Model Predictive Control of a Vehicle using Koopman Operator

Cibulka, Vít; Haniš, Tomáš; Korda, Milan; Hromčík, Martin

doi:10.1016/j.ifacol.2020.12.2469

Cited by 16 publications

(2 citation statements)

References 6 publications

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“…Model identification for nonlinear tire dynamics using EDMD is investigated in both [36] and [37], with the former utilizing a single-track model (making it applicable to motorcycles), while the latter further applies MPC control. Similarly, [5] develops an MPC controller with a single-track model obtained by learning Koopman-invariant observables directly from data to recover the vehicle from a nonlinear state (e.g., skidding), when present. MPC is also used to minimize bounce by means of adjusting propulsive force in [41] while using EDMD for their model generation, thus becoming an alternative method for suspension control.…”

Section: Automotive Model Identification and Controlmentioning

confidence: 99%

Vehicular Applications of Koopman Operator Theory—A Survey

2023

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Koopman operator theory has proven to be a promising approach to nonlinear system identification and global linearization. For nearly a century, there had been no efficient means of calculating the Koopman operator for applied engineering purposes. The introduction of a recent computationally efficient method in the context of fluid dynamics, which is based on the system dynamics decomposition to a set of normal modes in descending order, has overcome this long-lasting computational obstacle. The purely data-driven nature of Koopman operators holds the promise of capturing unknown and complex dynamics for reduced-order model generation and system identification, through which the rich machinery of linear control techniques can be utilized. Given the ongoing development of this research area and the many existing open problems in the fields of smart mobility and vehicle engineering, a survey of techniques and open challenges of applying Koopman operator theory to this vibrant area is warranted. This review focuses on the various solutions of the Koopman operator which have emerged in recent years, particularly those focusing on mobility applications, ranging from characterization and component-level control operations to vehicle performance and fleet management. Moreover, this comprehensive review of over 100 research papers highlights the breadth of ways Koopman operator theory has been applied to various vehicular applications with a detailed categorization of the applied Koopman operator-based algorithm type. Furthermore, this review paper discusses theoretical aspects of Koopman operator theory that have been largely neglected by the smart mobility and vehicle engineering community and yet have large potential for contributing to solving open problems in these areas.

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Section: Automotive Model Identification and Controlmentioning

confidence: 99%

Vehicular Applications of Koopman Operator Theory—A Survey

2023

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“…We note that deriving linear representations of finite-dimensional nonlinear systems can also be achieved through the use of Koopman operators (Goswami and Paley, 2017;Mesbahi et al, 2019). A Koopman operator approach has recently been used in model predictive control of vehicles with deterministic nonlinear dynamics (Cibulka et al, 2020).…”

Section: Related Workmentioning

confidence: 99%

Moment Propagation Through Carleman Linearization with Application to Probabilistic Safety Analysis

Pruekprasert¹,

Dubut²,

Takisaka³

et al. 2022

Preprint

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We develop a method to approximate the moments of a discrete-time stochastic polynomial system. Our method is built upon Carleman linearization with truncation. Specifically, we take a stochastic polynomial system with finitely many states and transform it into an infinitedimensional system with linear deterministic dynamics, which describe the exact evolution of the moments of the original polynomial system. We then truncate this deterministic system to obtain a finite-dimensional linear system, and use it for moment approximation by iteratively propagating the moments along the finite-dimensional linear dynamics across time. We provide efficient online computation methods for this propagation scheme with several error bounds for the approximation. Our result also shows that precise values of certain moments can be obtained when the truncated system is sufficiently large. Furthermore, we investigate techniques to reduce the offline computation load using reduced Kronecker power. Based on the obtained approximate moments and their errors, we also provide probability bounds for the state to be outside of given hyperellipsoidal regions. Those bounds allow us to conduct probabilistic safety analysis online through convex optimization. We demonstrate our results on a logistic map with stochastic dynamics and a vehicle dynamics subject to stochastic disturbance.

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