Visualizer of Controlled Polynomial Dynamical Systems v0.9
You can visualize a controlled Polynomial dynamical system. This is experimental, please be patient with us. Thank you for trying it out!
If you have any questions or comments, please email Franziska Hinkelmann!


Network Description

Enter number of state variables: (For more than 10 variables, no graph is generated)


Enter number of control variables:


Enter number of states per node: (Must be a prime number)


A controlled polynomial dynamical system has a number of state variables x1, ... xn
and a number of control variables u1, ..., um. The idea is, that the system evolves according
to certain rules, this corresponds to a regular PDS, but the control variables can be
externally controlled. Therefore the state space of a controlled PDS looks slightly different
than that of a regular PDS: There are p^n states where each state has out-degree at
most 2^u. Every edge in the graph is labeled with the control that has been applied at this transition.

Input Functions
Controller
Enter initial state, separated by spaces:
Enter a control sequence, the sequence will be repeatedly applied until a repeated node is found.
Enter final state, separated by spaces:  
A heuristic algorithm will try to find the cheapest trajectory from the initial to the
final state. Cheap means with the cheapest possible control. As this is an experimental
version, we consider uniform cost for every control variable that is set, i.e., not 0.
If a sequence of control inputs is found, that drives the system from the initial state
to the final state, this trajectory is highlighted in the state space graph in green. If
no sequence can be found, no trajectory will be highlighted in the phase space.

Find a truly optimal controller from the initial to the final state.
This is done by enumeration.

Cost Function
The algorithms find a control sequence that is best with respect to a cost
function. Please enter your cost function here:
The control variables are referred to as u = {u1, u2, ..., um},
where m is the number of control variables. The total cost for a
trajectory is the sum of the cost of the controls applied. For example, if
you applied the controls {0,1}, {2,1}, {0,0}, {1,1}, then the cost is
c({0,1}) + c({2,1}) + c({0,0}) + c({1,1}). Please note, for now, only the
default cost is possible, changing this field is not working yet.


Results will be displayed below.