settings_symbols.tex

% *********** Black-box model ***********
\newcommand{\bbsys}{\Sigma}
\newcommand{\bbstate}{\chi}
\newcommand{\bbssstate}{\tilde{\chi}}
\newcommand{\bbaux}{\upsilon}
\newcommand{\bbssaux}{\tilde{\bbaux}}
\newcommand{\bbout}{\eta}
\newcommand{\bbouto}{\bbout_o}
\newcommand{\bboutp}{\bbout_p}
\newcommand{\bbssoutp}{\tilde{\bbout}_p}
\newcommand{\bbssouto}{\tilde{\bbout}_o}
\newcommand{\bbssoutoa}{\tilde{\bbout}_o^a}
\newcommand{\bboutoa}{\bbout_o^a}
\newcommand{\bbvecf}{f}
\newcommand{\bbinmap}{g}
\newcommand{\bboutmap}{h}
\newcommand{\bboutmapp}{\bboutmap_p}
\newcommand{\bboutmapo}{\bboutmap_o}
\newcommand{\bbperiod}{T}
\newcommand{\bbcost}{\ell}
\newcommand{\bbreddeg}{\bbauxdim_a}

% *********** Black-box linear model ***********
\newcommand{\bbdynmat}{A_\bbsys}
\newcommand{\bbctrmat}{B_\bbsys}
\newcommand{\bboutmat}{C_\bbsys}

% *********** Black-box model dimensions ***********
\newcommand{\bbstatedim}{n}
\newcommand{\bbauxdim}{m}
\newcommand{\bboutdim}{q}
\newcommand{\bboutpdim}{{\bboutdim_p}}
\newcommand{\bboutodim}{{\bboutdim_o}}

% *********** Black-box model exosystem ***********
\newcommand{\bbexo}{E}
\newcommand{\bbexostate}{w}
\newcommand{\bbref}{r}
\newcommand{\bbexovecf}{\xi}
\newcommand{\bbexooutmap}{\psi}
\newcommand{\bbexostateset}{\mathcal{W}}
\newcommand{\bbexoinitset}{\bbexostateset^\circ}
\newcommand{\fbimap}{\pi}

% *********** Linear exosystem dynamics ***********
\newcommand{\exodynmat}{S}
\newcommand{\exooutmat}{C_e}
\newcommand{\dexodynmat}{\exodynmat_d}

% *********** Black-box model exosystem dimensions ***********
\newcommand{\bbexostatedim}{{n_e}}
\newcommand{\bbrefdim}{{n_r}}

% *********** Generic allocator ***********
\newcommand{\allin}{\varpi}
\newcommand{\allout}{\varsigma}
\newcommand{\allssin}{\tilde{\allin}}
\newcommand{\allssout}{\tilde{\allout}}

% *********** Plant ***********
\newcommand{\plant}{\Theta}
\newcommand{\plantstate}{x}
\newcommand{\plantinput}{u}
\newcommand{\plantoutput}{y}
\newcommand{\plantssinput}{\tilde{\plantinput}}
\newcommand{\plantssoutput}{\tilde{\plantoutput}}
\newcommand{\plantstatedim}{{n_p}}
\newcommand{\plantinputdim}{m}
\newcommand{\plantoutputdim}{\bboutodim}

% *********** Linear plant dynamics ***********
\newcommand{\plantdynmat}{A_p}
\newcommand{\plantctrmat}{B_p}
\newcommand{\plantoutmat}{C_p}
\newcommand{\planttf}{W_{\plantoutput\plantinput}}
\newcommand{\plantalltf}{W_{\plantoutput\bbaux}}
\newcommand{\plantlcfd}{D_p}
\newcommand{\plantlcfn}{N_p}
\newcommand{\plantalllcfd}{D_\Sigma}
\newcommand{\plantalllcfn}{N_\Sigma}

% *********** Discretized linear plant dynamics ***********
\newcommand{\dplantdynmat}{A_{p,d}}
\newcommand{\dplantctrmat}{B_{p,d}}
\newcommand{\dplantoutmat}{C_{p,d}}
\newcommand{\dplanttf}{W_{\plantoutput\plantinput}^{d}}
\newcommand{\dplantlcfd}{D_{p,d}}
\newcommand{\dplantlcfn}{N_{p,d}}

% *********** Controller ***********
\newcommand{\ctrl}{\Gamma}
\newcommand{\ctrlstate}{\varphi}
\newcommand{\ctrlouput}{\rho}
\newcommand{\ctrlssoutput}{\tilde{\ctrlouput}}
\newcommand{\ctrlstatedim}{{n_c}}
\newcommand{\ctrloutputdim}{m}

% *********** Linear controller ***********
\newcommand{\ctrldynmat}{A_c}
\newcommand{\ctrlctrmat}{B_c}
\newcommand{\ctrlrefmat}{P_c}
\newcommand{\ctrloutmat}{C_c}
\newcommand{\ctrldirgain}{D_c}
\newcommand{\ctrlrefgain}{Q_c}

% *********** Controller-centric feedback model ***********
% NOTE: This is introduced in LQRALL.
\newcommand{\feedbackdynmat}{A_\ctrlstate}
\newcommand{\feedbackctrmat}{B_\ctrlstate}
\newcommand{\feedbackoutmat}{C_\ctrlstate}

% *********** Sets ***********
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}

% *********** Symbols ***********
\newcommand{\xmark}{\ensuremath{\times}}
\newcommand{\plusmark}{\ensuremath{+}}
\newcommand{\ubar}[1]{\underaccent{\bar}{#1}}

% *********** Keywords ***********
\newcommand{\ROS}{ROS~2\xspace}

% *********** Mathematical operators ***********
\DeclareMathOperator{\setint}{int}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\row}{row}
\DeclareMathOperator{\spec}{spec}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\Mod}{mod}
\DeclareMathOperator{\Imag}{Im}
\DeclareMathOperator{\realpart}{Re}
\DeclareMathOperator{\imagpart}{Im}
\DeclareMathOperator{\poleset}{\mathcal{P}}
\DeclareMathOperator{\zeroset}{\mathcal{Z}}
\renewcommand{\Re}{\realpart}
\renewcommand{\Im}{\imagpart}

% *********** Delimiters ***********
\newcommand{\closestatement}{\hfill$\circ$}
\newcommand{\closeremark}{\hfill$\blacktriangle$}
\newcommand{\closeexample}{\hfill$\blacksquare$}

% *********** DDALL stuff ***********
\newcommand{\bbm}[1]{\begin{bmatrix}#1\end{bmatrix}}
\newcommand{\bsm}[1]{\left[\begin{smallmatrix}#1\end{smallmatrix}\right]}
\newcommand{\bbmat}[3]{\left[\begin{BMAT}{#1}{#2}#3\end{BMAT}\right]}
\newcommand\Tpz{\operatorname{Tpz}}
\newcommand\Cir{\operatorname{Cir}}
\newcommand{\pls}[1]{#1^+} \newcommand{\he}{\mathrm{He}}
\newcommand{\ve}[1]{\mathrm{vec}(#1)}
\newcommand{\re}{\realpart} % Adapted
\newcommand{\im}{\imagpart} % Adapted