user_manual.tex

由matlab开发的hybrid系统的描述语言

each \textsl{da-item} is one of the following: %
\bs \textsl{var} \verb@=@ \verb@{@ \verb@IF@ \textsl{Boolean-expr}
\verb@THEN@ \textsl{affine-expr} \verb@[@\textsl{min}\verb@,@
\textsl{max}\verb@,@ \textsl{epsilon}\verb@]@\opt\verb@};@
\\\textsl{var} \verb@=@ \verb@{@ \verb@IF@ \textsl{Boolean-expr}
\verb@THEN@ \textsl{affine-expr} \verb@[@\textsl{min}\verb@,@
\textsl{max}\verb@,@ \textsl{epsilon}\verb@]@\opt \\
    \verb@ELSE@ \textsl{affine-expr}
\verb@[@\textsl{min}\verb@,@ \textsl{max}\verb@,@
\textsl{epsilon}\verb@]@\opt\verb@};@ \es %
here, the variable \textsl{epsilon} is a placeholder and is
introduced for symmetry with the AD section\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.}. If the
\verb@ELSE@ part is omitted, is is assumed to be 0.

\begin{example} The command signal $u$ to an electric motor
is passed through a nonlinear amplifier, which has two modes of
operation: high gain and low gain. In ``low gain'' the amplifier
completely rejects the noise $d$, while in ``high gain'' it only
attenuates it. The Boolean input $l=1$ selects the low gain mode.
The actual signal $u_{\rm comp}$ applied to the motor is $ u_{\rm
comp} = u$ if $l=1$, otherwise $u_{\rm comp} = 2.3u + 0.4d$.
\vinput{l0002.hys}
\end{example}

\subsubsection{\hs{CONTINUOUS} Section}
The \hs{CONTINUOUS} section
describes the linear dynamics, expressed as difference equations.
This section models the remaining
Equation~(\ref{eq::z-transform-c}) of the SAS.

\noindent The general syntax is: %
\bs \verb@CONTINUOUS@\verb@{@\textsl{cont-item}\more\verb@}@\es %
and each \textsl{cont-item} has the form: %
\bs \textsl{var} \verb@=@ \textsl{affine-expr} \verb@;@ \es %

% Note that in some former version of \hysdel{}, \textsl{cont-item} had
% the form:
% \bs \textsl{var} \verb@=@ \textsl{linear-expr} \verb@;@ \es %
% see {\bf metti a posto qui}

\subsubsection{\hs{LINEAR} Section} \hysdel{} allows also to define a
continuous variable as an affine function of continuous variables
in the \hs{LINEAR} section.

\noindent The general syntax is: %
\bs \verb@LINEAR@\verb@{@\textsl{lin-item}\more\verb@}@\es %
and each \textsl{lin-item} has the form: %
\bs \textsl{var} \verb@=@ \textsl{affine-expr} \verb@;@ \es %

This section, together with the \hs{CONTINUOUS} and \hs{AD}
sections allows more flexibility when modeling the SAS. This extra
flexibility allows algebraic loops that may render undefined
trajectories of the model. The \hysdel{} compiler integrates a
semantic checker that is able to detect and report such abnormal
situations.

\subsubsection{\hs{AUTOMATA} Section} The \hs{AUTOMATA} section
specifies the state transition equations of the finite state
machine (FSM) as Boolean functions $x_b'(k) = f_{\rm
B}(x_b(k),u_b(k),\delta_e(k))$.

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

\begin{example} An outflow unit of a hydroelectric power plant is
described by the automaton of Figure~\ref{fig:auto}.
\begin{figure}
\begin{center}
\includegraphics[width=8cm]{fsm.eps}
\caption{Finite state machine of an outflow unit} \label{fig:auto}
\end{center}
\end{figure}
{\vinput{l0006.hys}}    % add in the header: \usepackage{verbatim}
\end{example}

\subsubsection{\hs{MUST} Section} \label{sec.must}
The \hs{MUST} section specifies constraints on continuous and
Boolean variables, i.e., linear constraints and Boolean formulas,
and therefore it allows defining the sets $\XX_r$, $\XX_b$,
$\UU_r$, $\UU_b$, $\YY_r$, $\YY_b$ (more generally, the \hs{MUST}
section allows also mixed constraints on states, inputs, and
outputs).

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

\begin{example} The level $h$ in a water tank must be nonnegative
and below the maximum height $h_{max}$ of the tank, $0 \leq h \leq
h_{max}$. {\vinput{l0007.hys}}
\end{example}

\subsubsection{Symbolic manipulation, and Cast operator}
\hysdel{} implements a simple symbolic computation tool. The
simple symbolic manipulator handles efficiently linear and affine
expression but cannot detect that an expression is linear if it
involves cancellation on nonlinear terms.
\begin{example}
\hysdel{} will report an error with the following source:
{\vinput{l0009.hys}}
\end{example}

A Boolean expression \textsl{Boolean-expr} has a conventional
value of 1 if true and 0 otherwise, the value of a Boolean
expression can be used in affine expressions by using the cast
operator: \verb@(REAL @ \textsl{Boolean-expr} \verb@)@.
\begin{example}
The flow through a pipe is 10 l/s if both valve v1 and valve v2
are opened, 0 otherwise {\vinput{l0008.hys}}
\end{example}

\subsection{\hysdel{} Compiler}
Once the \hysdel{} model of a system is available, the companion
\hysdel{} compiler is able to generate the equivalent MLD model.

\subsubsection{Mixed Logical Dynamical (MLD) Systems} \index{Mixed
Logical Dynamical Systems} In~\cite{BM99}, the authors proposed
discrete-time hybrid systems denoted as mixed logical dynamical
(MLD) systems. An MLD system is described by the following
relations: \MLDsystem{MLDS}{,} where $x_r \in \rr^{n_{xr}}$, $x_b
\in \{0,1\}^{n_{xb}}$, $u_r \in \rr^{n_{ur}}$, $u_b \in
\{0,1\}^{n_{ub}}$, $y_r \in \rr^{n_{yr}}$, $y_b \in
\{0,1\}^{n_{yb}}$, $z \in \rr^{n_{z}}$, and $\delta \in
\{0,1\}^{n_{\delta}}$. All the $E_i$ matrices have $n_e$ rows.

A more general form of the MLD systems is: \BDMLDsystem{XMLDS}{,}
where $x_{\;\!\centerdot}$, $u_{\;\!\centerdot}$,
$y_{\;\!\centerdot}$, $z$, and $\delta$ are as before, we denote
this variant as extended MLD form.  Note that the matrices
$B_{5c}$, $B_{5d}$, $D_{5c}$, and $D_{5d}$ do not introduce any
further expressivity in the MLD model but are useful to keep the
size of the models contained.

\index{parameters!Matlab declaration} The parameters declared in
the system form the coefficients of the $E$ matrices. If the
system has symbolic parameters, then \hysdel{} generates a
symbolic output and assumes a structure called \mcmd{params} width
a field with the same name as each symbolic parameter.

\begin{example}
The interface declaration:
\begin{verbatim}
INTERFACE {
    PARAMETER {
        REAL p1,p2;
    }
}
\end{verbatim}
assumes that the fields \mcmd{params.p1} and \mcmd{params.p2} are
defined in the structure \mcmd{params}.
\end{example}

Given the current state $x(k)$ and input $u(k)$, the
time-evolution of~(\ref{XMLDS}) could be determined by solving
$\delta(k)$ and $z(k)$ from~(\ref{XMLDS.c}), and then updating
$x'(k)$ and $y(k)$ from~(\ref{XMLDS.a})--(\ref{XMLDS.b}).

\index{Simulator} \hysdel{} can also produce a function to
simulate the hybrid system, this function directly uses the
definitions in the \hysdel{} source and does not rely on any mixed
integer solver.
\begin{verbatim}
function [xn, d, z, y] = sys_name (x, u, params)
\end{verbatim}
\code{x} is the current state, \code{u} the input, and
\code{params} the structure specifying the values for every
symbolic parameter and can be omitted if there is no symbolic
parameter. The function computes one time step and returns the new
state as \code{xn} and the output as \code{y}. It also provides
the auxiliary variables \code{d} and \code{z}. \code{xn},
\code{d}, \code{z}, \code{y}, \code{x} and \code{u} are vectors.
The order of the variables corresponds to the order in which the
real variables are stored before the Boolean ones, otherwise the
order corresponds to the order in which they are declared in the
\hysdel{}.

\subsubsection{Command Line}\index{Command Line Options}
\hysdel{} accepts the following command line options:
\begin{description}
\item[\texttt{-h},\texttt{--help}]Print help and exit.
\item[\texttt{-V},\texttt{--version}]Print version and exit.
\item[\texttt{-iSTRING},\texttt{--input=STRING}]\hysdel{} input
file
name (default=stdin). %
\item[\texttt{-mSTRING},\texttt{--MLDoutput=STRING}]   MLD output
file name (without extension) (default=stdout). %
\item[\texttt{-sSTRING},\texttt{--SIMoutput=STRING}] Simulator
file name (without extension). %
\item[\texttt{-p}, \texttt{--parametric}] Force all parameters to
be handled as symbolic parameters. %
\item[\texttt{-a}, \texttt{--allow-affine}] Allow affine state and
output functions. Former version of \hysdel{} did not allows
constant terms $a_0$ in the affine state and output functions.
This limitation comes directly from equation~(\ref{MLDS.a}) and
~(\ref{MLDS.b}). The option \texttt{-a} overrides that limitation
by adding an auxiliary variable $z = a_0$. The output generated is
backwards compatible
but somehow redundant. See also the next \texttt{-5} option.%
\item[\texttt{-5}, \texttt{--allow-B5-D5}] Use Extended MLD form
(\ref{XMLDS}) (implies -a). Note that the Extended MLD form may
produce
wrong results with old algorithms.%
\item[\texttt{--no-symbol-table}] Omit the symbol table
information. %
\item[\texttt{--no-row-info}] Omit row information.
\item[\texttt{--no-params-checks}] Omit checks for symbolic
parameters. %
\item[\texttt{--matlab-symbolic}] Support for \matlab{} symbolic
toolbox for parameters. %
\item[\texttt{-vINT}, \texttt{--verbose=INT}] Verbosity level
(0=silent, 3=max) (default=2).
\end{description}

\input{MLD_structure.tex}