This study challenges strictly guaranteeing ``dissipativity'' of a dynamical system represented by neural networks learned from given time-series data. Dissipativity is a crucial indicator for dynamical systems that generalizes stability and input-output stability, known to be valid across various systems including robotics, biological systems, and molecular dynamics. By analytically proving the general solution to the nonlinear Kalman–Yakubovich–Popov (KYP) lemma, which is the necessary and sufficient condition for dissipativity, we propose a differentiable projection that transforms any dynamics represented by neural networks into dissipative ones and a learning method for the transformed dynamics. Utilizing the generality of dissipativity, our method strictly guarantee stability, input-output stability, and energy conservation of trained dynamical systems. Finally, we demonstrate the robustness of our method against out-of-domain input through applications to robotic arms and fluid dynamics.

Learning stable dynamics from observed time-series data is an essential problem in robotics, physical modeling, and systems biology. Many of these dynamics are represented as an inputs-output system to communicate with the external environment. In this study, we focus on input-output stable systems, exhibiting robustness against unexpected stimuli and noise. We propose a method to learn nonlinear systems guaranteeing the input-output stability. Our proposed method utilizes the differentiable projection onto the space satisfying the Hamilton-Jacobi inequality to realize the input-output stability. The problem of finding this projection can be formulated as a quadratic constraint quadratic programming problem, and we derive the particular solution analytically. Also, we apply our method to a toy bistable model and the task of training a benchmark generated from a glucose-insulin simulator. The results show that the nonlinear system with neural networks by our method achieves the input-output stability, unlike naive neural networks. Our code is available at https://github.com/clinfo/DeepIOStability .

Human factors are becoming one of the most important factors that are considered for automobile design and test. However, the ride comfort of a passenger or driver is mainly dependent on a subjective assessment by a test driver or questionnaire investigation, and, therefore, a quantitative evaluation of the ride comfort is being pursued as one of the research goals in the automobile industry. In this paper, actual-vehicle and driving simulator (DS) experiments were carried out to evaluate the sternocleidomastoid (SCM) muscle activity of a passenger in response to a car's lateral acceleration while slalom driving. Interestingly, the SCM muscle of the passenger on the side opposite the direction of the car's lateral acceleration contracts to keep the head stable against the body shaking. The electromyography (EMG) signal of the SCM muscle in a modified car was significantly lower than in a normal car, because the 1-10 Hz low-frequency vibrations of the body frame of the modified car during the slalom driving were decreased through improvements of the rigidity of car's body frame. A passenger feels more discomfort when the EMG signal of the SCM muscle increases, and less as the signal decreases. The DS experiment, with the addition of more experimental conditions, arrived at the same conclusion, which testified that the DS is a powerful tool with which to evaluate passenger discomfort. In conclusion, the EMG of the SCM muscle can be considered as an objective and effective method with which to quantify the effect of vehicle properties on human discomfort in both actual-vehicle and DS experiments for slalom driving.

Sternocleidomastoid (SCM) muscle activity to keep the head stable in slalom driving is analyzed by surface electromyography (sEMG). Using sEMG signals of SCM muscles, this study evaluates a passenger's sensitivity to different vehicle dynamic characteristics, especially in terms of lateral and roll vabrations. In actual slalom driving, it is found that the sEMG signal is more active when the amplitude of the relative acceleration of the car body is higher. In a further experiment, a universal driving simulator is used to simulate the actual slalom driving for two kinds of slalom driving. Meanwhicle, 1–10 Hz white noise is input into the lateral and roll directions of the vehicle motion for the two types of slalom driving. The result shows that root-mean-square values of the sEMG signal of the SCM muscle in slalom driving with added lateral and roll vibrations are significantly higher than those in the normal slalom driving. Importantly, the study indicates that the amplitude of the sEMG is sensitive to lateral and roall vibrations of the vehicle, which may result in passenger discomfort.