$$\newcommand{\vmath}[1]{\mathsf{#1}} \newcommand{\mapsfrom}{\leftarrow\!\shortmid} \newcommand{\maps}{\mapsto} \newcommand{\exc}{\vmath{\colF{exec}}} \newcommand{\eval}{\vmath{\colR{eval}}} \newcommand{\ufloor}{{\vmath{\colL floor}}} \newcommand{\uceil}{{\vmath{\colU ceil}}} \newcommand{\triv}{\text{Triv}} \newcommand{\idFunc}{\mathrm{Id}} \newcommand{\reals}{\mathbb{R}} \newcommand{\One}{\mathbf{1}} \renewcommand{\mathbbm}[1]{\mathbb{#1}} \renewcommand{\mathscr}[1]{\mathcal{#1}} \newcommand{\varocircle}{⦾} \newcommand{\varotimes}{⊗} \newcommand{\varovee}{(\vee)} \newcommand{\colR}{\color{darkred}} \newcommand{\colF}{\color{darkgreen}} \newcommand{\colH}{\color{blue}} \newcommand{\colI}{\color{orange}} \newcommand{\rtof}{{\colH{\varphi}}} \newcommand{\ftor}{{\colH{h}}} \newcommand{\ftoR}{{\colH{H}}} \newcommand{\Rcomp}{{\mathbb{R}}^{*}_{\small+}} \newcommand{\nonNegRealsComp}{\Rcomp} \newcommand{\nonNegReals}{\mathbb{R}_+} \newcommand{\Rcpu}[1]{\Rcomp{}[\textrm{#1}]} \newcommand{\funsp}{{\colF{\mathscr{F}}}} \newcommand{\impsp}{{\colI{\mathscr{I}}}} \newcommand{\ressp}{{\colR{\mathscr{R}}}} \newcommand{\funleq}{\posleq_{\funsp}} \newcommand{\fun}{\vmath{\colF{f}}} \newcommand{\res}{\vmath{\colR{r}}} \newcommand{\funtop}{\top_\funsp} \newcommand{\funbot}{\bot_\funsp} \newcommand{\imp}{\vmath{i}} \newcommand{\paramsp}{\mathscr{P}} \newcommand{\resleq}{\posleq_{\ressp}} \newcommand{\restop}{\top_\ressp} \newcommand{\resbot}{\bot_\ressp} \newcommand{\resspleq}{\resleq} \newcommand{\tressp}{\trof(\ressp)} \newcommand{\trof}{\mathscr{T}} \newcommand{\tres}{T} \newcommand{\tresleq}{\leq_{\trof}} \newcommand{\trleq}{\leq_{\trof}} \newcommand{\dpisp}{\ensuremath{\vmath{DPI}}} \newcommand{\cdpisp}{\ensuremath{\vmath{CDPI}}} \newcommand{\dprobsp}{\ensuremath{\vmath{DP}}} \newcommand{\dprob}{\vmath{dp}} \newcommand{\dpseries}{\vmath{series}} \newcommand{\dppar}{\vmath{par}} \newcommand{\dploop}{\vmath{loop}} \newcommand{\dploopb}{\vmath{loopb}} \newcommand{\cdprobsp}{\ensuremath{\vmath{CDP}}} \newcommand{\cdprob}{\vmath{cdp}} \newcommand{\dpatoms}{\vmath{atoms}} \newcommand{\resMin}{{\Min_{\resleq}}} \newcommand{\unconnectedfun}{\mathsf{UF}} \newcommand{\unconnectedres}{\mathsf{UR}} \newcommand{\Aressp}{{\mathsf{\colR A}\colR\ressp}} \newcommand{\Afunsp}{{\mathsf{\colF A}\colF\funsp}} \newcommand{\udpa}{\boldsymbol{u}_a} \newcommand{\udpb}{\boldsymbol{u}_b} \newcommand{\udpL}{\boldsymbol{\mathsf{L}}} \newcommand{\udpU}{\boldsymbol{\mathsf{U}}} \newcommand{\udpsp}{\vmath{UDP}} \newcommand{\udpleq}{\posleq_\udpsp} \newcommand{\dpsp}{\vmath{DP}} \newcommand{\dpleq}{\posleq_\dpsp} \newcommand{\terms}{\vmath{Terms}} \newcommand{\udpsem}{\Phi} \newcommand{\dpsem}{\varphi} \newcommand{\atoms}{\mathcal{A}} \newcommand{\atree}{\boldsymbol{\vmath{T}}} \newcommand{\val}{\boldsymbol{v}} \newcommand{\ops}{\vmath{ops}} \newcommand{\ftorL}{\ftor_L} \newcommand{\ftorU}{\ftor_U} \newcommand{\acprod}{\mathbin{\boldsymbol{\times}}} \newcommand{\oploop}{\dagger} \newcommand{\opseries}{\mathbin{\varocircle}} \newcommand{\oppar}{\mathbin{\varotimes}} \newcommand{\opcoprod}{\mathbin{\varovee}} \newcommand{\UId}{\vmath{UId}} \newcommand{\vdc}{\vmath{vdc}} \newcommand{\makedp}{\Gamma} \newcommand{\colU}{\color{purple}} \newcommand{\colL}{\color{orange}} \newcommand{\R}[1]{{\colR{#1}}} \newcommand{\F}[1]{{\colF{#1}}} \newcommand{\I}[1]{{\colI{#1}}} \newcommand{\cdpiN}{\mathcal{V}} \newcommand{\cdpin}{v} \newcommand{\cdpinA}{v_1} \newcommand{\cdpinB}{v_2} \newcommand{\cdpiresind}{i} \newcommand{\cdpifunind}{j} \newcommand{\cdpiresindA}{i_1} \newcommand{\cdpifunindB}{j_2} \newcommand{\dpinumf}{\vmath{nf}} \newcommand{\dpinumr}{\vmath{nr}} \newcommand{\cdpinnumf}{\dpinumf_\cdpin} \newcommand{\cdpinnumr}{\dpinumr_\cdpin} \newcommand{\cdpiE}{\mathcal{E}} \newcommand{\subto}{\text{s.t.}} \newcommand{\with}{\text{using}} \newcommand{\pset}{\mathscr{P}} \DeclareMathOperator*{\Min}{Min} \DeclareMathOperator*{\Inf}{Inf} \DeclareMathOperator*{\Sup}{Sup} \DeclareMathOperator*{\Max}{Max} \newcommand{\lowerbounds}{\vmath{lowerbounds}} \newcommand{\upperbounds}{\vmath{upperbounds}} \newcommand{\posMin}{\Min} \newcommand{\posleq}{\preceq} \newcommand{\poslt}{\prec} \newcommand{\posgeq}{\succeq} \newcommand{\posA}{\mathcal{P}} \newcommand{\posAleq}{\mathrel{{\posleq_\posA}}} \newcommand{\posAMin}{\mathop{{\posMin_{\posAleq}}}} \newcommand{\posAmin}{\mathop{{\min_{\posAleq}}}} \newcommand{\posAmax}{\mathop{{\max_{\posAleq}}}} \newcommand{\posB}{\mathcal{Q}} \newcommand{\posBleq}{\mathrel{{\posleq_\posB}}} \newcommand{\posC}{\mathcal{R}} \newcommand{\lfp}{\vmath{lfp}} \newcommand{\prefixed}{\vmath{prefixed}} \newcommand{\CPOs}{\textsc{CPO}s\xspace} \newcommand{\CPO}{\textsc{CPO}\xspace} \newcommand{\DCPOs}{\textsc{DCPO}s\xspace} \newcommand{\DCPO}{\textsc{DCPO}\xspace} \newcommand{\antichains}{\vmath{A}} \newcommand{\upsets}{\vmath{U}} \newcommand{\downsets}{\vmath{D}} \newcommand{\upresleq}{\posleq_{\upressp}} \newcommand{\upressp}{\upsets\ressp} \newcommand{\allupsets}{\vmath{Up}} \newcommand{\upit}{{\uparrow\,}} \newcommand{\stupit}{\dot{\upit}} \newcommand{\posetwidth}{\vmath{width}} \newcommand{\posetheight}{\vmath{height}} \newcommand{\posdef}[1]{\mathcal{P}_{#1}} \newcommand{\MR}{\M{R}} \newcommand{\myacronym}[1]{\textsc{#1}\xspace} \newcommand{\T}[1]{\boldsymbol{{\mathsf{#1}}}} \newcommand{\Tel}[1]{{\mathsf{#1}}} \newcommand{\Te}[1]{\Tel{#1}} \newcommand{\M}[1]{\mathbf{#1}} \newcommand{\Mel}[1]{\mathrm{#1}} \newcommand{\aset}[1]{\mathscr{#1}} \newcommand{\agroup}[1]{\mathrm{#1}} \newcommand{\aseq}[1]{\boldsymbol{#1}} \newcommand{\aseqe}[1]{#1} \newcommand{\dummyIndices}{} \newcommand{\aword}[1]{\mathsf{#1}} \newcommand{\vmath}[1]{\aword{#1}} \newcommand{\codefunc}[1]{\texttt{#1}\xspace} \newcommand{\swpackage}[1]{\textsc{#1}\xspace} \newcommand{\MA}{\M{A}} \newcommand{\MB}{\M{B}} \newcommand{\MC}{\M{C}} \newcommand{\MG}{\M{G}} \newcommand{\MH}{\M{H}} \newcommand{\ML}{\M{L}} \newcommand{\MQ}{\M{Q}} \newcommand{\MP}{\M{P}} \newcommand{\MS}{\M{S}} \newcommand{\MSigma}{\M{\Sigma}} \newcommand{\MV}{\M{V}} \newcommand{\MW}{\M{W}} \newcommand{\SP}{P_{\text{s}}} \newcommand{\AP}{P_{\text{a}}} \newcommand{\SE}{E} \newcommand{\ER}{r} \newcommand{\HP}{\Theta} \newcommand{\np}{n} \newcommand{\ones}{\boldsymbol{1}} \newcommand{\idMat}{\M{I}} \newcommand{\matTrace}{\vmath{Tr}} \newcommand{\angleFun}{\angle} \newcommand{\flatten}{\mathsf{vec}} \newcommand{\batterymass}{{\colR{m}}} \newcommand{\batterycapacity}{{\colF{C}}} \newcommand{\batterycost}{{\colR{c}}} \newcommand{\specificenergy}{{\colR{\rho}}} \newcommand{\specificcost}{{\colR{\alpha}}} \newcommand{\D}{\,\textrm{d}} \newcommand{\ex}{\mathbb{E}} \newcommand{\mysymbol}{\text{This is defined in a.symbols.tex}} \newcommand{\mysymbol}{\text{This is defined in a.symbols.tex}} \newcommand{\aset}[1]{\mathcal{#1}} \newcommand{\amat}[1]{\mathbf{#1}} \newcommand{\avec}[1]{\mathbf{#1}} \newcommand{\rv}[1]{\boldsymbol{#1}} \newcommand{\definedas}{\triangleq} \newcommand{\nats}{\mathbb{N}} \newcommand{\ints}{\mathbb{Z}} \newcommand{\rats}{\mathbb{Q}} \newcommand{\reals}{\mathbb{R}} \newcommand{\comp}{\mathbb{C}} \newcommand{\Time}{\mathbb{T}} \newcommand{\SEthree}{\text{SE}(3)} \newcommand{\SEtwo}{\text{SE}(2)} \newcommand{\sethree}{\text{se}(3)} \newcommand{\setwo}{\text{se}(2)} \newcommand{\SOthree}{\text{SO}(3)} \newcommand{\pose}{\boldsymbol{q}} \newcommand{\state}{\boldsymbol{x}} \newcommand{\statesp}{\mathcal{X}} \newcommand{\bmu}{\boldsymbol{\mu}} \newcommand{\bSigma}{\boldsymbol{\Sigma}} \newcommand{\tup}[1]{\langle#1\rangle}$$