AWS CDK を用いて Systems Manager Automation をターゲットとした EventBridge ルールを作成する方法を教えてください

from aws_cdk import (
    Duration,
    Stack,
    aws_events as events,
    aws_events_targets as events_targets,
    aws_iam as iam,
)
from constructs import Construct

class HelloCdkStack(Stack):

    def __init__(self, scope: Construct, construct_id: str, **kwargs) -> None:
        super().__init__(scope, construct_id, **kwargs)

        # EventBridge ルールで利用する IAM ポリシー
        policy_statement = iam.PolicyStatement(
            actions=[
            'ssm:StartAutomationExecution',
            'tag:*',
            'ec2:*',
            ],
            effect=iam.Effect.ALLOW,
            resources=["*"]
        )

        # EventBridge ルール
        rule = events.Rule(self, "rule",
            enabled=True,
            schedule=events.Schedule.rate(Duration.minutes(1)),
            event_pattern=events.EventPattern(
                source=["aws.ec2"]
            )
        )

        # EventBridge ルールのターゲット
        targets = events_targets.AwsApi(
            action="StartAutomationExecution",
            service="ssm",
            parameters={
                "DocumentName": 'AWS-StopEC2Instance',
                "Parameters": {
                    "InstanceId": ['i-xxxxx'],
                },
            },
            policy_statement=policy_statement
        )

        rule.add_target(targets)