An Analysis of Closed-Loop Stability for Linear Model Predictive Control Based on Time-Distributed Optimization

Pherson, Dominic Liao-Mc; Skibik, Terrence; Leung, Jordan; Kolmanovsky, Ilya; Nicotra, Marco M.

doi:10.1109/tac.2021.3086295

Cited by 16 publications

(10 citation statements)

References 29 publications

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“…Apply the sub-optimal control law π K i (x i,t ); end if end for end for Remark 2 When all the constraints in (10) are polytopic, the Lipschitz constant L exists and can be determined as the maximal gain of the explicit MPC solution of (10) in [18]. When the DMPC problem (10) only contains input constraints, the Lipschitz constant L can be determined analytically in [9].…”

Section: A Dmpc With Coupled Cost Functionsmentioning

confidence: 99%

“…Inspired by [9], we choose ψ(x t ) := V (x t ), as an ISS-Lyapunov function for the sub-optimally controlled MAS (16). We also show C α,t and t := ∆z t are ISS-Lyapunov functions for the initial quantization interval update process (17) and the the quantized distributed optimization process (18), respectively, if n and K satisfy certain conditions.…”

Section: Iss-lyapunov Functions For Subsystem 1 2 Andmentioning

confidence: 99%

“…The difference between Proposition 2 and Theorem 3 in [9] is we define the Lipschitz constant L differently in (13). The following bound on ∆x t is used in Propositions 3 and 4.…”

Section: Iss-lyapunov Functions For Subsystem 1 2 Andmentioning

confidence: 99%

“…In [5], [6], and [7], different MPC schemes are combined with real-time stability-guaranteeing mechanisms that are verified on-line. In [8] and [9], the small-gain theorem is used to derive sufficient conditions for stability of dynamics-optimizer systems, where the former assumes Lipschitz continuity of the MPC problem and the latter considers MPC with only input constraints. In [10], the smallgain theorem is applied for stability analysis of an MAS interconnected with an output coordinator and nonlinear controllers.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: A Dmpc With Coupled Cost Functionsmentioning

confidence: 99%

Section: Iss-lyapunov Functions For Subsystem 1 2 Andmentioning

confidence: 99%

“…The difference between Proposition 2 and Theorem 3 in [9] is we define the Lipschitz constant L differently in (13). The following bound on ∆x t is used in Propositions 3 and 4.…”

Section: Iss-lyapunov Functions For Subsystem 1 2 Andmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…Another approach considers the combined system-optimizer dynamics. Timedistributed optimization [8], [9] or real-time iterative algorithms [10], [11] are examples of such an approach, where only a finite number of iterations of an optimization problem are performed at each time. 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.…”

Section: Introductionmentioning

confidence: 99%

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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The role of identification in data‐driven policy iteration: A system theoretic study

Song,

Iannelli

2024

Intl J Robust & Nonlinear

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The goal of this article is to study fundamental mechanisms behind so‐called indirect and direct data‐driven control for unknown systems. Specifically, we consider policy iteration applied to the linear quadratic regulator problem. Two iterative procedures, where data collected from the system are repeatedly used to compute new estimates of the desired optimal controller, are considered. In indirect policy iteration, data are used to obtain an updated model estimate through a recursive identification scheme, which is used in a certainty‐equivalent fashion to perform the classic policy iteration update. By casting the concurrent model identification and control design as a feedback interconnection between two algorithmic systems, we provide a closed‐loop analysis that shows convergence and robustness properties for arbitrary levels of excitation in the data. In direct policy iteration, data are used to approximate the value function and design the associated controller without requiring the intermediate identification step. After proposing an extension to a recently proposed scheme that overcomes potential identifiability issues, we establish under which conditions this procedure is guaranteed to deliver the optimal controller. Based on these analyses we are able to compare the strengths and limitations of the two approaches, highlighting aspects such as the required samples, convergence properties, and excitation requirement. Simulations are also provided to illustrate the results.

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An Analysis of Closed-Loop Stability for Linear Model Predictive Control Based on Time-Distributed Optimization

Cited by 16 publications

References 29 publications

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

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

On the Regret of H_∞ Control

The role of identification in data‐driven policy iteration: A system theoretic study

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An Analysis of Closed-Loop Stability for Linear Model Predictive Control Based on Time-Distributed Optimization

Cited by 16 publications

References 29 publications

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

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

On the Regret of H∞ Control

The role of identification in data‐driven policy iteration: A system theoretic study

Contact Info

Product

Resources

About

On the Regret of H_∞ Control