Controller.php

<?php
namespace app\components;

use yii\web\View;

/**
 * Class Controller
 * @package app\components
 * @author chabib nurozak <chabibdev@gmail.com>
 * @version 1
 */
class Controller extends \yii\web\Controller
{
    /**
     * @param string $view
     * @param array $params
     * @return string
     */
    public function render($view, $params = [])
    {
        $content = $this->getView()->render($view, $params, $this);
        $content = $this->getScript($content);
        $content = $this->getStyle($content);
        return $this->renderContent($content);
    }

    /**
     * @param string $content
     * @return mixed
     */
    protected function getScript($content){
        $scripts = $this->getStringByTag('script', $content);
        $view = $this->getView();
        foreach ($scripts as $script){
            if(!empty($script)) {
                $view->registerJs($script, View::POS_END);
            }
        }
        return $this->removeStringByTag('script', $content);
    }

    /**
     * @param string $content
     * @return mixed
     */
    protected function getStyle($content){
        $styles = $this->getStringByTag('style', $content);
        $view = $this->getView();
        foreach ($styles as $style){
            if(!empty($style)) {
                $view->registerCss($style);
            }
        }
        return $this->removeStringByTag('style', $content);
    }

    /**
     * @param string $tagName
     * @param string $string
     * @return mixed
     */
    protected function getStringByTag($tagName, $string){
        preg_match_all("/<{$tagName}>(.*?)<\/$tagName>/s", $string, $matches);
        return $matches[1];
    }

    /**
     * @param string $tagName
     * @param string $string
     * @return mixed
     */
    protected function removeStringByTag($tagName, $string){
        return preg_replace("/<{$tagName}>(.*?)<\/$tagName>/s",'', $string);
    }
}

file_view.php

controller dengan extends yii\web\Controller
======================================
<?php
$js = <<<JS
new Vue({
    data:{},
    methods: {}
})
JS;

$this->registerJs($js, \yii\web\View::POS_END);
?>

controller dengan extends app\components\Controller
======================================
<script>
    new Vue({
        data: {},
        methods:{},
        mounted:{}
    })
</script>