Short course on control theory for advanced CNS
Lecturer: Bert Kappen
The aim of lectures is to give some examples of control problems in
General background material:
The course starts with the notions of dynamic programming, Bellman equation and path integral control.
Differential Dynamic Programming or Iterative LQG. I show the optimal control computation for the linear
quadratic problem; I show how this solution can be used to iteratively compute the solution for a deterministic non-linear control problem using a method
called Differential Dynamic Programming (DDP, Mayne 1966). DDP is very similar to a method called Iterative LQG (ILQG), developed by Todorov and Li in 2005.
This latter method is applied to control of a biological arm in a reaching task.
- MAYNE, D., A Second-Order Gradient Method for Determining Optimal Trajectories
of Nonlinear Discrete-Time Systems, International Journal on Control, Vol. 3, pp. 85-95, 1966.
- D. M. Murray, S.J. Yakowitz, Differential Dynamic Programming and Newton's Method for Discrete Optimal Control Problems
pdf. This paper outlines the DDP method, which is similar to ILQG.
- D. Todorov, W. Li, A generalized iterative LQG method for locally optimal feedback control of constrained nonlinear stochastic systems
pdf. This paper outlines the ILQG method and applies to biological motor control task.
- Y. Tassa, T. Erez, E. Todorov, Fast Model Predictive Control for Reactive
Robotic Swimming pdf. This paper outlines the DDP
method for robotic swimming.
- Model free path integral control as described in Kappen notes.
Consider the motor control problem of the acrobot Kappen notes.
- Implement a controller based on ILQG for this problem
using the software given on Todorov software.
- Compare the performance with the model free path integral control solution described in Kappen
notes and implemented in this software.
- Goal directed planning in hippocampus Recently, it has been shown that rats hippocampal place cell show activity
to previously visited goal locations when the rat is planning its trajector.
Build a model to explain these findings using KL control theory KL Learning for rat