5 citations · 10 across the 11 of their papers we have counts for
15 papers
The Integrability of a knife-edge Billiard in a Disk
Alejandro Bravo-Doddoli, Huaidian Hou, William Clark +1
This paper proves the integrability of a nonholonomic billiard defined by a knife-edge in a disk. The paper begins by parametrizing the impact space using coordinates that reveal t…
Delay effects on the discontinuous stabilization of the nonholonomic integrator and its generalizations
William Clark, Anthony Bloch
The nonholonomic integrator is a famous example in feedback design - although it is small-time locally controllable to the origin, no continuous feedback law exists. Therefore, any…
Learning the Delay Using Neural Delay Differential Equations
Maria Oprea, Mark Walth, Robert Stephany +3
The intersection of machine learning and dynamical systems has generated considerable interest recently. Neural Ordinary Differential Equations (NODEs) represent a rich overlap bet…
Optimality of Zeno Executions in Hybrid Systems
William Clark, Maria Oprea
A unique feature of hybrid dynamical systems (systems whose evolution is subject to both continuous- and discrete-time laws) is Zeno trajectories. Usually these trajectories are av…
Optimal Control of Nonholonomic Systems via Magnetic Fields
Maria Oprea, Max Ruth, Dora Kassabova +1
Geometric optimal control utilizes tools from differential geometry to analyze the structure of a problem to determine the control and state trajectories to reach a desired outcome…
Lie Algebraic Cost Function Design for Control on Lie Groups
Sangli Teng, William Clark, Anthony Bloch +2
This paper presents a control framework on Lie groups by designing the control objective in its Lie algebra. Control on Lie groups is challenging due to its nonlinear nature and di…
How do we walk? Using hybrid holonomy to approximate non-holonomic systems
Maria Oprea, William Clark
Why do we move forward when we walk? Our legs undergo periodic motion and thus possess no net change in position; however, our bodies do possess a net change in position and we are…
A Geometric Approach to Optimal Control of Hybrid and Impulsive Systems
William Clark, Maria Oprea, Andrew J. Graven
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory is applied to these systems and a hybrid…
Invariant Forms in Hybrid and Impact Systems and a Taming of Zeno
William Clark, Anthony Bloch
Hybrid (and impact) systems are dynamical systems experiencing both continuous and discrete transitions. In this work, we derive necessary and sufficient conditions for when a give…
Existence of invariant volumes in nonholonomic systems subject to nonlinear constraints
William Clark, Anthony Bloch
We derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these…
The Bouncing Penny and Nonholonomic Impacts
William Clark, Anthony Bloch
The evolution of a Lagrangian mechanical system is variational. Likewise, when dealing with a hybrid Lagrangian system (a system with discontinuous impacts), the impacts can also b…
Time-minimum control of quantum purity for 2-level Lindblad equations
William Clark, Anthony Bloch, Leonardo Colombo +1
We study time-minimum optimal control for a class of quantum two-dimensional dissipative systems whose dynamics are governed by the Lindblad equation and where control inputs acts…
Poincaré-Bendixson Theorem for Hybrid Systems
William Clark, Anthony Bloch, Leonardo Colombo
The Poincaré-Bendixson theorem plays an important role in the study of the qualitative behavior of dynamical systems on the plane; it describes the structure of limit sets in such…
Density of Gabor Systems Via the Short Time Fourier Transform
Andrew Ahn, William Clark, Shahaf Nitzan +1
We apply a new approach to the study of the density of Gabor systems, and obtain a simple and straightforward proof of Ramanathan and Steger's well known result regarding the densi…
Optimal Control of Quantum Purity for Systems
William Clark, Anthony Bloch, Leonardo Colombo +1
The objective of this work is to study time-minimum and energy-minimum global optimal control for dissipative open quantum systems whose dynamics is governed by the Lindblad equati…