mld_structure.tex

由matlab开发的hybrid系统的描述语言

\hysdel{} stores the output in a file which describes a
MLD-structure according to \matlab{} syntax. If the system
contains symbolic parameters then the generated file assumes that
the structure \mcmd{params} is defined in the workspace.

In the next section we will present the complete format of the
MLD-structure.

\section{MLD structure}
\index{MLD!structure} The structure \mcmd{S} contains the
following fields:
\begin{itemize}
\item \mcmd{Arr} = $A_{rr}$, \mcmd{Arb} = $A_{rb}$, \mcmd{Abr}
 = $A_{br}$, \mcmd{Abb} = $A_{bb}$, \mcmd{A = [Arr, Arb; Abr, Abb]}.
\item \mcmd{B1rr} = $B_{1rr}$, \mcmd{B1rb} = $B_{1rb}$, \mcmd{B1br} = $B_{1br}$,
\mcmd{B1bb} = $B_{1bb}$,  \mcmd{B1 = [B1rr, B1rb; B1br, B1bb]}.
\item \mcmd{B2rb} = $B_{2rb}$, \mcmd{B2bb} = $B_{2bb}$, \mcmd{B2 = [B2rb; B2bb]}.
\item \mcmd{B3rr} = $B_{3rr}$, \mcmd{B3br} = $B_{3br}$, \mcmd{B3 = [B3rr; B3br]}.
\item \mcmd{B5r} = $B_{5r}$, \mcmd{B5b} = $B_{5b}$, \mcmd{B5 = [B5r; B5b]}.

\item \mcmd{Crr} = $C_{rr}$, \mcmd{Crb} = $C_{rb}$, \mcmd{Cbr}
 = $C_{br}$, \mcmd{Cbb} = $C_{bb}$, \mcmd{C = [Crr, Crb; Cbr, Cbb]}.
\item \mcmd{D1rr} = $D_{1rr}$, \mcmd{D1rb} = $D_{1rb}$, \mcmd{D1br} = $D_{1br}$,
\mcmd{D1bb} = $D_{1bb}$,  \mcmd{D1 = [D1rr, D1rb; D1br, D1bb]}.
\item \mcmd{D2rb} = $D_{2rb}$, \mcmd{D2bb} = $D_{2bb}$, \mcmd{D2 = [D2rb; D2bb]}.
\item \mcmd{D3rr} = $D_{3rr}$, \mcmd{D3br} = $D_{3br}$, \mcmd{D3 = [D3rr; D3br]}.
\item \mcmd{D5r} = $D_{5r}$, \mcmd{D5b} = $D_{5b}$, \mcmd{D5 = [D5r; D5b]}.

\item \mcmd{E1} = $E_{1}$, \mcmd{E2} = $E_{2}$, \mcmd{E3} = $E_{3}$,
\mcmd{E4} = $E_{4}$, \mcmd{E5} = $E_{5}$.
\item \mcmd{nxr} = $n_{xr}$,  \mcmd{nxb} = $n_{xb}$, \mcmd{nx =
nxr + nxb}, \mcmd{nur} = $n_{ur}$,  \mcmd{nub} = $n_{ub}$,
\mcmd{nu = nur + nub}, \mcmd{nyr} = $n_{yr}$,  \mcmd{nyb} =
$n_{yb}$, \mcmd{ny = nyr + nyb}, \mcmd{nd} = $n_{\delta}$,
\mcmd{nz} = $n_{z}$, \mcmd{ne} = $n_{e}$.
\item \mcmd{ul, uu} lower and upper bound on $u$, same for \mcmd{xl,
xu}, \mcmd{yl, yu}, \mcmd{dl, du}, and \mcmd{zl, zu}.
\item \mcmd{MLDisvalid} 1 if the model has passed a validity
check (sizes of the matrices, null entries,\ldots). User functions
can trust this information.
\item \mcmd{name} string containing the system name as specified
in the \hysdel{} declaration.
\item \mcmd{MLDstructver} integer containing the protocol version, needed for
future extentions. All the protocol versions should be backwards
compatible. User's function should check if the protocol version
is new enough. The protocol version presented in this document is
2. \hysdel{} version 1.3.0 and higher support protocol version 2.
\item \mcmd{MLDsymtable} 1 if the structure includes symbol table
informations.
\item \mcmd{MLDrowinfo} 1 if the structure includes debugging information for the generated constraints.
\item \mcmd{symtable} Cell array containing the symbols.
\begin{itemize}
    \item \mcmd{name} string containing the name of the symbol
    \item \mcmd{kind} \{'x'$\mid$'u'$\mid$'y'$\mid$'z'$\mid$'d'$\mid$'p'\} name of
    the array containing the variable, note that they are lower
    case. The letter 'p' stands for parameter, it is just a place
    holder as there is no parameter vector.
    \item \mcmd{type} \{'r'$\mid$'b'\}  type of
    the variable, note that they are lower
    case.
    \item \mcmd{index} position of the variable in the
    array $\mbox{\mcmd{kind}}_{\mbox{\mcmd{type}}}$. In case
    of parameters (kind = 'p') the content of this variable is
    of no relevance.
    \item \mcmd{line\_of\_declaration} line where the variable was
    declared in the \hysdel{} code. This index is -1 for the
    predefined parameters.
    \item \mcmd{line\_of\_first\_use} line where the variable was
    used for the first time in the \hysdel{} code.
    \item \mcmd{defined} group of constraints containing the
    definition of the variable (see the following \mcmd{rowinfo} entry).
    \item \mcmd{computable\_order} priority for computation. This
    information can be used as branching priority if the mixed
    integer solver supports this option.
    \item \mcmd{min} minimum of the variable.
    \item \mcmd{min\_computed} 1 if \hysdel{} computed the minimum.
    \item \mcmd{max} maximum of the variable.
    \item \mcmd{max\_computed} 1 if \hysdel{} computed the maximum.
    \item \mcmd{value} numerical value of the parameter (this field is present only if kind = 'p').
\end{itemize}
\item \mcmd{rowinfo} Structure containing the information on the matrices.
\begin{itemize}
\item \mcmd{state\_upd} Cell array containing the information on
the rows in the state update matrices~(\ref{XMLDS.a}). The cell
array has the same number of items as the number of rows of the
matrices, the $i$-th element of the array provides information on
the $i$-th constraint.
\begin{itemize}
\item \mcmd{section} Name of the section where the state update
was declared.
\item \mcmd{item\_type} Actual section the item belong to.
\item \mcmd{defines} Name of the variable that is defined.
\item \mcmd{depends} Cell array of variable names the definition.
depends on.
\item \mcmd{group}, \mcmd{subgroup}, \mcmd{subindex} unique
identification of the source declaration. Each statement in
\hysdel{} gets a sequential number, this statement is stored in
\mcmd{group}. A statement may correspond to more than one basic
element of \hysdel{} (i.e. in case of automatic introduction of
variables), each such a constituting element gets an sequential
number, stored in \mcmd{subgroup}. Each element may correspond to
more than one inequality or equality constraint, each constraint
gets a sequential number. Summing up, all the constraints coming
from a \hysdel{} statement share the same \mcmd{group} index, all
the constraints coming from a basic element share the same
\mcmd{subgroup} index and within the same
\mcmd{group},\mcmd{subgroup} each constraint gets a sequential
\mcmd{subindex}.
\item \mcmd{source} Code snippet of the original \hysdel{}
declaration.
\item \mcmd{sourceline} Line in the source code.
\item \mcmd{human} Human readable expression.
\end{itemize}
\item \mcmd{output} Cell array containing the information on the
rows in the output matrices~(\ref{XMLDS.b}). As before the $i$-th
element of the array provides information on the $i$-th constraint
and each item has the same fields as in the previous point. \item
\mcmd{ineq} Cell array containing the information on the rows of
the inequality constraints~(\ref{XMLDS.c}). As before the $i$-th
element of the array provides information on the $i$-th
constraint. The item has the same fields as described in the
previous point plus the following fields:
\begin{itemize}
\item \mcmd{aff\_min} value of $m$ used for the
transformations~(\ref{eq:if-ineq}) and~(\ref{eq:threshold-ineq}).
\item \mcmd{aff\_min\_computed} 1 if $m$ was computed, 0 if
provided. \item \mcmd{aff\_max} value of $M$ used for the
transformations~(\ref{eq:if-ineq}) and~(\ref{eq:threshold-ineq}).
\item \mcmd{aff\_max\_computed} 1 if $M$ was computed, 0 if
provided. \item \mcmd{aff\_eps} value of the tolerance $\epsilon$
used for the transformations~(\ref{eq:threshold-ineq}). \item
\mcmd{aff\_eps\_computed} 1 if a default value for $\epsilon$ was
used, 0 if provided.
\end{itemize}
\end{itemize}
\end{itemize}