Exercices & Solutions

[boisgera]

Create the solutions for:

ODES / Models & Stream Plots

• Pendulum, model
• Pendulum, streamplot
• Pendulum, overshoot (analytical)

ODES / Simulation

• Transfer IVP/Rotation from exo to example

ODES / Well-posedness / Local & Maximal Solutions

• Maximal Solutions

ODES / Well-posedness / Existence

• Sigmoid
• Pendulum
• Linear Systems

ODES / Well-posedness / Continuity

• Linear system
• Non-uniqueness
• Prey-Predator

Asymptotic Behavior

• Pendulum
• Vinograd

Linear Systems / Models

• Turn Heat Equation into exo
• Linearized Pendulum

Linear Systems / Solutions & Stability

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

Linear Systems / IO Behaviors / Impulse Response

• Integrator
• Double integrator
• Gain
• MIMO

Linear Systems / IO Behaviors / Laplace & Transfer Function

• Ramp
• Feedback

Controllability

• Pendulum
• Fully Actuated System
• Integrator Chain
• Heat Equation

Asymptotic Stabilization

• Pole Assignment, default
• Pendulum
• Double Spring System

Optimal Control

• Value of J

Observers

• Fully measured systems
• Integrator chain
• Heat equation