Exercices & Solutions

[boisgera]

Create the solutions for:

ODES / Models & Stream Plots

• [X] Pendulum, model
• [X] Pendulum, streamplot
• [X] Pendulum, overshoot (analytical)

ODES / Simulation

• [x] Transfer IVP/Rotation from exo to example

ODES / Well-posedness / Local & Maximal Solutions

• [x] Maximal Solutions

ODES / Well-posedness / Existence

• [x] Sigmoid
• [x] Pendulum
• [x] Linear Systems

ODES / Well-posedness / Continuity

• [x] Linear system
• [x] Non-uniqueness
• [x] Prey-Predator

Asymptotic Behavior

• [ ] Pendulum
• [X] Vinograd

Linear Systems / Models

• [x] ~~Turn Heat Equation into exo~~
• [x] Linearized Pendulum

Linear Systems / Solutions & Stability

• [x] Exponential Matrix
• [x] G.A.S <-> L.A.
• [x] Stability 2nd-order system
• [x] Stability of chain of integrators

Linear Systems / IO Behaviors / Impulse Response

• [x] Integrator
• [x] Double integrator
• [x] Gain
• [x] MIMO

Linear Systems / IO Behaviors / Laplace & Transfer Function

• [x] Ramp
• [x] Feedback

Controllability

• [x] Pendulum
• [x] Fully Actuated System
• [x] Integrator Chain
• [x] Heat Equation

Asymptotic Stabilization

• [x] Pole Assignment, default
• [x] Pendulum
• [x] Double Spring System

Optimal Control

• [x] Value of J

Observers

• [x] Fully measured systems
• [x] Integrator chain
• [x] Heat equation