Edit Errata: Errata: Example 8.10 missing factor of v, a1 and a2 flipped

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Example 8.10 (Steering control with velocity scheduling) is missing a factor of <math>v</math> in the definition of <math>A_\text{d}</math> that propagates through the example. In addition, the coefficients <math>a_1</math> and <math>a_2</math> are swapped in the definition of <math>w_2</math>. The equation for <math>A_\text{d}</math> should read <center><math> A_\text{d} = \left. \frac{\partial f}{\partial x} \right|_{(x_\text{d}, u_\text{d})} = \left. \begin{bmatrix} 0 & 0 & -{\color{blue} v} \sin\theta \\ 0 & 0 & {\color{blue} v} \cos\theta \\ 0 & 0 & 0 \end{bmatrix} \right|_{(x_\text{d}, u_\text{d})} = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & {\color{blue} v_\text{r}} \\ 0 & 0 & 0 \end{bmatrix}, </math></center> This leads to an error in the definition of <math>w_2</math> later in the example. In addition, the coefficients <math>a_1</math> and <math>a_2</math> are swapped and there was an error in the sign, so the definition of <math>w_2</math> should be <center><math> w_2 = {\color{blue} -} \frac{l}{v_\text{r}}(\frac{\color{blue} a_2}{\color{blue} v_\text{r}} e_y + {\color{blue} a_1} e_\theta). </math></center> The final controller then becomes <center><math> \begin{bmatrix} v \\ \phi \end{bmatrix} = - \begin{bmatrix} \lambda_1 & 0 & 0 \\ 0 & \dfrac{{\color{blue} a_2} l}{v_\text{r}^{\color{blue} 2}} & \dfrac{{\color{blue} a_1} l}{v_\text{r}} \end{bmatrix} \begin{bmatrix} x - v_\text{r} t \\ y - y_\text{r} \\ \theta \end{bmatrix} + \begin{bmatrix} v_\text{r} \\ 0 \end{bmatrix}. </math></center> These corrections also change the controller response in [[Figure 8.13: Vehicle steering using gain scheduling|Figure 8.13]]. The corrected response is <center> [[Image:Figure-8.13-steering-gainsched.png|320px]] </center> Acknowledgements: Thanks to Kaivalya Bakshi and Theunis Botha for pointing out the errors in this example.

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