Direct identification of continuous-time linear switched state-space models

This paper presents an algorithm for direct continuous-time (CT) identification of linear switched state-space (LSS) models. The key idea for direct CT identification is based on an integral architecture consisting of an LSS model followed by an integral block. This architecture is used to approximate the continuous-time state map of a switched system. A properly constructed objective criterion is proposed based on the integral architecture in order to estimate the unknown parameters and signals of the LSS model. A coordinate descent algorithm is employed to optimize this objective, which alternates between computing the unknown model matrices, switching sequence and estimating the state variables. The effectiveness of the proposed algorithm is shown via a simulation case study.Comment: Preprint submitted to IFAC World Congress 202

Direct Data-Driven Computation of Polytopic Robust Control Invariant Sets and State-Feedback Controllers

This paper presents a direct data-driven approach for computing robust control invariant (RCI) sets and their associated state-feedback control laws. The proposed method utilizes a single state-input trajectory generated from the system, to compute a polytopic RCI set with a desired complexity and an invariance-inducing feedback controller, without the need to identify a model of the system. The problem is formulated in terms of a set of sufficient LMI conditions that are then combined in a semi-definite program to maximize the volume of the RCI set while respecting the state and input constraints. We demonstrate through a numerical case study that the proposed data-driven approach can generate RCI sets that are of comparable size to those obtained by a model-based method in which exact knowledge of the system matrices is assumed. Under the assumption of persistency of excitation of the data, the proposed algorithm guarantees robust invariance even with a small number of data samples. Overall, the direct data-driven approach presented in this paper offers a reliable and efficient counterpart to the model-based methods for RCI set computation and state-feedback controller design.Comment: 9 pages, 4 figures, preprint submitted to 62nd IEEE Conference on Decision and Control 202

Data-Driven Computation of Robust Invariant Sets and Gain-Scheduled Controllers for Linear Parameter-Varying Systems

We present a direct data-driven approach to synthesize robust control invariant (RCI) sets and their associated gain-scheduled feedback control laws for linear parameter-varying (LPV) systems subjected to bounded disturbances. The proposed method utilizes a single state-input-scheduling trajectory to compute polytopic RCI sets, without requiring a model of the system. The problem is formulated in terms of a set of sufficient data-based LMI conditions that are then combined in a semi-definite program to maximize the volume of the RCI set, while respecting the state and input constraints. We demonstrate through a numerical example that the proposed approach can generate RCI sets with a relatively small number of data samples when the data satisfies certain excitation conditions.Comment: 7 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2303.1815

Parameter Dependent Robust Control Invariant Sets for LPV Systems with Bounded Parameter Variation Rate

Real-time measurements of the scheduling parameter of linear parameter-varying (LPV) systems enables the synthesis of robust control invariant (RCI) sets and parameter dependent controllers inducing invariance. We present a method to synthesize parameter-dependent robust control invariant (PD-RCI) sets for LPV systems with bounded parameter variation, in which invariance is induced using PD-vertex control laws. The PD-RCI sets are parameterized as configuration-constrained polytopes that admit a joint parameterization of their facets and vertices. The proposed sets and associated control laws are computed by solving a single semidefinite programing (SDP) problem. Through numerical examples, we demonstrate that the proposed method outperforms state-of-the-art methods for synthesizing PD-RCI sets, both with respect to conservativeness and computational load.Comment: 8 pages, 6 figure

Data-Driven Synthesis of Configuration-Constrained Robust Invariant Sets for Linear Parameter-Varying Systems

We present a data-driven method to synthesize robust control invariant (RCI) sets for linear parameter-varying (LPV) systems subject to unknown but bounded disturbances. A finite-length data set consisting of state, input, and scheduling signal measurements is used to compute an RCI set and invariance-inducing controller, without identifying an LPV model of the system. We parameterize the RCI set as a configuration-constrained polytope whose facets have a fixed orientation and variable offset. This allows us to define the vertices of the polytopic set in terms of its offset. By exploiting this property, an RCI set and associated vertex control inputs are computed by solving a single linear programming (LP) problem, formulated based on a data-based invariance condition and system constraints. We illustrate the effectiveness of our approach via two numerical examples. The proposed method can generate RCI sets that are of comparable size to those obtained by a model-based method in which exact knowledge of the system matrices is assumed. We show that RCI sets can be synthesized even with a relatively small number of data samples, if the gathered data satisfy certain excitation conditions.Comment: 7 pages, 4 figures, 2 table

Computation of Parameter Dependent Robust Invariant Sets for LPV Models with Guaranteed Performance

This paper presents an iterative algorithm to compute a Robust Control Invariant (RCI) set, along with an invariance-inducing control law, for Linear Parameter-Varying (LPV) systems. As the real-time measurements of the scheduling parameters are typically available, in the presented formulation, we allow the RCI set description along with the invariance-inducing controller to be scheduling parameter dependent. The considered formulation thus leads to parameter-dependent conditions for the set invariance, which are replaced by sufficient Linear Matrix Inequality (LMI) conditions via Polya\u27s relaxation. These LMI conditions are then combined with a novel volume maximization approach in a Semidefinite Programming (SDP) problem, which aims at computing the desirably large RCI set. In addition to ensuring invariance, it is also possible to guarantee performance within the RCI set by imposing a chosen quadratic performance level as an additional constraint in the SDP problem. The reported numerical example shows that the presented iterative algorithm can generate invariant sets which are larger than the maximal RCI sets computed without exploiting scheduling parameter information

Computation of Parameter Dependent Robust Invariant Sets for LPV Models with Guaranteed Performance

This paper presents an iterative algorithm to compute a Robust Control Invariant (RCI) set, along with an invariance-inducing control law, for Linear Parameter-Varying (LPV) systems. As the real-time measurements of the scheduling parameters are typically available, in the presented formulation, we allow the RCI set description along with the invariance-inducing controller to be scheduling parameter dependent. The considered formulation thus leads to parameter-dependent conditions for the set invariance, which are replaced by sufficient Linear Matrix Inequality (LMI) conditions via Polya's relaxation. These LMI conditions are then combined with a novel volume maximization approach in a Semidefinite Programming (SDP) problem, which aims at computing the desirably large RCI set. In addition to ensuring invariance, it is also possible to guarantee performance within the RCI set by imposing a chosen quadratic performance level as an additional constraint in the SDP problem. The reported numerical example shows that the presented iterative algorithm can generate invariant sets which are larger than the maximal RCI sets computed without exploiting scheduling parameter information.Comment: 32 pages, 5 figure

Shedding Light on the Ageing of Extra Virgin Olive Oil: Probing the Impact of Temperature with Fluorescence Spectroscopy and Machine Learning Techniques

This work systematically investigates the oxidation of extra virgin olive oil (EVOO) under accelerated storage conditions with UV absorption and total fluorescence spectroscopy. With the large amount of data collected, it proposes a method to monitor the oil's quality based on machine learning applied to highly-aggregated data. EVOO is a high-quality vegetable oil that has earned worldwide reputation for its numerous health benefits and excellent taste. Despite its outstanding quality, EVOO degrades over time owing to oxidation, which can affect both its health qualities and flavour. Therefore, it is highly relevant to quantify the effects of oxidation on EVOO and develop methods to assess it that can be easily implemented under field conditions, rather than in specialized laboratories. The following study demonstrates that fluorescence spectroscopy has the capability to monitor the effect of oxidation and assess the quality of EVOO, even when the data are highly aggregated. It shows that complex laboratory equipment is not necessary to exploit fluorescence spectroscopy using the proposed method and that cost-effective solutions, which can be used in-field by non-scientists, could provide an easily-accessible assessment of the quality of EVOO

Econometric notes

Lecture notes for a course of Introductory Econometrics (linear regression model and ordinary least squares, including concepts of Linear Algebra and Inferential Statistics), and for a second course of Econometrics (simultaneous equations, instrumental variables, limited and full information estimation methods, maximum likelihood)