If you have suggestions or find errors in the course notes please send to b-hajek@illinois.edu. We will post here and send back to the authors at the end of the semester. Thank you!

• p. 7 Perhaps note that $I_1$ and $I_2$ are moments of inertia of the two links
• p. 24 Vector space axioms should include distributive properties: a*(x+y)=a*x + a*y and (a+b)*x=a*x+b*x
• p. 25 Third example of a vector space. $C^n[a,b], R)$ is the vector space of n-times continuously differentiable real-valued functions. This is a matter of notation, but the sentence in the text states the functions are real-valued and take values in R^n. Same comment applies to the next example -- the vector space $D^n$.
• On page 31, at the very bottom where the closed-form expression of \beta is shown, the top-right variable in the matrix, \alpha_{in}, should be \alpha_{1n}, and the bottom-left variable should be \alpha_{m1}.
• p. 37 Sixth line in the Section 2.9. "By orthogonality we then have" should be "By linearity we have" (No orthogonality is assumed/needed at that point.)
• p. 38 Seven lines before Section 2.10, the line contains "to to"
• p. 45 Problem 2.11.20. the vector x should be from complex n dimensional space not $\reals^n$
• p. 77 In the seventh line of the proof. It is stated that the gradient of $V$ is a row vector. Most other places in the book (and in the literature) gradients are column vectors. There are some transposes taken in some of the lines that follow which would not be there if the gradient were a column vector.
• p. 90 In the equation in line 8 just after "Equivalently, we must have" the lambda_i in the exponent should have a complex conjugate symbol over it (or a star).
• p. 171 The variable y in (10.9) should be replaced by t. Also, the inequality in equation (10.9) is incorrect. It is is equivalent to \ell(x,u^o,t) \leq \ell(x,u,t) which is not true -- the optimal control does not simply minimize the local cost function. The proof of Theorem 10.2.1 needs fixing.
• p. 171 Four lines before Example 10.2.1, the apostrophe superscript on u in the integral should be removed.
• p. 207 Figure 11.1: If could be a problem with the pdf reader but the gradient vectors don't show up well in Figure 11.1.
• p. 218, the equations in part (b): $x_i(t_i)$ should be $x_i(t_1).$ In the next line it should be for $j\in I^c$ not for $i\in I^c$