TD3算法求解HJB方程的代码实现

以下是一个简单的TD3算法求解HJB方程的代码实现：

import numpy as np

# 定义HJB方程
def HJB(u, x, t):
    return -0.5 * u ** 2 + np.sin(x) + t

# 定义TD3算法
def TD3(x0, t0, u0, alpha, gamma, n_iter):
    x = x0
    t = t0
    u = u0
    for i in range(n_iter):
        u_old = u
        u = u_old - alpha * (HJB(u_old, x, t) - gamma * HJB(u_old, x, t + 1))
        x = x + u
        t = t + 1
    return u

# 测试
x0 = 0
t0 = 0
u0 = 0
alpha = 0.1
gamma = 0.9
n_iter = 100
u_star = TD3(x0, t0, u0, alpha, gamma, n_iter)
print("最优控制：", u_star)

注意：这只是一个简单的实现，实际应用中可能需要更复杂的算法和技巧。

相关问题

matlab写TD3算法优化PID参数代码

好的，下面是一个使用MATLAB实现TD3算法优化PID参数的简单示例代码：

%% 确定状态和动作空间
% 状态空间
state_min = -10;
state_max = 10;

% 动作空间
action_min = [0, 0, 0];
action_max = [1, 1, 1];

%% 定义Actor和Critic神经网络
% Actor神经网络
actor = rlSimpleNeuralNetworkRepresentation([state_min state_max], ...
                                             [action_min; action_max]);

% Critic神经网络
critic = rlValueRepresentation([state_min state_max], ...
                                [action_min; action_max]);

%% 制定奖励函数
% 这里的奖励函数可以根据具体的控制目标进行修改
rewardFcn = @(action,state) -abs(state);

%% 训练Actor和Critic神经网络
% 创建环境模型
env = rlFunctionEnv(@(action,state) PIDControl(action, state), ...
                    @(action,state) state, ...
                    1, 3);

% 创建TD3智能体
agent = rlTD3Agent(actor, critic);

% 设置训练参数
maxEpisodes = 1000;
maxSteps = 100;
trainOpts = rlTrainingOptions('MaxEpisodes', maxEpisodes, ...
                              'MaxStepsPerEpisode', maxSteps, ...
                              'ScoreAveragingWindowLength', 50, ...
                              'Verbose', false);

% 训练智能体
trainingStats = train(agent, env, trainOpts);

%% 参数优化
% 使用Actor神经网络输出的控制参数进行PID控制器的调节
% 这里的PIDControl函数是一个自定义的函数，用于进行PID控制
function [nextstate, reward, isdone] = PIDControl(action, state)
    % 读取PID控制器的参数
    Kp = action(1);
    Ki = action(2);
    Kd = action(3);
    
    % 计算控制信号
    u = Kp * state + Ki * sum(state) + Kd * diff(state);
    
    % 更新状态
    nextstate = state + u;
    
    % 计算奖励
    reward = -abs(nextstate);
    
    % 判断是否达到目标状态
    isdone = abs(nextstate) < 0.1;
end

需要注意的是，这只是一个简单的示例代码，实际应用中需要根据具体的问题进行修改。另外，这里的PID控制器是一个简单的一阶控制器，如果需要使用更高阶的控制器，需要进行相应的修改。

td3算法的matlab代码

TD3算法是一种强化学习算法，主要用于解决连续控制问题，它在深度强化学习中具有很高的实用性。下面是一个简单的MATLAB实现：

% TD3算法实现
% 请注意，这是一个简单的代码示例，可能需要根据实际情况进行修改

% 环境初始化
env = rlPredefinedEnv('Pendulum-Continuous');
obsInfo = getObservationInfo(env);
actInfo = getActionInfo(env);

% 神经网络参数初始化
actorNetwork = [
    imageInputLayer([obsInfo.Dimension(1) 1 1],'Normalization','none','Name','observation')
    fullyConnectedLayer(256,'Name','fc1')
    reluLayer('Name','relu1')
    fullyConnectedLayer(256,'Name','fc2')
    reluLayer('Name','relu2')
    fullyConnectedLayer(actInfo.Dimension(1),'Name','actorOutput')
    tanhLayer('Name','actorTanh')];
criticNetwork = [
    imageInputLayer([obsInfo.Dimension(1) 1 1],'Normalization','none','Name','observation')
    fullyConnectedLayer(256,'Name','fc1')
    reluLayer('Name','relu1')
    fullyConnectedLayer(256,'Name','fc2')
    reluLayer('Name','relu2')
    fullyConnectedLayer(1,'Name','criticOutput')];
actorOpts = rlRepresentationOptions('LearnRate',1e-3,'GradientThreshold',1);
criticOpts = rlRepresentationOptions('LearnRate',1e-3,'GradientThreshold',1);
actor = rlDeterministicActorRepresentation(actorNetwork,obsInfo,actInfo,'Observation',{'observation'},'Action',{'actorTanh'},actorOpts);
critic = rlValueRepresentation(criticNetwork,obsInfo,criticOpts,'Observation',{'observation'});

% TD3算法参数初始化
agentOpts = rlTD3AgentOptions;
agentOpts.SampleTime = 0.01;
agentOpts.DiscountFactor = 0.99;
agentOpts.ExperienceBufferLength = 1e6;
agentOpts.TargetSmoothFactor = 5e-3;
agentOpts.NoiseOptions.Variance = 0.2;
agentOpts.NoiseOptions.VarianceDecayRate = 1e-5;
agentOpts.NoiseOptions.StepSize = 0.01;

% 创建TD3代理
agent = rlTD3Agent(actor,critic,agentOpts);

% 训练代理
trainOpts = rlTrainingOptions;
trainOpts.MaxEpisodes = 500;
trainOpts.MaxStepsPerEpisode = ceil(env.Ts/env.StepSize);
trainOpts.ScoreAveragingWindowLength = 10;
trainOpts.StopTrainingCriteria = 'AverageReward';
trainOpts.StopTrainingValue = -100;
trainOpts.SaveAgentCriteria = 'EpisodeReward';
trainOpts.SaveAgentValue = -100;
trainOpts.Plots = 'training-progress';
trainOpts.Verbose = false;

% 训练代理
trainingStats = train(agent,env,trainOpts);

% 测试代理
simOptions.ResetFcn = @(in) setVariable(env,in,env.ResetFcn());
simOptions.StopTime = 20;
experience = sim(env,agent,simOptions);