user_manual.tex

由matlab开发的hybrid系统的描述语言

\chapter{\hysdel{} Models}

We designed a modeling language to describe DHA\index{Discrete
Hybrid Automata} models, called HYbrid System DEscription Language
(\hysdel{}). In this section we will detail the language
capabilities and we will show how DHA systems can be modeled
within \hysdel{}. As we will explain better in the next section,
the \hysdel{} description is an abstract modeling step. The
associated \hysdel{} compiler then translates the description into
several computational models, in particular into MLD and PWA form.

\section{\hysdel{} List}
A \hysdel{} list is composed by two parts \hs{INTERFACE} and
\hs{IMPLEMENTATION}. The declaration of an empty system is as
follows: \index{SYSTEM}\\
\verb@SYSTEM @\textsl{name} \verb@{@ \\%
\verb@/* C-style comments */@\\%
\verb@    INTERFACE {@\\
\verb@    }@\\
\verb@    IMPLEMENTATION {@\\
\verb@    }@\\
\verb@}@\\
\hysdel{} has a syntax based on C-language, it allows C-style
comments (\verb@/* ... */@) and uses the curly braces
(``\verb@{@'' and ``\verb@}@'') delimiters. All the sections start
with the section name in capital letters followed by the content
of the section enclosed in curly braces. In the informal
description of the grammar that follows, we use \texttt{courier}
font to specify keywords and language constructs (or terminals
tokens), \textsl{slanted roman} font to denote user defined
content (or intermediate lexical tokens). We denote by the
subscript \opt{} optional parts and by \more{} a declaration that
can be repeated one or more times. We will omit the definitions of
some tokens, if intuitive. A formal description of the grammar is
reported in~\cite{HYSDELP02} and the file hys.y of the source
distribution contains the bison description of the grammar.

\subsection{\hs{INTERFACE} Section}
The \hs{INTERFACE} section contains the declarations, divided into
subsections called \hs{STATE}, \hs{INPUT}, \hs{OUTPUT} and
\hs{PARAMETER}, the order in which those sections are declared is
not relevant. The first three declarations are referred to as
variable declaration, while the last is a parameter declaration. A
real variable declaration has the general form: \verb@REAL@
\textsl{name} \verb@[@\textsl{min}\verb@,@
\textsl{max}\verb@]@\opt\verb@;@ where the optional declaration
\verb@[@\textsl{min}\verb@,@ \textsl{max}\verb@]@ contains the
bounds of the variable. The type specifier \verb@REAL@ can be
replaced with the keyword \verb@BOOL@ if the variable is Boolean,
in such a case the bound declaration is forbidden and defaults to
\verb@[0, 1]@. Two or more variable declarations can share the
type specifier by using a ``\verb@,@'' in the declaration:
\verb@BOOL@ \textsl{name1}\verb@,@ \textsl{name2}\more\verb@;@.

\begin{table}[t]
  \centering
  \begin{minipage}[b]{.45\textwidth}
  \begin{tabular}{ll}
    Operator & \hysdel{} representation \\
    \hline
    $\cdot$ & \verb@*@ \\
    $/$ & \verb@/@ \\
    $+$ & \verb@+@ \\
    $-$ & \verb@-@ \\
    $a^b$ & \verb@a ^ b@ \\
    $e^b = \exp(b)$ & \verb@exp(b)@ \\
    $\sqrt{a}$ & \verb@sqrt(a)@ \\
    $\log{a}$ & \verb@log(a)@ \\
    $\cos(a)$ & \verb@cos(a)@ \\
    $\sin(a)$ & \verb@sin(a)@ \\
  \end{tabular}
  \caption{List of operators supported on parameter declarations}\label{tab:p_op}
  \end{minipage}
  ~~
  \begin{minipage}[b]{.45\textwidth}
  \begin{tabular}{ll}
    Operator & \hysdel{} representation \\
    \hline
    $\ANd$ & \verb@&@ or \verb@&&@ \\
    $\OR$ & \verb@|@ or \verb@||@ \\
    $\Rightarrow$ & \verb@->@ \\
    $\Leftarrow$ & \verb@<-@ \\
    $\Leftrightarrow$ & \verb@<->@ \\
    $\NOT$ & \verb@~@ or \verb@!@\\
& \\
& \\
& \\ % to preserve alignement!!!
& \\
  \end{tabular}
  \vfill
  \caption{List of operators supported on Boolean expressions}\label{tab:l_op}
  \end{minipage}
\end{table}

\noindent There are three kinds of parameter declarations:
\begin{description}
\index{parameters} \item{Boolean
parameters:}\index{parameters!boolean} \verb@BOOL@ \verb@parname@
\verb@=@ \verb@value@ where \verb@value;@ can be either
\verb@TRUE@ or \verb@FALSE@; any further occurrence of the
parameter is then replaced with the corresponding value.
\item{Real numeric parameters:}\index{parameters!real!numeric}
\verb@REAL@ \verb@parname@ \verb@=@ \verb@number;@, any further
occurrence of the parameter is then replaced with the
corresponding value. \item{Real symbolic
parameters:}\index{parameters!real!symbolic} \verb@REAL@
\verb@parname;@, the parameter is handled symbolicaly.
\end{description} Any parameter can be defined in terms of other
parameters declared before using the operators and functions in
Table~\ref{tab:p_op}, and can be used thereinafter as it was a
number. \hysdel{} predefines two real parameters
\index{parameters!real!predefined} \verb@pi@ $= \pi$ and the
tolerance \verb@MLD_epsilon@ $= 10^{-6}$ used for the relations
(\ref{eq:ti3}). Both the parameters can be redefined to different
values.

Currently \hysdel{} supports only scalar data types, there is no
support for vectors and matrices.

Before describing in detail the \hs{IMPLEMENTATION} section, we
recall some definitions.

\subsubsection{\textsl{Boolean-expr}, \textsl{affine-expr}, \textsl{linear-expr}}
\index{Boolean-expr@\textsl{Boolean-expr}} A \textsl{Boolean-expr}
is the combination of Boolean variables and the operators reported
in Table~\ref{tab:l_op}.

\index{affine-expr@\textsl{affine-expr}}An \textsl{affine-expr} is
linear affine combination of real variables
\begin{equation}
a_0 + a_1x_1 + a_2x_2 + \ldots + a_n x_n{\rm ,} \label{eq:affexp}
\end{equation}
where $a_i$ is a function of parameters, and $x_i$ are real
(state, input, output, and auxiliary) variables. If $a_0 = 0$ then
(\ref{eq:affexp}) is a
\index{linear-expr@\textsl{linear-expr}}\textsl{linear-expr}.


\subsection{\hs{IMPLEMENTATION} Section}
The second part, \hs{IMPLEMENTATION}, is composed of specialized
sections describing the relations among the variables. The
\hs{IMPLEMENTATION} section starts with an optional \hs{AUX}
section which contains the declarations of the internal signals of
the DHA system, called also auxiliary variables. The declaration
follows the general syntax of the variable declaration.

\subsubsection{\hs{OUTPUT} Section} The \hs{OUTPUT} section allows
specifying static linear and logic relations for the output vector
$y=\smallmat{y_r\\y_b}$.

\noindent The general syntax is: %
\bs \verb@OUTPUT@\verb@{@\textsl{output-item}\more\verb@}@\es %
and each \textsl{output-item} is one of the following: %
\bs \textsl{var} \verb@=@ \textsl{affine-expr} \verb@;@ \\
    \textsl{var} \verb@=@ \textsl{Boolean-expr} \verb@;@ \es %

\subsubsection{\hs{AD} Section}
The \hysdel{} section \hs{AD} allows to define Boolean variables
from continuous ones, and is based exactly on the same semantics
of the event generator (EG) described earlier.

\noindent The general syntax is: %
\bs \verb@AD@\verb@{@\textsl{ad-item}\more\verb@}@\es %
and each \textsl{ad-item} is one of the following: %
\bs \textsl{var} \verb@=@ \textsl{affine-expr} \verb@<=@
\textsl{real-number} \verb@;@ \\
 \textsl{var} \verb@=@ \textsl{affine-expr} \verb@>=@
\textsl{real-number} \verb@;@ \es %
and the syntax (used by the former version of the \hysdel{}
compiler) %
\bs \textsl{var} \verb@=@ \textsl{affine-expr} \verb@<=@ \verb@0@
\verb@[@\textsl{min}\verb@,@ \textsl{max}\verb@,@
\textsl{epsilon}\verb@];@ \es %
is still accepted but not recommended because of the error prone
specification of the bounds \verb@[@\textsl{min}\verb@,@
\textsl{max}\verb@,@ \textsl{epsilon}\verb@]@ on
\textsl{affine-expr}\footnote{The old bounds declaration
\texttt{[}\textsl{max}\texttt{,} \textsl{min}\texttt{,}
\textsl{epsilon}\texttt{]} is still accepted but is deprecated and
will raise a warning.}. The variable \textsl{epsilon} is the
tolerance used for the translation in MLD form according to
(\ref{eq:ti3}), if omitted, the  value of \verb@MLD_epsilon@ is
used.

\hysdel{} does not provide explicit access to the time instance,
however this limitation can be easily overcome by adding a
continuous state variable $t$ such that $t' = t + T_s$, where
$T_s$ is the sampling time. Examples include level indicator
variables, operational alarms, etc.

\begin{example} In a water tank with inflow $Q$,
the sensor $\delta$ provides the signal 1 if and only if the
liquid level $h \ge 0.5 h_{\max}$.
{\vinput{l0001.hys}}\end{example}

\subsubsection{\hs{LOGIC} Section} The section \hs{LOGIC} allows to
specify arbitrary functions of Boolean variables: In particular
the mode selector is a Boolean function and therefore it can be
modeled in this section.

\noindent The general syntax is: %
\bs \verb@LOGIC@\verb@{@\textsl{logic-item}\more\verb@}@\es %
and each \textsl{logic-item} is as follows: %
\bs \textsl{var} \verb@=@ \textsl{Boolean-expr} \verb@;@ \es %

\begin{example} The passengers of a train can pull the handle of
the emergency stop, generating the binary signal $u_{\rm
alarm}=1$. Usually, this causes an emergency stop of the train, by
setting the emergency braking signal $u_{\rm brake}=1$. However,
the brake should not be activated if fire is detected while the
train is in a tunnel. We define the indicator variables for fire
as $s_{\rm fire}=1$ and tunnel transition as $s_{\rm tunnel}=1$.
Then we can describe this system as:
\begin{equation}
    u_{\rm brake} =  u_{\rm alarm} \wedge \left( \lnot s_{\rm tunnel}  \vee  \lnot {s}_{\rm fire}
    \right).
\end{equation}
 {\vinput{l0003.hys}}\end{example}

\subsubsection{\hs{DA} Section} The \hysdel{} section \hs{DA} defines
continuous variables according to if-then-else conditions on
Boolean variables. This section models part of the switched affine
system (SAS), namely the variables $z_i$ defined
in~(\ref{eq::z-transform-a})--(\ref{eq::z-transform-b}).

\noindent The general syntax is: %
\bs \verb@DA@\verb@{@\textsl{da-item}\more\verb@}@\es %