Research

Dynamics of the Conditional PDF of the state
for open- and closed-loop systems

All systems are externally and/or parameterically excited by white noise. Global optimal control solutions with a fixed state terminal condition and range bounded controls are found via Bellman's Principle. Time responses of the state vector are evaluated by discretizing the corresponding Fokker-Plank-Kolgomorov (FPK) equation. This leads to stationary Markov processes for the uncontrolled and controlled responses. This strategy is applied herein to linear and non-linear plants of low state dimension.

1D State non-linear system: uncontrolled and controlled responses.
Spring mass oscillator: uncontrolled and controlled responses.
Van der Pol oscillator: uncontrolled and controlled responses.
Non-linear oscillator with dry friction: uncontrolled and controlled responses.
Optimal crossing of a vortex field: uncontrolled and controlled responses.
Oscillator under elastic imapacts: uncontrolled and controlled responses.
Failure Domain of the impulse response of a controlled non-collocated sensor-actuator system

Dynamics of the Conditional PDF of the state for open- and closed-loop systems

Dynamics of the Conditional PDF of the state
for open- and closed-loop systems