The paper introduces novel methodologies for the identification of coefficients of switched autoregressive and switched autoregressive exogenous linear models. We consider cases which system's outputs are contaminated by possibly large values of noise for the both case of measurement noise in switched autoregressive models and process noise in switched autoregressive exogenous models. It is assumed that only partial information on the probability distribution of the noise is available. Given input-output data, we aim at identifying switched system coefficients and parameters of the distribution of the noise, which are compatible with the collected data. We demonstrate the efficiency of the proposed approach with several academic examples. The method is shown to be extremely effective in the situations where a large number of measurements is available; cases in which previous approaches based on polynomial or mixed-integer optimization cannot be applied due to very large computational burden.
Identification of Switched Autoregressive Systems from Large Noisy Data Sets
School of Electrical Engineering and Computer Science, The Pennsylvania State University（宾夕法尼亚州立大学电气与计算机工程学院）；CNR-IEIIT, Politecnico di Torino（都灵理工大学意大利国家研究委员会信息与电子工程研究所）
California Institute of Technology（加州理工学院）；Purdue University（普渡大学）
Autoregressive exogenous (ARX) systems are the general class of input-output dynamical systems used for modeling stochastic linear dynamical systems (LDS) including partially observable LDS such as LQG systems. In this work, we study the problem of system identification and adaptive control of unknown ARX systems. We provide finite-time learning guarantees for the ARX systems under both open-loop and closed-loop data collection. Using these guarantees, we design adaptive control algorithms for unknown ARX systems with arbitrary strongly convex or convex quadratic regulating costs. Under strong…
In this paper, we present a methodology to identify discrete-time state-space switched linear systems (SLSs) from input-output measurements. Continuous-state is not assumed to be measured. The key step is a deadbeat observer based transformation to a switched auto-regressive with exogenous input (SARX) model. This transformation reduces the state-space identification problem to a SARX model estimation problem. Overfitting issues are tackled. The switch and parameter identifiability and the persistence of excitation conditions on the inputs are discussed in detail. The discrete-states are ident…
Understanding the models that characterize the thermal dynamics in a smart building is important for the comfort of its occupants and for its energy optimization. A significant amount of research has attempted to utilize thermodynamics (physical) models for smart building control, but these approaches remain challenging due to the stochastic nature of the intermittent environmental disturbances. This paper presents a novel data-driven approach for indoor thermal model inference, which combines an Autoregressive Moving Average with eXogenous inputs model (ARMAX) with a Normalized Mutual Informa…
Models can be built directly from input and output data trough a process known as system identification. The Nonlinear AutoRegressive with eXogenous inputs (NARMAX) models are among the most used mathematical representations in the area and has many successful applications on data-driven modeling in different fields. Such models become extremely large when they have high degree of non-linearity and long-term dependencies. Hence, a structure selection process must be performed to make them parsimonious. In the present paper, it is introduced a toolbox in Python that performs the structure selec…
We introduce a concept of $autoregressive$ (AR)state-space realization that could be applied to all transfer functions $\boldsymbol{T}(L)$ with $\boldsymbol{T}(0)$ invertible. We show that a theorem of Kalman implies each Vector Autoregressive model (with exogenous variables) has a minimal $AR$-state-space realization of form $\boldsymbol{y}_t = \sum_{i=1}^p\boldsymbol{H}\boldsymbol{F}^{i-1}\boldsymbol{G}\boldsymbol{x}_{t-i}+\boldsymbolε_t$ where $\boldsymbol{F}$ is a nilpotent Jordan matrix and $\boldsymbol{H}, \boldsymbol{G}$ satisfy certain rank conditions. The case $VARX(1)$ corresponds to…
Eindhoven University of Technology（埃因霍温理工大学）；IDSIA Dalle Molle Institute for Artificial Intelligence USI-SUPSI（IDSIA 达莱·莫勒人工智能研究所（USI-SUPSI））
This work presents a novel regularization method for the identification of Nonlinear Autoregressive eXogenous (NARX) models. The regularization method promotes the exponential decay of the influence of past input samples on the current model output. This is done by penalizing the sensitivity of the NARX model simulated output with respect to the past inputs. This promotes the stability of the estimated models and improves the obtained model quality. The effectiveness of the approach is demonstrated through a simulation example, where a neural network NARX model is identified with this novel me…
Ensuring Stability of Non-Minimal Modes in Input-Output Data-Driven Representation
KTH Royal Institute of Technology（皇家理工学院）；Soongsil University（崇实大学）；Seoul National University（首尔大学）；ETH Zürich（苏黎世联邦理工学院）；Hyundai Motor Company（现代汽车公司）
A turbocharger plays an essential part in reducing emissions and increasing the fuel efficiency of road vehicles. The pulsating flow of exhaust gases, along with high heat exchange from the turbocharger casing, makes developing control-oriented models difficult. Several researchers have used maps provided by manufacturers to solve this problem. These maps often fail to incorporate any heat transfer effects and are unsuitable for wide operating regions. Also, with the availability of more and better sensor data, there is a need for a method that can exploit this to obtain a better predictive mo…
