Related papers: Nonlinear Trajectory-Based Region of Attraction Es…
We introduce algorithms for learning nonlinear dynamical systems of the form $x_{t+1}=\sigma(\Theta^{\star}x_t)+\varepsilon_t$, where $\Theta^{\star}$ is a weight matrix, $\sigma$ is a nonlinear link function, and $\varepsilon_t$ is a…
This paper studies the contraction properties of nonlinear differential-algebraic equation (DAE) systems. Specifically we develop scalable techniques for constructing the attraction regions associated with a particular stable equilibrium,…
In this work, we present a novel Reinforcement Learning (RL) algorithm for the off-road trajectory tracking problem. Off-road environments involve varying terrain types and elevations, and it is difficult to model the interaction dynamics…
This paper presents a novel reinforcement learning framework for trajectory tracking of unmanned aerial vehicles in cluttered environments using a dual-agent architecture. Traditional optimization methods for trajectory tracking face…
This paper presents a novel modeling approach for unsteady aircraft airflow, leveraging the Lorenz attractor framework. The proposed model is based on the force distribution exerted by a lift-generating wing on the surrounding fluid. It…
This work presents a nonlinear system identification framework for modeling the power extraction dynamics of wind turbines, including both freestream and waked conditions. The approach models turbine dynamics using data-driven power…
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
This paper presents an approach to trajectory-centric learning control based on contraction metrics and disturbance estimation for nonlinear systems subject to matched uncertainties. The approach uses deep neural networks to learn uncertain…
Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple…
Trajectory optimization methods have achieved an exceptional level of performance on real-world robots in recent years. These methods heavily rely on accurate analytical models of the dynamics, yet some aspects of the physical world can…
Certifying the Region of Attraction (ROA) for high-dimensional nonlinear dynamical systems remains a severe computational bottleneck. Traditional deterministic verification methods, such as Sum-of-Squares (SOS) programming and…
We introduce a residence-time approach (RTA) for determining position-dependent diffusivities from biased molecular dynamics simulations. The method is formulated for trajectory segments in which the effective drift along the transport…
This paper considers the robustness of an uncertain nonlinear system along a finite-horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients.…
This paper concerns identification of uncontrolled or closed loop nonlinear systems using a set of trajectories that are generated by the system in a domain of attraction. The objective is to ensure that the trajectories of the identified…
Classification of movement trajectories has many applications in transportation and is a key component for large-scale movement trajectory generation and anomaly detection which has key safety applications in the aftermath of a disaster or…
New quadrotor UAV control algorithms are developed, based on nonlinear surfaces composed of tracking errors that evolve directly on the nonlinear configuration manifold, thus inherently including in the control design the nonlinear…
In this article, it is described how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by the means of backfitting…
This work presents an algorithm for determining the parameters of a nonlinear dynamic model of the respiratory system in patients undergoing assisted ventilation. Using the pressure and flow signals measured at the mouth, the model's…
The estimation for the region of attraction (ROA) of an asymptotically stable equilibrium point is crucial in the analysis of nonlinear systems. There has been a recent surge of interest in estimating the solution to Zubov's equation, whose…
Accurate actuation models are critical for bridging the gap between simulation and real robot behavior, yet obtaining high-fidelity actuator dynamics typically requires dedicated test stands and torque sensing. We present a trajectory-based…