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Hybrid physics-based data-driven models, namely, augmented physics-based models (APBMs), are capable of learning complex state dynamics while maintaining some level of model interpretability that can be controlled through appropriate regularizations of the data-driven component. In this article, we extend the APBM formulation for high-order Markov models, where the state space is further augmented with past states (AG-APBM). Typically, state augmentation is a powerful method for state estimation for a high-order Markov model, but it requires the exact knowledge of the system dynamics. The proposed approach, however, does not require full knowledge of dynamics, especially the Markovity order. To mitigate the extra computational burden of such augmentation we propose an approximated-state APBM (AP-APBM) implementation leveraging summaries from past time steps. We demonstrate the performance of AG- and AP-APBMs in an autoregressive model and a target-tracking scenario based on the trajectory of a controlled aircraft with delay-feedback control. The experiments showed that both proposed strategies outperformed the standard APBM approach in terms of estimation error and that the AP-APBM only degraded slightly when compared to AG-APBM. For example, the autoregressive (AR) model simulation in our settings showed that AG-APBM and AP-APBM reduced the estimate error by 31.1% and 26.7%. The time cost and memory usage were reduced by 37.5% and 20% by AP-APBM compared to AG-APBM.
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Robust Optimal Control of Nonlinear Systems via Homotopy Shooting Method
This paper introduces an algorithm for solving robust optimal controllers for nonlinear systems using the homotopy shooting method. Robustness is ensured by penalizing the sensitivity states of the models during the transition and at the final time. In two examples, the cost is represented by the tracking error and terminal residual energy for a rest-to-rest maneuver. The proposed approach is illustrated on a double mass-spring-damper system and on a Type 1 Diabetes model where the cost function includes the integral of the tracking error. Our method can be readily extended for de-sensitization of multiple states over the whole time interval.
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- Award ID(s):
- 2021710
- PAR ID:
- 10531988
- Publisher / Repository:
- IEEE Xplore
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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