I have a lambda function that was deployed using cdk, it contains several rules that runs on a schedule determined by cron expression. For example, one of them need to run according to cron(0 16 ? * MON-SAT *) during fall and according to cron(0 15 ? * MON-SAT *) during spring time. Currently we need to update the cron expression manually twice a year and we are looking for a way to automate it. How can we do it (using cdk)?

new cdk.aws_events.Rule(this, `example${name}EventRule${appEnv}`, {
    enabled: event.enabled ??  true,
    description: `example-${name}-Schedule-${appEnv}`,
    ruleName: `example-${name}-Schedule-${appEnv}`,
    targets: [
      new cdk.aws_events_targets.LambdaFunction(exampleLambda, {
        event: RuleTargetInput.fromObject({
          Endpoint,
          suiteName,
          sendMail,
          deliveryCondition,
          pagerDuty,
          emailList
        })
      })
    ],
    schedule: aws_events.Schedule.expression(schedule)
  });
});

Tried to update the cron expression, but it didn’t work.
Is there another way for doing that?