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1. Clustering-based Mode Reduction for Markov Jump Systems

   Du, Zhe; Ozay, Necmiye; Balzano, Laura (January 2022, Conference on Learning for Decision and Control)

   While Markov jump systems (MJSs) are more appropriate than LTI systems in terms of modeling abruptly changing dynamics, MJSs (and other switched systems) may suffer from the model complexity brought by the potentially sheer number of switching modes. Much of the existing work on reducing switched systems focuses on the state space where techniques such as discretization and dimension reduction are performed, yet reducing mode complexity receives few attention. In this work, inspired by clustering techniques from unsupervised learning, we propose a reduction method for MJS such that a mode-reduced MJS can be constructed with guaranteed approximation performance. Furthermore, we show how this reduced MJS can be used in designing controllers for the original MJS to reduce the computation cost while maintaining guaranteed suboptimality. 

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2. Clustering-based Mode Reduction for Markov Jump Systems

   Du, Zhe; Ozay, Necmiye; Balzano, Laura (January 2022, Proceedings of Machine Learning Research, 4th Annual Conference on Learning for Dynamics and Control)

   While Markov jump systems (MJSs) are more appropriate than LTI systems in terms of modeling abruptly changing dynamics, MJSs (and other switched systems) may suffer from the model complexity brought by the potentially sheer number of switching modes. Much of the existing work on reducing switched systems focuses on the state space where techniques such as discretization and dimension reduction are performed, yet reducing mode complexity receives few attention. In this work, inspired by clustering techniques from unsupervised learning, we propose a reduction method for MJS such that a mode-reduced MJS can be constructed with guaranteed approximation performance. Furthermore, we show how this reduced MJS can be used in designing controllers for the original MJS to reduce the computation cost while maintaining guaranteed suboptimality. Keywords: Markov Jump Systems, System Reduction, Clustering 

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3. 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. 

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4. Belief-prefix Control for Autonomously Dodging Switching Disturbances

   https://doi.org/10.23919/ECC51009.2020.9143990  

   Rutledge, Kwesi; Ozay, Necmiye (January 2020, European Control Conference)

   null (Ed.)

   This paper presents a new method of controller synthesis for hidden mode switched systems, where the disturbances are the quantities that are affected by the unobserved switches. Rather than using model discrimination techniques that rely on modifying desired control actions to achieve identification, the controller uses consistency sets which map the measured external behaviors to a belief about which mode signal is being executed and a control action. This hybrid controller is a prefix-based controller, where the prefixes come from an offline constructed belief graph that incorporates prior information about switching sequences with potential reachable sets of the dynamics. While the mode signal is hidden to the controller, the system’s location on the belief graph is fully observed and allows for this problem to be transformed into a design problem in which a discrete mode, in terms of beliefs, is directly observed. Finally, it is shown that affine controllers dependent on prefixes of such beliefs can be synthesized via linear programming. 

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5. Allan Variance-based Granulation Technique for Large Temporal Databases

   Sinanaj, Lorina; Haeri, Hossein; Gao, Liming; Maddipatla, Satya Prasad; Chen, Cindy; Jerath, Kshitij; Beal, Craig; Brennan, Sean (October 2021, 13th International Conference on Knowledge Management and Information Systems)

   null (Ed.)

   decrease query response time with limited main memory and storage space, data reduction techniques that preserve data quality are needed. Existing data reduction techniques, however, are often computationally expensive and rely on heuristics for deciding how to split or reduce the original dataset. In this paper, we propose an effective granular data reduction technique for temporal databases, based on Allan Variance (AVAR). AVAR is used to systematically determine the temporal window length over which data remains relevant. The entire dataset to be reduced is then separated into granules with size equal to the AVAR-determined window length. Data reduction is achieved by generating aggregated information for each such granule. The proposed method is tested using a large database that contains temporal information for vehicular data. Then comparison experiments are conducted and the outstanding runtime performance is illustrated by comparing with three clustering-based data reduction methods. The performance results demonstrate that the proposed Allan Variance-based technique can efficiently generate reduced representation of the original data without losing data quality, while significantly reducing computation time. 

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