Erratum

The online version of the book can be found at http://dx.doi.org/10.1007/978-1-4471-4396-3

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

ERRATA LIST

Robust and Adaptive Control with Aerospace Applications – 1 ^st Edition, Springer, 2013

Eugene Lavretsky and Kevin A. Wise

Revised on 23 Jul 2013

Part I

Introduction

1) Page 10, change the top equation to:

$$\left( {\begin{array}{c} {\dot x} \cr {\dot y} \cr { - \dot h} \cr \end{array}} \right) = \left( {\begin{array}{ccl} {\cos \psi } & {\sin \psi } & 0 \cr { - \sin \psi } & {\cos \psi } & 0 \cr 0 & 0 & 1 \cr \end{array}} \right)\left( {\begin{array}{clc} {\cos \theta } & 0 & { - \sin \theta } \cr 0 & 1 & 0 \cr {\sin \theta } & 0 & {\cos \theta } \cr \end{array}} \right)\left( {\begin{array}{lcc} 1 & 0 & 0 \cr 0 & {\cos \varphi } & {\sin \varphi } \cr 0 & { - \sin \varphi } & {\cos \varphi } \cr \end{array}} \right)\left( {\begin{array}{l} u \cr v \cr w \cr \end{array}} \right)$$

Chapter 1

1) Page 21, remove boxes from around the equations

Chapter 2

1) Page 34, change

to

${H}^{*}\left(x,{\nabla}_x{J}^{*}\kern-.1em ,t\right)={x}_1^4+\frac{1}{4}{\left(\frac{\partial {J}^{*}}{\partial {x}_2}\right)}^2+\frac{\partial {J}^{*}}{\partial {x}_1}{x}_2-2\frac{\partial {J}^{*}}{\partial {x}_2}{x}_1-3\frac{\partial {J}^{*}}{\partial {x}_2}{x}_2-\frac{1}{2}{\left(\frac{\partial {J}^{*}}{\partial {x}_2}\right)}^2$

2) Page 34, change

to

$\begin{array}{l}-\frac{\partial {J}^{*}}{\partial t}={H}^{*}\left(x,{\nabla}_x{J}^{*}\left(x,t\right),t\right)\\ {}\kern2.5em ={x}_1^4-\frac{1}{4}{\left(\frac{\partial {J}^{*}}{\partial {x}_2}\right)}^2+\frac{\partial {J}^{*}}{\partial {x}_1}{x}_2-\frac{\partial {J}^{*}}{\partial {x}_2}\left(2{x}_1-3{x}_2\right)\end{array}$

3) Page 36, change

to

$-\frac{\partial {J}^{*}}{\partial t}={x}^T Qx-{\scriptscriptstyle \frac{1}{4}}\frac{\partial {J}^{*}}{\partial x}B{R}^{-1}{B}^T{\nabla}_x{J}^{*}+\frac{\partial {J}^{*}}{\partial x} Ax$

4) Page 36, change

to

${u}^{*}\left(x,t\right)=-{\scriptscriptstyle \frac{1}{2}}\ {R}^{-1}{B}^T{\nabla}_x{J}^{*}=-\underset{K(t)}{\underbrace{R^{-1}{B}^TP(t)}}x=-K(t)\;x$

5) Page 46, change

to

−Q(sI − A)⁻¹

Chapter 3

1) Page 57, change

to (need comma and space)

$\begin{array}{l}\dot{z}=\tilde{A}z+\tilde{B}\mu, \kern1em z=\left[\begin{array}{c}\hfill e\hfill \\ {}\hfill \dot{x}\hfill \end{array}\right],\mu =\dot{u}\\ {}\tilde{A}=\left[\begin{array}{cc}\hfill 0\hfill & \hfill {C}_c\hfill \\ {}\hfill 0\hfill & \hfill A\hfill \end{array}\right],\tilde{B}=\left[\begin{array}{c}\hfill {D}_c\hfill \\ {}\hfill B\hfill \end{array}\right]\end{array}$

2) Page 57, change

to

$\begin{array}{l}\dot{z}=\tilde{A}z+\tilde{B}\mu, \kern0.5em z=\left[\begin{array}{c}\hfill e\hfill \\ {}\hfill \xi \hfill \end{array}\right],\xi =\ddot{x}-{\omega}^2x,\mu =\ddot{u}-{\omega}^2u,\\ {}\tilde{A}=\left[\begin{array}{ccc}\hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \\ {}\hfill -{\omega}^2\hfill & \hfill 0\hfill & \hfill {C}_c\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill A\hfill \end{array}\right],\tilde{B}=\left[\begin{array}{c}\hfill 0\hfill \\ {}\hfill {D}_c\hfill \\ {}\hfill B\hfill \end{array}\right]\end{array}$

3) Page 59, change

to

n _u  × (pn _r  + n _x )

4) Page 60, change

to

$u=-{K}_xx+{\displaystyle \sum_{i=1}^p{s}^{-i}\left({a}_i\left(u+{K}_xx\right)-{K}_ie\right)}$

5) Page 60, change

to

${\dot{x}}_e=\left(\tilde{A}-\tilde{B}{K}_c\right){x}_e+ Fr$

where the extended state x _e is (3.18) integrated p-times, and $F={\left[\begin{array}{cc}\hfill -{I}_{n_u\times {n}_u}\hfill & \hfill {0}_{n_u\times {n}_x}\hfill \end{array}\right]}^T.$

6) Page 63, change the following figure

to the same figure as in Figure 1.3, page 8.

7) Page 63, Change

to

${A}_z=-V\dot{\gamma}={Z}_{\alpha}\alpha +{Z}_{\delta}\delta$

8) Page 63, change

to

$\begin{array}{l}{\dot{A}}_z=\frac{Z_{\alpha }}{V}{A}_z+{Z}_{\alpha }q+{Z}_{\delta }{\dot{\delta}}_e\\ {}\dot{q}=\frac{M_{\alpha }}{Z_{\alpha }}{A}_z+{M}_qq+\left({M}_{\delta }-\frac{M_{\alpha }{Z}_{\delta }}{Z_{\alpha }}\right){\delta}_e\end{array}$

9) Page 64, change

to

$\left[\begin{array}{c}\hfill {\dot{A}}_z\hfill \\ {}\hfill \dot{q}\hfill \\ {}\hfill {\dot{\delta}}_e\hfill \\ {}\hfill {\ddot{\delta}}_e\hfill \end{array}\right]=\left[\begin{array}{cccc}\hfill \frac{Z_{\alpha }}{V}\hfill & \hfill {Z}_{\alpha}\hfill & \hfill 0\hfill & \hfill {Z}_{\delta}\hfill \\ {}\hfill {M}_{\alpha }/{Z}_{\alpha}\hfill & \hfill {M}_q\hfill & \hfill \left({M}_{\delta }-{\scriptscriptstyle \frac{M_{\alpha }{Z}_{\delta }}{Z_{\alpha }}}\right)\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill -{\omega_a}^2\hfill & \hfill -2{\zeta}_a{\omega}_a\hfill \end{array}\right]\left[\begin{array}{c}\hfill {A}_z\hfill \\ {}\hfill q\hfill \\ {}\hfill {\delta}_e\hfill \\ {}\hfill {\dot{\delta}}_e\hfill \end{array}\right]+\left[\begin{array}{c}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill {\omega_a}^2\hfill \end{array}\right]{\delta}_c$

10) Page 64, change

to

$\left[\begin{array}{c}\hfill \dot{e}\hfill \\ {}\hfill {\ddot{A}}_z\hfill \\ {}\hfill \ddot{q}\hfill \\ {}\hfill {\ddot{\delta}}_e\hfill \\ {}\hfill {\overset{\dddot{}}{\delta}}_e\hfill \end{array}\right]=\left[\begin{array}{ccccc}\hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill \frac{Z_{\alpha }}{V}\hfill & \hfill {Z}_{\alpha}\hfill & \hfill 0\hfill & \hfill {Z}_{\delta}\hfill \\ {}\hfill 0\hfill & \hfill {M}_{\alpha }/{Z}_{\alpha}\hfill & \hfill {M}_q\hfill & \hfill \left({M}_{\delta }-{\scriptscriptstyle \frac{M_{\alpha }{Z}_{\delta }}{Z_{\alpha }}}\right)\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill -{\omega_a}^2\hfill & \hfill -2{\zeta}_a{\omega}_a\hfill \end{array}\right]\left[\begin{array}{c}\hfill e\hfill \\ {}\hfill {\dot{A}}_z\hfill \\ {}\hfill \dot{q}\hfill \\ {}\hfill {\dot{\delta}}_e\hfill \\ {}\hfill {\ddot{\delta}}_e\hfill \end{array}\right]+\left[\begin{array}{c}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \\ {}\hfill {\omega_a}^2\hfill \end{array}\right]{\dot{\delta}}_c$

11) Page 65, change

to

${z}^T Qz={z}^T\left[\begin{array}{ccccc}\hfill {q}_{11}\hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill \\ {}\hfill \hfill & \hfill 0\hfill & \hfill \hfill & \hfill \underset{\sim }{0}\hfill & \hfill \hfill \\ {}\hfill \hfill & \hfill \hfill & \hfill 0\hfill & \hfill \hfill & \hfill \hfill \\ {}\hfill \hfill & \hfill \underset{\sim }{0}\hfill & \hfill \hfill & \hfill 0\hfill & \hfill \hfill \\ {}\hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill \hfill & \hfill 0\hfill \end{array}\right]\left[\begin{array}{c}\hfill e\hfill \\ {}\hfill {\dot{A}}_z\hfill \\ {}\hfill \dot{q}\hfill \\ {}\hfill {\dot{\delta}}_e\hfill \\ {}\hfill {\ddot{\delta}}_e\hfill \end{array}\right]$

12) Page 67, change

to

$\underset{\bar{\mkern6mu}}{\sigma}\left(I+L\right)$

13) Page 67, change

to (keep together on same line)

$\underset{\bar{\mkern6mu}}{\sigma}\left(I+L\right)$

Chapter 4

1) Page 75, change

to

$\begin{array}{l}{\left\Vert u\right\Vert}_1={\displaystyle \underset{-\infty }{\overset{\infty }{\int }}\left|u(t)\right| dt}\\ {}{\left\Vert u\right\Vert}_2={\left({\displaystyle \underset{-\infty }{\overset{\infty }{\int }}{\left|u(t)\right|}^2 dt}\right)}^{\frac{1}{2}}\\ {}{\left\Vert u\right\Vert}_{\infty }=\underset{t}{ \sup}\left|u(t)\right|\end{array}$

2) Page 77, change

to

3) Page 88, change

to

section 4.4

4) Page 94, change

to

K _∞  = [−0.927881 64.7534  −13.1623  −0.11795  −3.21046 0.151197]

Chapter 5

1) Page 101 change

to

1 × 2

2) Page 102, change

to

$\begin{array}{l}u= Ke\\ {}y= GKe+w\\ {}z= GKe+w+v\\ {}e=r-z=r- GKe-w-v\\ {}E(s)=S(s)\left(R(s)-W(s)-V(s)\right)\end{array}$

3) Page 114, change

to

det[I + L(s,ε)] ≠ 0

4) Page 115, add space between x and is

5) Page 116, change

to

$\underset{\bar{\mkern6mu}}{\sigma}\left(I+{L}^{-1}(s)\right)>\overline{\sigma}\left(\varDelta (s)\right)$

6) Page 119, change

to

$\underset{\bar{\mkern6mu}}{\sigma}\left(I+{L}^{-1}\right)$

7) Page 119,

to

a _z  = 2.0 and a _q  = 2.0

8) Page 122, change

to

$\begin{array}{c}G{M}_{I+{L}^{-1}}=\left[0.2695\kern1em 1.7305\right];\kern2.75em P{M}_{I+{L}^{-1}}=\pm 42.84\ \deg \\ {}\kern-9.5em =\left[-11.4\kern1em 4.7\right]\ \mathrm{dB}\end{array}$

9) Page 122, change

to

GM = [−11.4 7.28] dB;  PM = ± 42.84 deg 

10) Page 124, change

to

should be examined

11) Page 127, change

to

is

12) Page 130, change

to

add space in front and after M, and change 5.8 to 5.7

13) Page 133, change

to

14) Page 136, change

to

$$ A = \left[ \begin{array}{lcc} {- 0.0251} & {0.10453} & { - 0.99452} \\ {574.7} & 0 & 0 \\ {16.2} & 0 & 0 \\ \end{array} \right]; B = \left[ \begin{array}{cc} {0.1228} & { - 0.2763} \\ {195.5} & { - 529.4} \\ { - 53.61} & {33.25} \\ \end{array} \right] $$

(0.2)

15) Page 138, change

to

$\left[\begin{array}{cc}\hfill {A}_p\hfill & \hfill {B}_p\hfill \\ {}\hfill {C}_p\hfill & \hfill {D}_p\hfill \end{array}\right]=\left[\begin{array}{l}\left[\begin{array}{l}-0.0251\kern0.75em 0.10453\kern0.5em -0.99452\\ {}\kern0.5em 574.70\kern2.5em 0\kern4.3em 0\\ {}\kern1em 16.2\kern3.em 0\kern4.3em 0\end{array}\right]\left[\begin{array}{l}\kern0.5em 0.1228\kern0.5em -0.27630\\ {}-53.610\kern1.8em 33.25\\ {}\kern0.5em 195.5\kern1.25em -529.40\end{array}\right]\\ {}\kern4.75em \left[\begin{array}{ccc}\hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right]\kern7.5em \left[\begin{array}{cc}\hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill \end{array}\right]\end{array}\right]$

16) Page 158, change

to

$\underset{\bar{\mkern6mu}}{\sigma }$

Chapter 6

1) Page 164, change

to

${N}_0={X}_{n_{y2}}{X}_{n_{y1}}^{-1}$

2) Page 166, change

to: make bracket same size as other brackets.

3) Page 169, change

to

$\begin{array}{rr} {X}_{n_y}=\left[\left[\begin{array}{lllr}2.2295\mathrm{e}-001\\ {}-9.4676\mathrm{e}-001\\ {}-1.6075\mathrm{e}-002\\ {}-5.3104\mathrm{e}-002\\ {}\kern0.5em 2.2551\mathrm{e}-001\end{array}\right]\right]\left[\begin{array}{r}-1.0379\mathrm{e}-001-9.1764\mathrm{e}-002j\\ {}\ 9.1946\mathrm{e}-001\kern6.9em \\ {}-1.4240\mathrm{e}-003-1.0897\mathrm{e}-002j\\ {}-4.3324\mathrm{e}-002-3.3555\mathrm{e}-002j\\ {}\ 3.6293\mathrm{e}-001-2.3622\mathrm{e}-002j\end{array}\right] \\ \times \left[\begin{array}{r}-1.0379\mathrm{e}-001+9.1764\mathrm{e}-002j\\ {}\ 9.1946\mathrm{e}-001\kern7.4em \\ {}-1.4240\mathrm{e}-003+1.0897\mathrm{e}-002j\\ {}-4.3324\mathrm{e}-002+3.3555\mathrm{e}-002j\\ {}\ 3.6293\mathrm{e}-001+2.3622\mathrm{e}-002j\end{array}\right]\end{array}$

4) Page 173, change

to

A _re

5) Page 173, change

to

$\begin{array}{c}{N}_0={X}_{n_{y2}}{X}_{n_{y1}}^{-1}\\ {}=\left[\begin{array}{l}-1.6565\mathrm{e}-001-5.8888\mathrm{e}-002\kern0.5em 4.4744\mathrm{e}+000\\ {}\kern0.5em 2.4157\mathrm{e}+000\kern0.5em 6.3925\mathrm{e}-001-1.8175\mathrm{e}+001\end{array}\right]\end{array}$

6) Page 173, change

to

delete (6.46)

7) Page 173, change

to

−6.6917e + 003

8) Page 174, change

to

(6.46)

8) Page 177, change

to

(6.53)

9) Page 177, change

to

(6.54)

10) Page 178, change

to

(6.53)

11) Page 179, change

to

(6.57)

12) Page 179, change

to

(6.58)

13) Page 179, change

to

(6.59)

14) Page 179, change

to

$\begin{array}{l}{L}_{LQG}(s)={K}_c{\left( sI-A+B{K}_c+{K}_fC\right)}^{-1}{K}_fC{\left( sI-A\right)}^{-1}B\\ {}{L}_{LQG}(s)\approx {K}_c{\left( sI-A\right)}^{-1}B\end{array}$

15) Page 179, change

to

$\underset{\bar{\mkern6mu}}{\sigma}\left({P}_f\right)\to 0$

16) Page 179, change

to

$\begin{array}{lll} u & =-{K}_c{\left( sI-\tilde{A}+\tilde{B}{K}_c+{K}_fC\right)}^{-1}{K}_f\left( Cx+v\right)\\ & =-{K}_c{\left( sI-\tilde{A}+\tilde{B}{K}_c+{K}_fC\right)}^{-1}{K}_f Cx-{K}_c{\left( sI-\tilde{A}+\tilde{B}{K}_c+{K}_fC\right)}^{-1}{K}_fv\\ & \approx -{K}_cx-{K}_c{\left( sI-\tilde{A}+\tilde{B}{K}_c+{K}_fC\right)}^{-1}{K}_fv\end{array}$

17) Page 180, change

to

(6.62) change to (6.51)

(6.55) change to (6.54)

(6.59) change to (6.58)

(6.62) change to (6.61)

18) Page 180, change the following text:

to

in which the first term approximately equals the state feedback control law, but the second term amplifies the sensor noise. This feature limits the amount of recovery possible. In the use of this design method for making the LQG system robust, the sensor noise amplification in (6.62) must be examined.

19) Page 181, change

to

(6.53)

20) Page 183, change

to

(6.64)

21) Page 183, change

to: need to add the “e” e-006, e-002 to these two numbers

22) Page 185, change

to

(6.74)

23) Page 185, change

to

$\begin{array}{l}\left[\begin{array}{c}\hfill {A}_c\hfill \\ {}\hfill {C}_c\hfill \end{array}\right]=\kern0.75em \left[\begin{array}{c}\hfill \left[\begin{array}{l}\kern8.2em 0\kern23em 0\kern19em 0\kern21.5em 0\kern20.5em 0\\ {}\kern8.2em 0\kern11.9em -1.0854\mathrm{e}+000\kern4.2em 3.4041\mathrm{e}+002\kern12em 0\kern12.25em -1.1289\mathrm{e}+001\\ {}\kern8.2em 0\kern14.5em 6.8202\mathrm{e}-003\kern2.5em -1.1116\mathrm{e}+000\kern1.5em -1.0925\mathrm{e}+000\kern11.75em 0\\ {}\kern8.2em 0\kern12em -3.9887\mathrm{e}-009\kern4.2em 1.2264\mathrm{e}-006\kern12em 0\kern19.75em 1.0\\ {}-3.3010\mathrm{e}+003\kern1.5em -1.1944\mathrm{e}+003\kern3.5em 9.3804\mathrm{e}+004\kern3.3em -2.1408\mathrm{e}+004\kern1.5em -1.1005\mathrm{e}+002\end{array}\right]\hfill \\ {}\hfill \left[\begin{array}{ccccc}\hfill -4.9477\mathrm{e}-001\kern1.5em \hfill & \hfill -1.7903\mathrm{e}-001\kern1.5em \hfill & \hfill 1.4060\mathrm{e}+001\kern2.8em \hfill & \hfill -2.2087\mathrm{e}+000\kern1em \hfill & \hfill -1.8035\mathrm{e}-003\hfill \end{array}\right]\hfill \end{array}\right]\\ {}\left[\begin{array}{cc}\hfill {B}_{c_1}\hfill & \hfill {B}_{c_2}\hfill \\ {}\hfill {D}_{c_1}\hfill & \hfill {D}_{c_2}\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill \left[\begin{array}{l}1.0\kern10em 0\\ {}\kern0.5em 3.2707\mathrm{e}-002\kern4em -6.0760\mathrm{e}+000\\ {}-9.7217\mathrm{e}-005\kern4em 7.8188\mathrm{e}-002\\ {}\kern0.5em 3.9887\mathrm{e}-009\kern4em -1.2264\mathrm{e}-006\\ {}-9.0547\mathrm{e}-007\kern4em 1.3375\mathrm{e}-004\end{array}\right]\hfill & \hfill \left[\begin{array}{c}-1\ \\ {}\kern0.5em 0\\ {}\kern0.5em 0\\ {}\kern0.5em 0\\ {}\kern0.5em 0\end{array}\right]\hfill \\ {}\hfill \left[\kern0.5em 0\kern1.25em 0\kern0.5em \right]\hfill & \hfill \left[\kern0.5em 0\kern0.5em \right]\hfill \end{array}\right]\end{array}$

24) Page 186, change

to

(6.73)

25) Page 189

to$\underset{\bar{\mkern6mu}}{\sigma }$

26) Page 190, change

to: This text should not be italic

27) Page 191, change

to: (6.80), and the text in the boxes should not be italic.

28) Page 192

to: Change (6.83) to (6.82). The text on this page should not be italic.

29) Page 193, change

to: (6.88) to (6.87), (6.86) to (6.85), (6.92) to (6.91). This page should not be italic.

30) Page 194, change

to: (6.94) to (6.93), (6.94) to (6.93), (6.88) to (6.87), (6.88) to (6.87). The text in the box should not be italic.

31) Page 196, change

to: ), (6.89) to (6.88), (6.88) to (6.87).

32) Page 197, change

to: (6.101) to (6.100)

33) Page 198, change

to: (6.102) to (6.101), (6.103) to (6.102), (6.110) to (6.109), (6.107) to (6.106)

34) Page 199, change

to: (6.110) to (6.109), (6.111) to (6.110), (6.111) to (6.110), (6.112) to (6.111)

35) Page 200, change

to: (6.102) to (6.101),

36) Page 201, change

to: (6.108) to (6.107)

37) Page 201, change

to: (6.112) to (6.111)

38) Page 201, change

to: (6.108) to (6.107), (6.112) to (6.111)

39) Page 205, change

to: remove the “e”

40) Page 206, change

to$\underset{\bar{\mkern6mu}}{\sigma }$

41) Page 206 change

to: (6.59) to (6.58)

42) Page 207

to

$\underset{\bar{\mkern6mu}}{\sigma }$, (6.88) to (6.87)

ERRATA LIST

Robust and Adaptive Control with Aerospace Applications – 1 ^st Edition, Springer, 2013

Eugene Lavretsky

Revised on 27 Jul 2013

Part II

Chapter 7

• 1. Page 222: Exercise 7.3: Change “(7.13), (7.14), (7.15), (7.16), (7.17), (7.18), (7.19), (7.20), (7.21), (7.22), and (7.23).” to “(7.13) through (7.23).”

• 2. Page 239: Example 8.9: Change $6 \sin t-6\;t \cos t-{t}^2\le 6+\underset{\le \frac{1}{4}}{\underbrace{\left(t-{t}^2\right)}}\le 6.25$ to $6 \sin t-6\;t \cos t-{t}^2\le 6+\underset{\le 9}{\underbrace{\left(6\;t-{t}^2\right)}}\le 15$

• 3. Page 239: Example 8.9: Change $\left|x(t)\right|\le \left|x\left({t}_0\right)\right|\;\underset{c\left({t}_0\right)}{\underbrace{ \exp \left(6.25-6 \sin {t}_0+6\;{t}_0 \cos {t}_0+{t}_0^2\right)}}=\left|x\left({t}_0\right)\right|\;c\left({t}_0\right)$ to $\left|x(t)\right|\le \left|x\left({t}_0\right)\right|\;\underset{c\left({t}_0\right)}{\underbrace{ \exp \left(15-6 \sin {t}_0+6\;{t}_0 \cos {t}_0+{t}_0^2\right)}}=\left|x\left({t}_0\right)\right|\;c\left({t}_0\right)$

Chapter 8

• 1. Page 261: Example 8.10: Change ${\dot{x}}_{ref}=A\;{x}_{ref}+b\;r$ to ${\dot{x}}_{ref}=A\;{x}_{ref}+b\;{K}_r\;r$

• 2. Page 258: Change sentence

  

  to”regressor vector”, which is assumed to be uniformly bounded and Lipschitz-continuous in t.

• 3. Page 258: Change $V\left( {e,\Delta K} \right) = {e^T}Pe + {\Delta K^T \Delta K}$ to $V\left( {e,\Delta K} \right) = {e^T}Pe + {1 \over \gamma }\Delta {K^T}\Delta K.$

• 4. Page 258: Change the next equation for ${{\dot V}{e,\Delta K}= }\ ...$ to

  $$ \begin{array}{llll} \dot V\left( {e,\Delta K} \right) = & {{\dot e}^T}\,P\,e + {e^T}\,P\,\dot e + 2{1 \over \gamma }\Delta {K^T}\,\dot \hat K = {\left( {A\,e + b\,\Delta {K^T}\Phi } \right)^T}\\ & P\,e + {e^T}P\left( {A\,e + b\,\Delta {K^T}\Phi } \right) - 2\Delta {K^T}\Phi {e^T}\,P\,b = - {e^T}Q\,e \le 0 \end{array} $$

• 5. Page 261: Change equation ${{\dot x}_{ref}} = A{x_{ref}} + br$ to ${{\dot x}_{ref}} = A{x_{ref}} + b{K_r}r.$

Chapter 9

• 1. Page 282: Eq. (9.47): Right-justify the equation number (i.e., move it to the right).

Chapter 10

• 1. Page 311: Table 2.10: Change the third equation from the bottom to: $u = \left( {{I_{m \times m}} - \hat K_u^T} \right){u_{bl}} - {{\hat \Theta }^T}\Phi \left( {{x_p}} \right).$

  This equation in the current book version has an incomplete sub-index in I.

• 2. Page 314: Exercise 10.1: In the problem statement, replace “have” with “has”.

• 3. Page 314: Exercise 10.2: Add the minus sign to the last equation in the problem statement: ${\hat K_x}\left( 0 \right) = - {K_x}.$

Chapter 11

• 1 Page 325: Replace text and equations starting from Eq. 11.26 through Eq. 11.29 with:

  

  

• 2 Page 327: Change section number from “11.3” to subsection # “11.2.3”

• 3 Page 328: Replace the first sentence and the second sentences with the sentence shown below in yellow:

• 4 Page 329: Change Eq. (11.59) to:

  $$\nabla {f_j} = \frac{{(1 + \varepsilon _j^\Theta )}}{{\varepsilon _j^\Theta {{(\Theta _j^{\max })}^2}}}\nabla [||\mathop {{\widehat \Theta _j}} \wedge |{|^2}] = \frac{{2(1 + \varepsilon _j^\Theta )}}{{\varepsilon _j^\Theta {{(\Theta _j^{\max })}^2}}}\mathop {{\widehat \Theta _j}.} $$

Chapter 12

• 1 Page 364: Replace δ with δ R in Fig 12.5, as shown below:

  

• 2 Page 372: Change “Example 12.3” to “Example 12.1”

• 3 Page 373: In the sentence “In addition, we impose a restriction on the runway distance …” : Change ${\tau _{fl}}$ to $4{\tau _{h}}$.

• 4 Page 374: Change the second equation as shown below (change B(2,2) to 0.00044):$\begin{array}{l}\underset{\dot{x}}{\underbrace{\left(\begin{array}{c}\hfill \dot{V}\hfill \\ {}\hfill \dot{\alpha}\hfill \\ {}\hfill \dot{q}\hfill \\ {}\hfill \dot{\theta}\hfill \\ {}\hfill \dot{h}\hfill \end{array}\right)}}=\underset{A}{\underbrace{\left(\begin{array}{ccccc}\hfill -0.038\hfill & \hfill 18.984\hfill & \hfill 0\hfill & \hfill -32.174\hfill & \hfill 0\hfill \\ {}\hfill -0.001\hfill & \hfill -0.632\hfill & \hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill -0.759\hfill & \hfill -0.518\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill -250\hfill & \hfill 0\hfill & \hfill 250\hfill & \hfill 0\hfill \end{array}\right)}}\;\underset{x}{\underbrace{\left(\begin{array}{c}\hfill V\hfill \\ {}\hfill \alpha \hfill \\ {}\hfill q\hfill \\ {}\hfill \theta \hfill \\ {}\hfill h\hfill \end{array}\right)}}\\ {}\kern1.2em +\underset{B}{\underbrace{\left(\begin{array}{cc}\hfill 10.1\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0.00044\hfill \\ {}\hfill 0.025\hfill & \hfill -0.011\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill \end{array}\right)}}\;\underset{u}{\underbrace{\left(\begin{array}{c}\hfill {\delta}_{th}\hfill \\ {}\hfill {\delta}_e\hfill \end{array}\right)}}\iff \boxed{\dot{x}=A\;x+B\;u}\end{array}$

• 5 Page 375: Change equation at the top of the page as shown below (change B(2,2) to 0.00044):$\begin{array}{l}\underset{\dot{x}}{\underbrace{\left(\begin{array}{c}\hfill \dot{V}\hfill \\ {}\hfill \dot{\alpha}\hfill \\ {}\hfill \dot{q}\hfill \\ {}\hfill \dot{\theta}\hfill \\ {}\hfill \dot{h}\hfill \end{array}\right)}}=\underset{A}{\underbrace{\left(\begin{array}{ccccc}\hfill -0.038\hfill & \hfill 18.984\hfill & \hfill 0\hfill & \hfill -32.174\hfill & \hfill 0\hfill \\ {}\hfill -0.001\hfill & \hfill -0.632\hfill & \hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill -0.759\hfill & \hfill -0.518\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill -250\hfill & \hfill 0\hfill & \hfill 250\hfill & \hfill 0\hfill \end{array}\right)}}\;\underset{x}{\underbrace{\left(\begin{array}{c}\hfill V\hfill \\ {}\hfill \alpha \hfill \\ {}\hfill q\hfill \\ {}\hfill \theta \hfill \\ {}\hfill h\hfill \end{array}\right)}}\\ {}\kern1.2em +\underset{B}{\underbrace{\left(\begin{array}{cc}\hfill 10.1\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0.00044\hfill \\ {}\hfill 0.025\hfill & \hfill -0.011\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill \end{array}\right)}}\;\underset{u}{\underbrace{\left(\begin{array}{c}\hfill {\delta}_{th}\hfill \\ {}\hfill {\delta}_e\hfill \end{array}\right)}}+\underset{B_g}{\underbrace{\left(\begin{array}{c}\hfill -18.984\hfill \\ {}\hfill 0.632\hfill \\ {}\hfill 0.759\hfill \\ {}\hfill 0\hfill \\ {}\hfill 0\hfill \end{array}\right)}}\;{\alpha}_g(h)\end{array}$

• 6 Page 376: Change 4^th from the bottom equation as shown below:${Q}_{lqr}=\mathrm{diag}\left(\begin{array}{ccccc}\hfill 0.2\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right),\kern1em {R}_{lqr}=\mathrm{diag}\left(\begin{array}{cc}\hfill 10\hfill & \hfill 10\hfill \end{array}\right)$

Chapter 13

• 1 Page 406: Insert space between “y_cmd” and “y” in Eq. 13.87. There are two equations there, not one, as shown below.

  

• 2 Page 409: Move superscript “T” in Eq. 13.99 to the right and outside of parenthesis, as in:

  

• 3 Page 416: Exercise 13.4: Change “Example 13.3” to “Example 10.2”.

Chapter 14

• 1 Page 429: Eq. 14.46: Change to:$\begin{array}{l}\dot{V}\left({e}_x,\varDelta \overline{\varTheta}\right)=-\left(1+\frac{1}{v}\right)\;{e}_y^T\;{R}_0^{-1}\;{e}_y-{e}_x^T\;{\tilde{P}}_v\;{Q}_0\;{\tilde{P}}_v\;{e}_x\\ {}-\left(1+\frac{1}{v}\right)\kern0.24em {\left\Vert {B}^T{\tilde{P}}_v\;{e}_x\right\Vert}^2-2\;\eta\;{e}_x^T\;{\tilde{P}}_v\;{e}_x+2\;{e}_x^T\;{\tilde{P}}_v\;B\;\varLambda\;g\\ {}+2\;\mathrm{trace}\left(\varLambda\;\varDelta {\overline{\varTheta}}^T\;\left\{{\varGamma}_{\Theta}^{-1}\;\dot{\widehat{\overline{\varTheta}}}+\overline{\varPhi}\left(\widehat{x},,,{u}_{bl}\right)\underset{e_y^T}{\underbrace{\left({e}_x^T\;{C}^T\right)}}\;{R}_0^{-\frac{1}{2}}\;W\;{S}^T\right\}\right)\\ {}+2\;{e}_x^T\;\mathrm{O}(v)\;\varLambda\;\varDelta {\overline{\varTheta}}^T\;\overline{\varPhi}\left(\widehat{x},,,{u}_{bl}\right)\end{array}$

• 2 Page 430: Eq. 14.48: Change to:$\begin{array}{l}\dot{V}\left({e}_x,\varDelta \overline{\varTheta}\right)\le -2\;\eta\;{\lambda}_{\min}\left({\tilde{P}}_v\right)\;{\left\Vert {e}_x\right\Vert}^2-{\lambda}_{\min}\left({Q}_0\right)\;{\lambda}_{\min}^2\left({\tilde{P}}_v\right)\;{\left\Vert {e}_x\right\Vert}^2\\ {}-\left(1+\frac{1}{v}\right)\;{\lambda}_{\min}\left({R}_0^{-1}\right)\;{\left\Vert {e}_y\right\Vert}^2-\left(1+\frac{1}{v}\right)\kern0.24em {\left\Vert {B}^T{\tilde{P}}_v\;{e}_x\right\Vert}^2+2\;{\varLambda}_{\max}\;{k}_g\left\Vert {B}^T{\tilde{P}}_v\;{e}_x\right\Vert\;\left\Vert {e}_x\right\Vert \\ {}+2\;v\;\left\Vert {e}_x\right\Vert\;k\;{\varLambda}_{\max}\;\varDelta {\overline{\varTheta}}_{\max}\;\left\Vert \overline{\varPhi}\left(\widehat{x},,,{u}_{bl}\right)\right\Vert \end{array}$

• 3 Page 430: Eq. 14.49: Change to:$\begin{array}{l}\dot{V}\left({e}_x,\varDelta \overline{\varTheta}\right)\le -\left(2\;\eta +{\lambda}_{\min}\left({Q}_0\right)\;{\lambda}_{\min}\left({\tilde{P}}_v\right)\right)\kern0.24em {\lambda}_{\min}\left({\tilde{P}}_v\right)\kern0.24em {\left\Vert {e}_x\right\Vert}^2\\ {}-\left(1+\frac{1}{v}\right)\;{\lambda}_{\min}\left({R}_0^{-1}\right)\;{\left\Vert {e}_y\right\Vert}^2-\left(1+\frac{1}{v}\right)\kern0.24em {w}^2+2\;{\varLambda}_{\max}\;{k}_gw\;\left\Vert {e}_x\right\Vert \\ {}+2\;v\;\left\Vert {e}_x\right\Vert\;k\;{\varLambda}_{\max}\;\varDelta {\overline{\varTheta}}_{\max}\;\left\Vert \overline{\varPhi}\left(\widehat{x},,,{u}_{bl}\right)\right\Vert \end{array}$

• 4 Page 430: Eq. 14.50: Change to:$\begin{array}{l}\dot{V}\left({e}_x,\varDelta \overline{\varTheta}\right)\le -\left(2\;\eta +{\lambda}_{\min}\left({Q}_0\right)\;{\lambda}_{\min}\left({\tilde{P}}_0\right)\right)\kern0.24em {\lambda}_{\min}\left({\tilde{P}}_0\right)\kern0.24em {\left\Vert {e}_x\right\Vert}^2\\ {}-\left(1+\frac{1}{v}\right)\;{\lambda}_{\min}\left({R}_0^{-1}\right)\;{\left\Vert {e}_y\right\Vert}^2-\left(1+\frac{1}{v}\right)\kern0.24em {w}^2+2\;{\varLambda}_{\max}\;{k}_gw\;\left\Vert {e}_x\right\Vert \\ {}+2\;v\;\left\Vert {e}_x\right\Vert\;k\;{\varLambda}_{\max}\;\varDelta {\overline{\varTheta}}_{\max}\;\left\Vert \overline{\varPhi}\left(\widehat{x},,,{u}_{bl}\right)\right\Vert \end{array}$

• 5 Page 431: Eq. 14.52: Change to:$\begin{array}{l}\dot{V}\left({e}_x,\varDelta \overline{\varTheta}\right)\le -\left(1+\frac{1}{v}\right)\;{\lambda}_{\min}\left({R}_0^{-1}\right)\;{\left\Vert {e}_y\right\Vert}^2\\ {}-\left[\left(2\;\eta +{\lambda}_{\min}\left({Q}_0\right)\;{\lambda}_{\min}\left({\tilde{P}}_0\right)\right)\kern0.24em {\lambda}_{\min}\left({\tilde{P}}_0\right)-2\;v\;k\;{\varLambda}_{\max}\;\varDelta {\overline{\varTheta}}_{\max}\;{b}_2\right]\kern0.24em {\left\Vert {e}_x\right\Vert}^2\\ {}-\left(1+\frac{1}{v}\right)\kern0.24em {w}^2+2\;{\varLambda}_{\max}\;{k}_gw\;\left\Vert {e}_x\right\Vert +2\;v\;{\varLambda}_{\max}\;k\;\varDelta {\overline{\varTheta}}_{\max}\;{b}_1\;\left\Vert {e}_x\right\Vert \end{array}$

• 6 Page 431: Eq. 14.53: Change to:$\begin{array}{l}{c}_1={\lambda}_{\min}\left({Q}_0\right)\;{\lambda}_{\min}^2\left({\tilde{P}}_0\right)-2\;v\;k\;{\varLambda}_{\max}\;\varDelta {\varTheta}_{\max}\;{b}_2,\kern1em {c}_2={\varLambda}_{\max}\;{k}_g\\ {}{c}_3=1+\frac{1}{v},\kern1em {c}_4=v\;{\varLambda}_{\max}\;k\;\varDelta {\varTheta}_{\max}\;{b}_1\end{array}$

• 7 Page 431: Eq. 14.54: Change to:$\begin{array}{l}\dot{V}\left({e}_x,\varDelta \overline{\varTheta}\right)\le -{c}_3\;{\lambda}_{\min}\left({R}_0^{-1}\right)\;{\left\Vert {e}_y\right\Vert}^2-2\;\eta\;{\lambda}_{\min}^2\left({\tilde{P}}_0\right)\;{\left\Vert {e}_x\right\Vert}^2\\ {}-\underset{\varphi \left(\left\Vert {e}_x\right\Vert, w\right)}{\underbrace{\left[{c}_1\kern0.24em {\left\Vert {e}_x\right\Vert}^2-2\;{c}_2\;\left\Vert {e}_x\right\Vert\;w+{c}_3\;{w}^2-2\;{c}_4\;\left\Vert {e}_x\right\Vert \right]}}\\ {}=-{c}_3\;{\lambda}_{\min}\left({R}_0^{-1}\right)\;{\left\Vert {e}_y\right\Vert}^2-2\;\eta\;{\lambda}_{\min}^2\left({\tilde{P}}_0\right)\;{\left\Vert {e}_x\right\Vert}^2-\varphi \left(\left\Vert {e}_x\right\Vert, w\right)\end{array}$

• 8 Page 432: Eq. 14.61: Change to:${v}_1=\frac{\lambda_{\min}\left({Q}_0\right)\;{\lambda}_{\min}^2\left({\tilde{P}}_0\right)}{2\;k\;{\varLambda}_{\max}\;\varDelta {\overline{\varTheta}}_{\max}\;{b}_2}$

• 9 Page 432: Eq. 14.62: Change to:$\begin{array}{l} \det\;C={c}_1\;{c}_3-{c}_2^2\\ {}=\left(1+\frac{1}{v}\right)\kern0.24em \left[{\lambda}_{\min}\left({Q}_0\right)\;{\lambda}_{\min}^2\left({\tilde{P}}_0\right)-2\;v\;k\;{\varLambda}_{\max}\;\varDelta {\varTheta}_{\max}\;{b}_2\right]-{\varLambda}_{\max}^2\;{k}_g^2=\mathrm{O}\left(\frac{1}{v}\right)\end{array}$

• 10 Page 433: Eq. 14.66: Change to:$\dot{V}\left({e}_x,\varDelta \overline{\varTheta}\right)\le -\left(1+\frac{1}{v}\right)\;{\lambda}_{\min}\left({R}_0^{-1}\right)\;{\left\Vert {e}_y\right\Vert}^2-2\;\eta\;{\lambda}_{\min}^2\left({\tilde{P}}_0\right)\;{\left\Vert {e}_x\right\Vert}^2+\left|{\varphi}_{\min }(v)\right|$

• 11 Page 433: Eq. 14.67: Change to:${\varOmega}_{e_x}=\left\{{e}_x:\kern1em {\left\Vert {e}_x\right\Vert}^2\le \frac{\left|{\varphi}_{\min }(v)\right|}{2\;\eta\;{\lambda}_{\min}^2\left({\tilde{P}}_0\right)}={r}_{v,\eta}^2=\mathrm{O}\left(\frac{v^2}{\eta}\right)\right\}$

• 12 Page 435: Table 14.1: Change 11^th and 12^th equations in the table as shown below:

  

Back cover

Second paragraph: Change “The text is a three-part treatment” to “The text is a two-part treatment”. “Errata List”,6,1