9 papers
A Dynamical Systems view of Feedback Synthesis
William Clark
Control theory and dynamical systems are closely intertwined fields. Pontryagin's maximum principal offers a strong connection by providing a constructive way to synthesize feedbac…
LieIPM: Lie Group Interior Point Method for Direct Trajectory Optimization of Rigid Bodies
Sangli Teng, Ruiqi Zhang, Tzu-Yuan Lin +5
Designing dynamically feasible trajectories for rigid bodies is a fundamental problem in robotics. While direct methods are widely used, the existing constrained optimizers typical…
Dissipation-assisted stabilization of periodic orbits via actuated exterior impacts in hybrid mechanical systems with symmetry
William Clark, Leonardo Colombo, Anthony Bloch
Impulsive mechanical systems exhibit discontinuous jumps in their state, and when such jumps are triggered by spatial events, the geometry of the impact surface carries information…
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…
A Generalized Metriplectic System via Free Energy and System~Identification via Bilevel Convex Optimization
Sangli Teng, Kaito Iwasaki, William Clark +4
This work generalizes the classical metriplectic formalism to model Hamiltonian systems with nonconservative dissipation. Classical metriplectic representations allow for the descr…
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…
The Interplay Between Symmetries and Impact Effects on Hybrid Mechanical Systems
William Clark, Leonardo Colombo, Anthony Bloch
Hybrid systems are dynamical systems with continuous-time and discrete-time components in their dynamics. When hybrid systems are defined on a principal bundle we are able to defin…
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…