9 papers
Symplectic Geometry in Hybrid and Impulsive Optimal Control
William Clark, Maria Oprea
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory was applied to these systems and a hybrid…
Optimal Control of Reduced Left-Invariant Hybrid Control Systems
William Clark, Maria Oprea
Optimal control is ubiquitous in many fields of engineering. A common technique to find candidate solutions is via Pontryagin's maximum principle. An unfortunate aspect of this met…
Optimal Control of Hybrid Systems with Submersive Resets
William Clark, Maria Oprea, Aden Shaw
Hybrid dynamical systems are systems which posses both continuous and discrete transitions. Assuming that the discrete transitions (resets) occur a finite number of times, the opti…
A Study of the Long-Term Behavior of Hybrid Systems with Symmetries via Reduction and the Frobenius-Perron Operator
Maria Oprea, Aden Shaw, Robi Huq +3
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. As typical in dynamical analysis, an essential goal is to study the long-term behavior…
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…
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…