1,720,998 research outputs found
Kernel-Based Continuous-Time System Identification: A Parametric Approximation
No full textIn this paper, we discuss the non-parametric estimate problem using kernel-based LTI system identification techniques by constructing a Loewner-based interpolant of the estimated model. Through this framework, we have been able to retrieve a finite-dimensional approximation of the infinite-dimensional estimate obtained using the classical kernel-based methodologies. The employment of the Loewner framework constitutes an enhancement of recent results which propose to use a Pade approximant to obtain a rational transfer function from an irrational transfer function corresponding to the identified impulse response. The enhancement has been illustrated for the identification of the Rao-Garnier benchmark
Kernel-Based Identification of Incrementally Input-to-State Stable Nonlinear Systems
Full text linkMethods based on Reproducing Kernel Hilbert Spaces (RKHS) have proven to be a valuable tool for the identification of linear time-invariant systems in both discrete- and continuous-time. In particular, unlike most other techniques, they enable to systematically confer a priori desirable properties, such as stability, on the estimated models. However, existing RKHS methods mainly target impulse responses and, hence, do not extend well to the context of nonlinear systems. In this work, we propose a novel RKHS-based methodology for the identification of discrete-time nonlinear systems guaranteeing that the identified system is incrementally input-to-state stable (dISS). We model the identified system using a predictor function that, given past input and output samples, yields the output prediction at the next time instant. The predictor is selected from an RKHS by solving a constrained optimization problem that guarantees its dISS properties. The proposed approach is validated via numerical simulations. Copyright (c) 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/
Group-Based Dimensionality Reduction and Estimation for Heterogeneous Large-Scale Traffic Networks
No full textState estimation for traffic networks is a particu-larly challenging problem in view of their large dimensionality, and since models are often inaccurate and the interaction pat-terns unpredictable. In this article, we approach the problem by mixing aggregation-based complexity reduction and nonlinear filtering. We subdivide vehicles into groups and derive a lower-dimensional approximate model where vehicles belonging to the same group are represented by a unique random variable matching their average characteristics. Then, we propose a procedure to estimate the statistical properties of the group variables from partial measurements. Connections to car-following models are discussed, and the developed methodology is illustrated through numerical simulations
Nonlinear Data-Driven Moment Matching in Reproducing Kernel Hilbert Spaces
No full textThe continuously increasing amount of noisy data demands the development of accurate and efficient models for analysis, modeling, and control. In this article, we propose a novel data-driven moment matching method which employs Tikhonov regularization in the Reproducing Kernel Hilbert Spaces (RKHSs). Specifically, considering a realistic scenario in which the system's plant is unknown and only noisy measured data are available, we provide an estimation of the moment of the unknown plant by solving a regularized optimization problem on RKHS. For, we first demonstrate that the estimation of the moment can be improved via tuning the regularization term, and further, we show under which condition the effect of the transient improves the performance of the estimation. Then, we construct a parameterized model characterized by a kernel-based output mapping. Finally, the proposed data-driven approach is validated and discussed by means of a DC-to-DC Cuk converter driven by a Van der Pol oscillator
Moment Matching by Kernel-Based Learning
Full text linkWe introduce a kernel-based moment matching theory which relies upon a novel data-driven model reduction method that employs the estimation of moments within a Reproducing Kernel Hilbert Space. We demonstrate that moment estimation can be enhanced by appropriately tuning the regularization term, regardless of the kernel choice. Additionally, we present conditions to ensure that the Reproducing Kernel Hilbert Space contains only functions which are bona fide moments. While exact moment matching with finite data is impractical in this scenario, we introduce the concepts of weak moment matching and moment matching almost everywhere onto the L2-space. Additionally, we address scenarios in which the dataset contains noisy measurements of outputs that are not yet in a steady-state, which typically biases the estimation due to the effect of the output transients. We further prove that estimating over a Reproducing Kernel Hilbert Space can ensure weak moment matching asymptotically and, with additional assumptions, also moment matching almost everywhere despite these transients. Finally, we provide a probabilistic bound that guarantees weak moment matching for an arbitrarily finite amount of data
Are Artificial Neural Networks suitable for data-driven moment matching?
Full text linkWe investigate the use of artificial neural networks in the context of data-driven moment matching for nonlinear systems, comparing it with state-of-the-art approaches that rely on regularized kernel methods or least squares. We propose a novel neural network model that shares the properties of the moment function of a nonlinear system, which can be learned by means of surrogate-based black-box optimization methods (such as Bayesian optimization). To validate the proposed approach, we conduct an extensive simulation analysis of the method on two benchmark model reduction problems, employing different settings and comparing with state-of-the-art methods. This investigation suggests that neural networks are a suitable and promising approach for data-driven moment matching, and they appear to show comparable performance to state-of-the-art methods based on regularized kernel methods
Traffic-Light Control at Urban Intersections Using Expected Waiting-Time Information
No full textWe consider an optimal traffic-light control framework for urban traffic intersections to alleviate congestion phenomena. We analyze a scenario in which we provide drivers with information about the waiting time at the intersections. We model the drivers' lane-changing information-based behavior as the solution of a convex optimization problem. We compute the optimal traffic-light control mechanism as the solution to a bi-level optimization problem. We provide a complete analysis in terms of (i) the existence of a solution; (ii) an iterative algorithm to compute it; (iii) sufficient conditions for the solution's uniqueness and the algorithm's convergence. Early simulation results show the proposed control scheme's effectiveness compared with an optimal control algorithm in the absence of waiting-time information
Automated Data-Driven Tuning of Learning-Based Model Predictive Control (SelfMPC): A Maximum-Likelihood Approach
No full textThe practical implementation of Model Predictive Control (MPC) often presents challenges that remain unaddressed in theoretical formulations. Among these challenges, the tuning of the receding horizon cost becomes particularly intricate in the context of data-driven learning-based MPC, where models exhibit partial uncertainty. This paper introduces SelfMPC, a pioneering approach within a Gaussian process learning framework, illustrating that a tracking MPC cost can be formulated as the maximum likelihood estimation of the reference output. This formulation provides automatic cost shaping and effective regularization, eliminating the need for manual tuning efforts. Moreover, the proposed formulation provides a natural way to employ information from empirical experiments into the definition of the MPC optimization problem for unknown systems. Empirical validation against conventional weighting matrix selection methods confirms the effectiveness of the proposed approach
Traffic-light control in urban environment exploiting drivers’ reaction to the expected red lights duration
Full text linkTraffic congestion in urban environment is one of the most critical issue for drivers and city planners for both environment and efficiency reasons. Traffic lights are one of the main tools used to regulate traffic by diverting the drivers between different paths. Rational drivers, in turn, react to the traffic light duration by evaluating their options and, if necessary, by changing direction in order to reach their destination quicker. In this paper, we introduce a macroscopic traffic model for urban intersections that incorporates this rational behavior of the drivers. Then, we exploit it to show that, by providing additional information about the expected red -time duration to the drivers, one can decrease the amount of congestion in the network and the overall length of the queues at the intersections. Additionally, we develop a control policy for the traffic lights that exploits the reaction of the drivers in order to divert them to a different route to further increase the performances. These claims are supported by extensive numerical simulations
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