prediction error norm.

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Section: B Suboptimal Mpcmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the Regret of H_∞ Control

Karapetyan¹,

Iannelli²,

Lygeros³

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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show abstract

“…Lemma 1 (Lemma 6, [19]) Consider the MAS (9) controlled by π K (x t ) defined in (12). The change in the state ∆x t = x t+1 − x t of the MAS satisfies…”

Section: Iss-lyapunov Functions For Subsystem 1 2 Andmentioning

confidence: 99%

“…where t := ∆z t . Bounding the right hand side of (42) with ( 44) and (45) gives (19). Since L ≥ 1 and λ(H) ≥ λ(Q), we know that α 1 ∈ (0, 1).…”

Section: B Proof Of Propositionmentioning

confidence: 99%

Real-time Distributed MPC for Multiple Underwater Vehicles with Limited Communication Data-rates

Yang

Wang

Manzie

et al. 2021

2021 American Control Conference (ACC)

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The application of distributed model predictive controllers (DMPC) for multi-agent systems (MASs) necessitates communication between agents, yet the consequence of communication data rates is typically overlooked. This work focuses on developing stability-guaranteed control methods for MASs with limited data rates. Initially, a distributed optimization algorithm with dynamic quantization is considered for solving the DMPC problem. Due to the limited data rate, the optimization process suffers from inexact iterations caused by quantization noise and premature termination, leading to suboptimal solutions. In response, we propose a novel real-time DMPC framework with a quantization refinement scheme that updates the quantization parameters on-line so that both the quantization noise and the optimization sub-optimality decrease asymptotically. To facilitate the stability analysis, we treat the sub-optimally controlled MAS, the quantization refinement scheme, and the optimization process as three interconnected subsystems. The cyclic-small-gain theorem is used to derive sufficient conditions on the data rate for guaranteeing the asymptotic stability of the system. Finally, the proposed algorithm and theoretical findings are demonstrated on a multi-AUV formation control example.

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Robust reference governor for input-constrained model predictive control to enforce state constraints at low computational cost

Castroviejo-Fernandez,

Leung,

Kolmanovsky

2024

International Journal of Control

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A Computable Plant-Optimizer Region of Attraction Estimate for Time-distributed Linear Model Predictive Control

Cited by 11 publications

References 15 publications

On the Regret of H_∞ Control

On the Regret of H_∞ Control

Real-time Distributed MPC for Multiple Underwater Vehicles with Limited Communication Data-rates

Robust reference governor for input-constrained model predictive control to enforce state constraints at low computational cost

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A Computable Plant-Optimizer Region of Attraction Estimate for Time-distributed Linear Model Predictive Control

Cited by 11 publications

References 15 publications

On the Regret of H∞ Control

On the Regret of H∞ Control

Real-time Distributed MPC for Multiple Underwater Vehicles with Limited Communication Data-rates

Robust reference governor for input-constrained model predictive control to enforce state constraints at low computational cost

Contact Info

Product

Resources

About

On the Regret of H_∞ Control

On the Regret of H_∞ Control