Figure 4.1 shows the inverted pendulum setup. The control problem is to start the cart from anywhere with the rod in a vertical position and bring the cart to the origin with the rod in an upright position. In other words, make x = 0, x ˙ = 0 https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315218649/440f893e-4f5f-4deb-8640-640b11fb473f/content/eq086.tif"/> , θ = 0, θ ˙ = 0 https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315218649/440f893e-4f5f-4deb-8640-640b11fb473f/content/eq087.tif"/> . Inverted pendulum arrangement. The cart is free to move in one direction. The pendulum is mounted on the cart with a free joint. https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315218649/440f893e-4f5f-4deb-8640-640b11fb473f/content/fig4_1.tif"/>