解决方案：

AWS API Gateway可以与现有设备集成，使其能够通过Websockets与应用程序进行实时通信。下面是一个包含代码示例的解决方法：

1. 创建一个AWS API Gateway Websockets API。

2. 创建一个API资源和一个与该资源关联的Websocket路由。

Resources:
  MyWebSocketAPI:
    Type: AWS::ApiGatewayV2::Api
    Properties:
      Name: MyWebSocketAPI
      ProtocolType: WEBSOCKET

  MyWebSocketRoute:
    Type: AWS::ApiGatewayV2::Route
    Properties:
      ApiId: !Ref MyWebSocketAPI
      RouteKey: $default
      AuthorizationType: NONE
      Target: integrations/${MyWebSocketIntegration}

3. 创建一个与Websockets API Gateway关联的Lambda函数，以处理来自设备的实时消息。

exports.handler = async (event) => {
  const connectionId = event.requestContext.connectionId;
  const body = JSON.parse(event.body);

  // 在这里处理设备消息
  // ...

  return {
    statusCode: 200
  };
};

4. 创建一个与Lambda函数关联的集成。

MyWebSocketIntegration:
  Type: AWS::ApiGatewayV2::Integration
  Properties:
    ApiId: !Ref MyWebSocketAPI
    IntegrationType: AWS_PROXY
    IntegrationUri: arn:aws:lambda:us-east-1:1234567890:function:MyWebSocketHandler
    PayloadFormatVersion: '1.0'

5. 使用AWS SDK或AWS CLI将设备连接到Websockets API Gateway。

const AWS = require('aws-sdk');
const apigatewaymanagementapi = new AWS.ApiGatewayManagementApi({
  apiVersion: '2018-11-29',
  endpoint: 'https://your-api-id.execute-api.your-region.amazonaws.com/your-stage'
});

// 设备连接到Websockets API Gateway
const connectionId = 'your-device-connection-id';
const endpoint = 'wss://your-api-id.execute-api.your-region.amazonaws.com/your-stage';
const params = {
  ConnectionId: connectionId,
  Endpoint: endpoint
};

apigatewaymanagementapi.postToConnection(params, (error, data) => {
  if (error) {
    console.error('Failed to connect device:', error);
  } else {
    console.log('Device connected:', data);
  }
});

// 发送消息到设备
const message = 'Hello, device!';
const postData = {
  action: 'sendToDevice',
  message: message
};

const connectionId = 'your-device-connection-id';
const endpoint = 'wss://your-api-id.execute-api.your-region.amazonaws.com/your-stage';
const params = {
  ConnectionId: connectionId,
  Data: JSON.stringify(postData),
  Endpoint: endpoint
};

apigatewaymanagementapi.postToConnection(params, (error, data) => {
  if (error) {
    console.error('Failed to send message to device:', error);
  } else {
    console.log('Message sent to device:', data);
  }
});

通过以上步骤，您可以使用AWS API Gateway Websockets API与现有设备进行实时通信。您可以在Lambda函数中处理来自设备的实时消息，并使用API Gateway的postToConnection方法将消息发送回设备。