Block diagram using Tikz picture

Question

I am trying to generate the following figure using Tikz.

However, I am not able to replicate the arrows.

PS: So far, I have done the following:

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{shapes,arrows}
\usepackage{amsmath}
\tikzstyle{sensor}=[draw, fill=blue!20, text width=5em, 
    text centered, minimum height=2.5em]
\tikzstyle{plant} = [sensor, text width=2em, fill=blue!20, 
    minimum height=5em, rounded corners]   
\tikzstyle{agent} = [sensor, text width=2em, fill=red!10, 
    minimum height=5em, rounded corners]
\tikzstyle{intercon} = [sensor, text width=2em, fill=green!20, 
    minimum height=20em, rounded corners]

\def\PtoI{3}
\def\AtoP{2}
\begin{tikzpicture}
    \node (interconn) [intercon] {\rotatebox{270}{$\mu = M Y^d$}};
    \path (interconn.80)+(-\PtoI,0) node (plant1) [plant] {$\Sigma^1$};
    \path (interconn.-80)+(-\PtoI,0) node (plantn) [plant] {$\Sigma^N$};
    \path (plant1.0)+(-\AtoP,0) node (agent1) [agent] {\rotatebox{270}{Agent 1}};
    \path (plantn.0)+(-\AtoP,0) node (agentn) [agent] {\rotatebox{270}{Agent N}};
    \path [draw, <-] (interconn.85) -- node [above] {$\nu$} (plant1.50);
\end{tikzpicture}
\end{document}

which produces the following picture:

Answer 1

You can use rotate from TikZ. This rotates also the anchors but is IMHO still more intuitive than the \rotatebox. Then you can add the arrows by using -| syntax to take the y coordinate of one node and the x coordinate of the other, and likewise |-, see here for an explanation. Finally you can avoid repetition with \foreach.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\definecolor{fgreen}{RGB}{204,223,181}
\definecolor{dblue}{RGB}{85,113,192}
\definecolor{dgreen}{RGB}{132,171,80}   
\begin{document}
\begin{tikzpicture}[>=stealth,
sensor/.style={draw, fill=dblue, text width=5em, 
    text centered, minimum height=2.5em},
plant/.style={sensor, text width=2em, fill=dblue, 
    minimum height=5em, rounded corners},   
agent/.style={sensor, minimum width=5em, fill=dgreen, 
    minimum height=2em, rounded corners},
intercon/.style={sensor, minimum width=20em, fill=fgreen, 
    minimum height=2em, rounded corners},
    Dotted/.style={% https://tex.stackexchange.com/a/52856/194703
    line width=1.2pt,
    dash pattern=on 0.01\pgflinewidth off #1\pgflinewidth,line cap=round,
    shorten >=0.5em,shorten <=0.5em},
    Dotted/.default=6,
    ]
    \def\PtoI{2}
    \def\AtoP{2}
    \node (interconn) [intercon,rotate=-90] {$\mu = M Y^d$};
    \path ([yshift=-3em]interconn.south west)+(-\PtoI,0) node (plant1) [plant] {$\Sigma^1$};
    \path ([yshift=3em]interconn.south east)+(-\PtoI,0) node (plantN) [plant] {$\Sigma^N$};
    \path (plant1.0)+(-\AtoP,0) node (agent1) [agent,rotate=-90]
        {Agent\textsuperscript{1}};
    \path (plantN.0)+(-\AtoP,0) node (agentN) [agent,rotate=-90]
        {Agent\textsuperscript{$N$}};
    \begin{scope}[semithick]
    \foreach \X/\Y/\Z in {1/u/u,N/\nu/a}
     {\draw[->] ([yshift=1em]plant\X.east) -- node[above]{$\bar y^{\X}$}
     ([yshift=1em]plant\X.east-|interconn.south);
     \draw[<-] ([yshift=-1em]plant\X.east) --
      node[below]{$\Y^{\X}$}
     ([yshift=-1em]plant\X.east-|interconn.south);
     \draw[->] (agent\X.west) -- ++ (0,1em) -| 
        node[pos=0.25,above](\Z-\X){$\Z^{\X}$}(plant\X);
     \draw[<-] (agent\X.east) -- ++ (0,-1em) -|  
        node[pos=0.25,below](y-\X){$y^{\X}$}(plant\X);
     }
    \draw[Dotted] (y-1) -- (a-N); 
    \end{scope}
\end{tikzpicture}

EDIT: Added dotted line (with proper attribution, of course).

Answer 2

With use of relative coordinates and recent syntax for defining nodes styles:

\documentclass[tikz, margin=3mm]{standalone}
\usetikzlibrary{arrows.meta,
                fit,
                positioning}

\begin{document}
\tikzset{
    sensor/.style = {draw, rounded corners, fill=#1, 
                     text width=2em, minimum height=22mm, align=center}, 
     plant/.style = {sensor=blue!20},
     agent/.style = {sensor=red!10},
  intercon/.style = {sensor=green!20, inner ysep=0pt, fit=#1},
                > = {Triangle[angle=60:3pt 2]}
        }

\begin{tikzpicture}[
node distance = 32mm and 8mm
                    ]
\node (agent1) [agent] {\rotatebox{90}{Agent$^1$}};
\node (plant1) [plant,right=of agent1] {$\Sigma^1$};
    \draw[->]   (agent1.north) -- ++ (0, 4mm) -| (plant1) 
                node (u1) [pos=0.25,above] {$\nu^1$};
    \draw[->]   (plant1.south) -- ++ (0,-4mm) -| (agent1)
                node (y1) [pos=0.25,below] {$y^1$};
\node (agentN) [agent,below=of agent1] {\rotatebox{90}{Agent$^N$}};
\node (plantN) [plant,right=of agentN] {$\Sigma^N$};
    \draw[->]   (agentN.north) -- ++ (0, 4mm) -| (plantN)
                node (uN) [pos=0.25,above] {$\nu^N$};
    \draw[->]   (plantN.south) -- ++ (0,-4mm) -| (agentN)
                node (yN) [pos=0.25,below] {$y^N$};
\draw[thick,dotted, shorten >=3mm, shorten <=3mm]
    (y1) -- (uN);
%
\coordinate[right=of u1 -| plant1.east] (aux1);
\coordinate[right=of yN -| aux1]        (aux2);
\node (interconn) [intercon=(aux1) (aux2), right,
                   label={[rotate=90]center:$\mu = M Y^d$}] {};
\scoped[transform canvas={yshift=+3mm}]  {
     \draw[->] (plant1) -- node[above] {$\bar{y}^1$} (plant1 -| interconn.west);
     \draw[->] (plantN) -- node[above] {$\bar{y}^N$} (plantN -| interconn.west);
                                        }
\scoped[transform canvas={yshift=-3mm}]  {
     \draw[<-] (plant1) -- node[below] {$\bar{\nu}^1$} (plant1 -| interconn.west);
     \draw[<-] (plantN) -- node[below] {$\bar{\nu}^N$} (plantN -| interconn.west);
                                        }
    \end{tikzpicture}
\end{document}

Note: The use of transform canvas you need to take a should be used with great care. See warnings in TikZ & PGF manual, section 25.4 Canvas Transformations, pp 387 (at version 3.1.5b). Its use in the your case you are on the safe side.