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This paper presents a disturbance rejection control strategy for hybrid dynamic systems exposed to model uncertainties and external disturbances. The focus of this work is the gait control of dynamic bipedal robots. The proposed control strategy integrates continuous and discrete control actions. The continuous control action uses a novel model-based active disturbance rejection control (ADRC) approach to track gait trajectory references. The discrete control action resets the gait trajectory references after the impact produced by the robot's support-leg exchange to maintain a zero tracking error. A Poincaré return map is used to search asymptotic stable periodic orbits in an extended hybrid zero dynamics (EHZD). The EHZD reflects a lower-dimensional representation of the full hybrid dynamics with uncertainties and disturbances. A physical bipedal robot testbed, referred to as Saurian, is fabricated for validation purposes. Numerical simulation and physical experiments show the robustness of the proposed control strategy against external disturbances and model uncertainties that affect both the swing motion phase and the support-leg exchange.

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The optimal design of magnetic devices becomes intractable using current computational methods when the number of design parameters is high. The emerging physics-informed deep learning framework has the potential to alleviate this curse of dimensionality. The objective of this paper is to investigate the ability of physics-informed neural networks to learn the magnetic field response as a function of design parameters in the context of a two-dimensional (2-D) magnetostatic problem. Our approach is as follows. We derive the variational principle for 2-D parametric magnetostatic problems, and prove the existence and uniqueness of the solution that satisfies the equations of the governing physics, i.e., Maxwell's equations. We use a deep neural network (DNN) to represent the magnetic field as a function of space and a total of ten parameters that describe geometric features and operating point conditions. We train the DNN by minimizing the physics-informed loss function