More Like this

1. Identification of Error-in-Variables Switched Systems using a Riemannian Embedding

   https://doi.org/10.1109/TAC.2023.3275973  

   Sznaier, M.; Zhang, X.; Camps, O. (May 2023, IEEE Transactions on Automatic Control)

   This paper considers the problem of error in variables identification for switched affine models. Since it is well known that this problem is generically NP hard, several relaxations have been proposed in the literature. However, while these approaches work well for low dimensional systems with few subsystems, they scale poorly with both the number of subsystems and their memory. To address this difficulty, we propose a computationally efficient alternative, based on embedding the data in the manifold of positive semidefinite matrices, and using a manifold metric there to perform the identification. Our main result shows that, under dwell-time assumptions, the proposed algorithm is convergent, in the sense that it is guaranteed to identify the system for suitably low noise. In scenarios with larger noise levels, we provide experimental results showing that the proposed method outperforms existing ones. The paper concludes by illustrating these results with academic examples and a non-trivial application: action video segmentation. 

   more » « less
2. Global system errors to simultaneously improve the identification of subsystems with mixed data Gaussian process regression

   https://doi.org/10.1088/2632-2153/ad4e05  

   LaMack, Cameron_J; Schearer, Eric_M (May 2024, Machine Learning: Science and Technology)

   Abstract This paper explores the use of Gaussian process regression for system identification in control engineering. It introduces two novel approaches that utilize the data from a measured global system error. The paper demonstrates these approaches by identifying a simulated system with three subsystems, a one degree of freedom mass with two antagonist muscles. The first approach uses this whole-system error data alone, achieving accuracy on the same order of magnitude as subsystem-specific data ( $9.28\pm 0.87\text{N\hspace{0.17em}}\text{vs.\hspace{0.17em}}6.96\pm 0.32\text{N}$of total model errors). This is significant, as it shows that the same data set can be used to identify unique subsystems, as opposed to requiring a set of data descriptive of only a single subsystem. The second approach demonstrated in this paper mixes traditional subsystem-specific data with the whole system error data, achieving up to 98.71% model improvement. 

   more » « less
3. Fast Two-View Motion Segmentation Using Christoffel Polynomials.

   Ozbay, B. (November 2022, 2022 European Computer Vision Conference)

   Avidan, S. (Ed.)

   We address the problem of segmenting moving rigid objects based on two-view image correspondences under a perspective camera model. While this is a well understood problem, existing methods scale poorly with the number of correspondences. In this paper we propose a fast segmentation algorithm that scales linearly with the number of correspondences and show that on benchmark datasets it offers the best trade-off between error and computational time: it is at least one order of magnitude faster than the best method (with comparable or better accuracy), with the ratio growing up to three orders of magnitude for larger number of correspondences. We approach the problem from an algebraic perspective by exploiting the fact that all points belonging to a given object lie in the same quadratic surface. The proposed method is based on a characterization of each surface in terms of the Christoffel polynomial associated with the probability that a given point belongs to the surface. This allows for efficiently segmenting points “one surface at a time” in O(number of points) 

   more » « less
4. A Principal-Agent Model of Systems Engineering Processes with Application to Satellite Design

   Safarkhani, Salar; Kattakuri, Vikranth; Bilionis, I.; Panchal, Jitesh H. (July 2018, Council of Engineering Systems Universities (CESUN) Global Conference)

   We present a principal-agent model of a one-shot, shallow, systems engineering process. The process is "one-shot" in the sense that decisions are made during a one-time step and that they are final. The term "shallow" refers to a one-layer hierarchy of the process. Specifically, we assume that the systems engineer has already decomposed the problem in subsystems and that each subsystem is assigned to a different subsystem engineer. Each subsystem engineer works independently to maximize their own expected payoff. The goal of the systems engineer is to maximize the system-level payoff by incentivizing the subsystem engineers. We restrict our attention to requirements-based system-level payoffs, i.e., the systems engineer makes a profit only if all the design requirements are met. We illustrate the model using the design of an Earth-orbiting satellite system where the systems engineer determines the optimum incentive structures and requirements for two subsystems: the propulsion subsystem and the power subsystem. The model enables the analysis of a systems engineer's decisions about optimal passed-down requirements and incentives for sub-system engineers under different levels of task difficulty and associated costs. Sample results, for the case of risk-neutral systems and subsystems engineers, show that it is not always in the best interest of the systems engineer to pass down the true requirements. As expected, the model predicts that for small to moderate task uncertainties the optimal requirements are higher than the true ones, effectively eliminating the probability of failure for the systems engineer. In contrast, the model predicts that for large task uncertainties the optimal requirements should be smaller than the true ones in order to lure the subsystem engineers into participation. 

   more » « less
5. Worst-Case Optimal Data-Driven Estimators for Switched Discrete-Time Linear Systems

   https://doi.org/10.1109/CDC40024.2019.9030130  

   Dai, T.; Sznaier, M. (December 2019, 2019 IEEE 58th Conference on Decision and Control (CDC))

   This paper proposes a data-driven framework to address the worst-case estimation problem for switched discrete-time linear systems based solely on the measured data (input & output) and an ℓ ∞ bound over the noise. We start with the problem of designing a worst-case optimal estimator for a single system and show that this problem can be recast as a rank minimization problem and efficiently solved using standard relaxations of rank. Then we extend these results to the switched case. Our main result shows that, when the mode variable is known, the problem can be solved proceeding in a similar manner. To address the case where the mode variable is unmeasurable, we impose the hybrid decoupling constraint(HDC) in order to reformulate the original problem as a polynomial optimization which can be reduced to a tractable convex optimization using moments-based techniques. 

   more » « less