Stabilizing predictive control with persistence of excitation for constrained linear systems

Vicente, Bernardo A. Hernandez; Trodden, Paul

doi:10.1016/j.sysconle.2019.03.003

Cited by 13 publications

(3 citation statements)

References 27 publications

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“…In dual control, the cost function often includes a term to maximize the level of excitation in the resulting trajectory [31,32,33,34,35,36]. According to Willems' lemma, a loss of full row rank means a loss of persistent excitation in a Hankel matrix.…”

Section: A Note On Singular Values Of the Trajectory Matricesmentioning

confidence: 99%

Comparison of behavioral systems theory and conventional linear models for predicting building zone temperature in long-term in situ measurements

Koch¹,

Jones²

2023

Preprint

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The potential of Model Predictive Control in buildings has been shown many times, being successfully used to achieve various goals, such as minimizing energy consumption or maximizing thermal comfort. However, mass deployment has thus far failed, in part because of the high engineering cost of obtaining and maintaining a sufficiently accurate model. This can be addressed by using adaptive data-driven approaches. The idea of using behavioral systems theory for this purpose has recently found traction in the academic community. In this study, we compare variations thereof with different amounts of data used, different regularization weights, and different methods of data selection. Autoregressive models with exogenous inputs (ARX) are used as a well-established reference. All methods are evaluated by performing iterative system identification on two long-term data sets from real occupied buildings, neither of which include artificial excitation for the purpose of system identification. We find that: (1) Sufficient prediction accuracy is achieved with all methods. (2) The ARX models perform slightly better, while having the additional advantages of fewer tuning parameters and faster computation. (3) Adaptive and non-adaptive schemes perform similarly. (4) The regularization weights of the behavioral systems theory methods show the expected trade-off characteristic with an optimal middle value. ( 5) Using the most recent data yields better performance than selecting data with similar weather as the day to be predicted. ( 6) More data improves the model performance.

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Section: A Note On Singular Values Of the Trajectory Matricesmentioning

confidence: 99%

Comparison of behavioral systems theory and conventional linear models for predicting building zone temperature in long-term in situ measurements

Koch¹,

Jones²

2023

Preprint

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show abstract

“…The objective is to maintain the system state within a secure region centered around the origin, typically formulated as a convex problem. Introducing greater flexibility, an adaptive MPC [19], [20], [21] is devised, incorporating the fulfillment of the Persistence of Excitation (PE) condition [22]. This approach aims to ensure the controlled system exhibits properties of robust stability and recursive feasibility.…”

Section: Introductionmentioning

confidence: 99%

Efficient Motion Planning With Minimax Objectives: Synergizing Interval Prediction and Tree-Based Planning

Vo,

Jung,

Kim

et al. 2024

IEEE Access

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“…We omit the proof for brevity, but refer the reader to[8],[38] for the proof and to[41] for a discussion about model uncertainty.…”

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confidence: 99%

Fast Tube Model Predictive Control for Driverless Cars Using Linear Data-Driven Models

Vicente

Trodden

Anderson

2023

IEEE Trans. Contr. Syst. Technol.

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Model predictive control (MPC) has been widely applied to different aspects of autonomous driving, typically employing nonlinear physically derived models for prediction. However, feedback control systems inherently correct for model errors, thus in many applications it is sufficient to use a linear time-invariant (LTI) model for control design, especially when using robust control methods. This philosophy of approach appears to have been neglected in current driverless car research, and is the research gap that we aim to address here. Namely, instead of deriving meticulous nonlinear physical models of vehicle dynamics, and solving a correspondingly complex optimal control problem, we identify a low-order data-driven LTI model and handle its uncertainty via robust linear MPC methods. We develop a two-step control scheme for driverless cars based on tube MPC (TMPC), which introduces structural robustness, ensuring constraint compliance despite modelling error in the data-driven prediction model. Furthermore, we employ fast optimisation methods designed to exploit the special structure of the linear MPC problem. We evaluate the proposed control scheme using a vehicle model identified from real-world data, and simulations in IPGCarmaker, where the model of the vehicle under control is inherently nonlinear and uses detailed 3D physics. Our results show that an LTI model can be effectively employed for the task of lane-keeping, that TMPC can prevent lane departure and possible collisions due to model uncertainty, and that linear models allow for several algorithmic improvements that can decrease computation time by an order of magnitude compared to naive MPC implementations.

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Stabilizing predictive control with persistence of excitation for constrained linear systems

Abstract: Article:Hernandez Vicente, B.A. orcid.org/0000-0003-0701-5590 and Trodden, P.A. orcid.org/0000-0002-8787-7432 (2019) Stabilizing predictive control with persistence of excitation for constrained linear systems. Systems and Control Letters,

Cited by 13 publications

References 27 publications

Comparison of behavioral systems theory and conventional linear models for predicting building zone temperature in long-term in situ measurements

Comparison of behavioral systems theory and conventional linear models for predicting building zone temperature in long-term in situ measurements

Efficient Motion Planning With Minimax Objectives: Synergizing Interval Prediction and Tree-Based Planning

Fast Tube Model Predictive Control for Driverless Cars Using Linear Data-Driven Models

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