# Mouse & Maze

To illustrate the use of both several switching possibilities and controls, we designed the following maze problem. A mouse trapped in a maze tries to get out. This mouse has a ”bomberman” control space. The state can be described with the variable $Latex formula$ which defines the position of the unlucky pointlike mouse. The mouse has 4 modes modeling its direction: north, east, west, south. In addition to the direction modes, the mouse has a control variable for its velocity, which is positive and upper-bounded. We consider a running cost of 10 per unit of time in the maze, and each change of direction costs 1 as a switching cost. The mouse starts at the lower right corner while the exit of the maze is fixed at the upper left corner.