Employing the Staticization Operator in Conservative Dynamical Systems and the Schrödinger Equation
- Resource Type
- Conference
- Authors
- McEneaney, William M.; Zhao, Ruobing
- Source
- 2019 12th Asian Control Conference (ASCC) Control Conference (ASCC), 2019 12th Asian. :1179-1184 Jun, 2019
- Subject
- Aerospace
Bioengineering
Communication, Networking and Broadcast Technologies
Components, Circuits, Devices and Systems
Computing and Processing
General Topics for Engineers
Nuclear Engineering
Power, Energy and Industry Applications
Robotics and Control Systems
Signal Processing and Analysis
Transportation
Control theory
Boundary value problems
Riccati equations
Potential energy
Minimization
Standards
Dynamic programming
dynamic programming
stationary action
staticization
two-point boundary value problems
Schrödinger equation
conservative dynamical systems
- Language
Conservative dynamical systems propagate as stationary points of the action functional. Hence, dynamical-systems questions may be addressed by control-theoretic methods. Using this representation, it has previously been demonstrated that one may obtain fundamental solutions for two-point boundary value problems for some classes of conservative systems via solution of an associated dynamic program. It is also known that the gravitational and Coulomb potentials may be represented as stationary points of cubicly-parameterized quadratic functionals. Hence, stationary points of the action functional may be represented via iterated staticization of polynomial functionals. This leads to representations through operations on sets of solutions of differential Riccati equations (DREs). A key step in this process is the reordering of staticization operations.