matlab实现自适应动态规划算法

自适应动态规划（Adaptive Dynamic Programming, ADP）是一种结合了动态规划和机器学习技术的算法，用于解决复杂的决策和控制问题。ADP算法通常包括两个主要部分：Actor（执行者）和Critic（评估者）。Actor负责选择最优的动作，而Critic负责评估当前策略的性能。

基于Python的简单ADP算法实现示例，使用了深度学习库（如TensorFlow或PyTorch）来构建Actor和Critic网络。这个示例将展示如何在连续动作空间中实现ADP算法。

1. 环境设置

首先，我们需要定义一个环境，用于模拟决策过程。这里我们使用一个简单的连续动作空间环境。

import numpy as np

class SimpleEnvironment:
    def __init__(self):
        self.state = np.array([0.0])
        self.goal = np.array([1.0])
        self.max_steps = 100

    def reset(self):
        self.state = np.array([0.0])
        self.steps = 0
        return self.state

    def step(self, action):
        self.state += action
        reward = -np.abs(self.state - self.goal)
        self.steps += 1
        done = self.steps >= self.max_steps or np.abs(self.state - self.goal) < 0.1
        return self.state, reward, done, {}

2. Actor和Critic网络

接下来，我们定义Actor和Critic网络。Actor网络负责选择动作，Critic网络负责评估当前状态的价值。

import tensorflow as tf
from tensorflow.keras import layers

class ActorNetwork(tf.keras.Model):
    def __init__(self, action_dim):
        super(ActorNetwork, self).__init__()
        self.fc1 = layers.Dense(64, activation='relu')
        self.fc2 = layers.Dense(64, activation='relu')
        self.output_layer = layers.Dense(action_dim, activation='tanh')

    def call(self, state):
        x = self.fc1(state)
        x = self.fc2(x)
        return self.output_layer(x)

class CriticNetwork(tf.keras.Model):
    def __init__(self):
        super(CriticNetwork, self).__init__()
        self.fc1 = layers.Dense(64, activation='relu')
        self.fc2 = layers.Dense(64, activation='relu')
        self.output_layer = layers.Dense(1)

    def call(self, state):
        x = self.fc1(state)
        x = self.fc2(x)
        return self.output_layer(x)

参考代码 matlab实现自适应动态规划算法，二维轨迹跟踪，acor-critic网络

3. ADP算法实现

现在，我们实现ADP算法的核心部分，包括Actor和Critic的训练。

class ADP:
    def __init__(self, env, actor_lr=0.001, critic_lr=0.001, gamma=0.99):
        self.env = env
        self.actor = ActorNetwork(action_dim=1)
        self.critic = CriticNetwork()
        self.actor_optimizer = tf.keras.optimizers.Adam(learning_rate=actor_lr)
        self.critic_optimizer = tf.keras.optimizers.Adam(learning_rate=critic_lr)
        self.gamma = gamma

    def train(self, episodes=1000):
        for episode in range(episodes):
            state = self.env.reset()
            done = False
            rewards = 0.0

            while not done:
                with tf.GradientTape() as actor_tape, tf.GradientTape() as critic_tape:
                    action = self.actor(state)
                    next_state, reward, done, _ = self.env.step(action)
                    rewards += reward

                    target_value = reward + self.gamma * self.critic(next_state) * (1 - done)
                    critic_loss = tf.reduce_mean(tf.square(target_value - self.critic(state)))

                    actor_loss = -tf.reduce_mean(self.critic(state) * action)

                actor_gradients = actor_tape.gradient(actor_loss, self.actor.trainable_variables)
                critic_gradients = critic_tape.gradient(critic_loss, self.critic.trainable_variables)

                self.actor_optimizer.apply_gradients(zip(actor_gradients, self.actor.trainable_variables))
                self.critic_optimizer.apply_gradients(zip(critic_gradients, self.critic.trainable_variables))

                state = next_state

            if episode % 100 == 0:
                print(f"Episode {episode}, Total Reward: {rewards}")

# 创建环境和ADP实例
env = SimpleEnvironment()
adp = ADP(env)

# 训练ADP
adp.train()

4. 测试和验证

训练完成后，我们可以测试ADP算法的性能，看看它是否能够成功地将状态推向目标。

def test_adp(env, adp, episodes=10):
    for episode in range(episodes):
        state = env.reset()
        done = False
        rewards = 0.0

        while not done:
            action = adp.actor(state)
            state, reward, done, _ = env.step(action)
            rewards += reward

        print(f"Test Episode {episode}, Total Reward: {rewards}")

# 测试ADP
test_adp(env, adp)

总结

以上代码展示了如何使用Python和TensorFlow实现一个简单的自适应动态规划（ADP）算法。这个示例包括了环境的定义、Actor和Critic网络的构建以及ADP算法的训练和测试。通过调整网络结构和超参数，可以进一步优化算法的性能。