Nonlinear systems

A nonlinear control system can be generally expressed as follows: ˙ x = f (x, u) y = h(x, u) where x ∈ M ⊂ R n is the state variable, u ∈ R m the input, and y ∈ R p the output. In this course we focus on the so-called affine control systems: ˙ x = f (x) + g(x)u (8.1) y = h(x) Here we use two examples to illustrate why sometimes we have to deal with nonlinear control systems. Example 8.1 (Car steering system). Here is a simplified model of a car: L h h w x y φ θ (x,y) (x,y) Figure 1. The geometry of the car-like robot, with position (x, y), orientation θ and steering angle φ.