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In this work we solve the position-aided 3D navigation problem using a nonlinear estimation scheme. More precisely, we propose a nonlinear observer to estimate the full state of the vehicle (position, velocity, orientation and gyro bias)…

The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…

We investigate the dynamics of a bicycle on an uneven mountain bike track split into straight sections with small jumps (kickers) and banked corners. A basic bike-rider model is proposed and used to derive equations of motion, which capture…

We consider the problem of learning a realization of a partially observed dynamical system with linear state transitions and bilinear observations. Under very mild assumptions on the process and measurement noises, we provide a finite time…

The knowledge of the states of a vehicle is a necessity to perform proper planning and control. These quantities are usually accessible through measurements. Control theory brings extremely useful methods -- observers -- to deal with…

We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…

Hybrid systems theory has become a powerful approach for designing feedback controllers that achieve dynamically stable bipedal locomotion, both formally and in practice. This paper presents an analytical framework 1) to address…

In this paper, we introduce a new sliding mode observer for Lur'e set-valued dynamical systems, particularly addressing challenges posed by uncertainties not within the standard range of observation. Traditionally, most of Luenberger-like…

This work provides a framework for nonlinear model-free control of systems with unknown input-output dynamics, but outputs that can be controlled by the inputs. This framework leads to real-time control of the system such that a feasible…

A general framework for performing event-driven simulations of systems with semi-flexible or rigid bodies interacting under impulsive torques and forces is outlined. Two different approaches are presented. In the first, the dynamics and…

Scientific machine learning for inferring dynamical systems combines data-driven modeling, physics-based modeling, and empirical knowledge. It plays an essential role in engineering design and digital twinning. In this work, we primarily…

Nonlinear dynamical effects are crucial to the operation of many agile robotic systems. Koopman-based model learning methods can capture these nonlinear dynamical system effects in higher dimensional lifted bilinear models that are amenable…

A new approach to design of nonlinear observers (state estimators) is proposed. The main idea is to (i) construct a convex set of dynamical systems which are contracting observers for a particular system, and (ii) optimize over this set for…

Dynamical models are often corrupted by model uncertainties, external disturbances, and measurement noise. These factors affect the performance of model-based observers and as a result, affect the closed-loop performance. Therefore, it is…

This paper considers the problem of attitude, position and linear velocity estimation for rigid body systems relying on landmark measurements. We propose two hybrid nonlinear observers on the matrix Lie group $SE_2(3)$, leading to global…

An adaptive state observer is proposed for a class of overparametrized uncertain linear time-invariant systems without restrictive requirement of their representation in the observer canonical form. It evolves the method of generalized…

Nonlinear systems play a significant role in numerous scientific and engineering disciplines, and comprehending their behavior is crucial for the development of effective control and prediction strategies. This paper introduces a novel…

We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…

This work introduces a non-intrusive model reduction approach for learning reduced models from partially observed state trajectories of high-dimensional dynamical systems. The proposed approach compensates for the loss of information due to…

We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…