Train DDPG Agent to Swing Up and Balance Pendulum

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This example shows how to train a deep deterministic policy gradient (DDPG) agent to swing up and balance a pendulum modeled in Simulink®.

For more information on DDPG agents, seeDeep Deterministic Policy Gradient Agents. For an example that trains a DDPG agent in MATLAB®, seeTrain DDPG Agent to Control Double Integrator System.

Pendulum Swing-Up Model

The reinforcement learning environment for this example is a simple frictionless pendulum that initially hangs in a downward position. The training goal is to make the pendulum stand upright without falling over using minimal control effort.

Open the model.

mdl ='rlSimplePendulumModel'; open_system(mdl)

For this model:

The upward balanced pendulum position is0radians, and the downward hanging position ispiradians.
The torque action signal from the agent to the environment is from –2 to 2 N·m.
The observations from the environment are the sine of the pendulum angle, the cosine of the pendulum angle, and the pendulum angle derivative.
The reward $r_{t}$ , provided at every time step, is

$r_{t} = - ({θ_{t}}^{2} + 0.1 {\dot{θ_{t}}}^{2} + 0.001 u_{t - 1}^{2})$

Here:

$θ_{t}$ is the angle of displacement from the upright position.
$\dot{θ_{t}}$ is the derivative of the displacement angle.
$u_{t - 1}$ is the control effort from the previous time step.

For more information on this model, seeLoad Predefined Simulink Environments.

Create Environment Interface

Create a predefined environment interface for the pendulum.

env =rlPredefinedEnv('SimplePendulumModel-Continuous')

env =SimulinkEnvWithAgent with properties: Model : rlSimplePendulumModel AgentBlock : rlSimplePendulumModel/RL Agent ResetFcn : [] UseFastRestart : on

The interface has a continuous action space where the agent can apply torque values between –2 to 2 N·m to the pendulum.

Set the observations of the environment to be the sine of the pendulum angle, the cosine of the pendulum angle, and the pendulum angle derivative.

numObs = 3; set_param('rlSimplePendulumModel/create observations','ThetaObservationHandling','sincos');

定义摆的初始条件hanging downward, specify an environment reset function using an anonymous function handle. This reset function sets the model workspace variabletheta0topi.

env.ResetFcn = @(in)setVariable(in,'theta0',pi,'Workspace',mdl);

Specify the simulation timeTfand the agent sample timeTsin seconds.

Ts = 0.05; Tf = 20;

Fix the random generator seed for reproducibility.

rng(0)

Create DDPG Agent

DDPG代理接近长期奖励,胃肠道ven observations and actions, using a critic value function representation. To create the critic, first create a deep neural network with two inputs (the state and action) and one output. For more information on creating a deep neural network value function representation, seeCreate Policies and Value Functions.

statePath = [ featureInputLayer(numObs,'Normalization','none','Name','observation') fullyConnectedLayer(400,'Name','CriticStateFC1') reluLayer('Name','CriticRelu1') fullyConnectedLayer(300,'Name','CriticStateFC2')]; actionPath = [ featureInputLayer(1,'Normalization','none','Name','action') fullyConnectedLayer(300,'Name','CriticActionFC1','BiasLearnRateFactor',0)]; commonPath = [ additionLayer(2,'Name','add') reluLayer('Name','CriticCommonRelu') fullyConnectedLayer(1,'Name','CriticOutput')]; criticNetwork = layerGraph(); criticNetwork = addLayers(criticNetwork,statePath); criticNetwork = addLayers(criticNetwork,actionPath); criticNetwork = addLayers(criticNetwork,commonPath); criticNetwork = connectLayers(criticNetwork,'CriticStateFC2','add/in1'); criticNetwork = connectLayers(criticNetwork,'CriticActionFC1','add/in2'); criticNetwork = dlnetwork(criticNetwork);

View the critic network configuration.

figure plot(layerGraph(criticNetwork))

Figure contains an axes object. The axes object contains an object of type graphplot.

Specify options for the critic representation usingrlOptimizerOptions.

criticOpts = rlOptimizerOptions(“LearnRate”,1e-03,'GradientThreshold',1);

Create the critic representation using the specified deep neural network and options. You must also specify the action and observation info for the critic, which you obtain from the environment interface. For more information, seerlQValueRepresentation.

obsInfo = getObservationInfo(env); actInfo = getActionInfo(env); critic = rlQValueFunction(criticNetwork,obsInfo,actInfo,'ObservationInputNames','observation','ActionInputNames','action');

A DDPG agent decides which action to take given observations using an actor representation. To create the actor, first create a deep neural network with one input, the observation, and one output, the action.

Construct the actor in a manner similar to the critic. For more information, seerlDeterministicActorRepresentation.

actorNetwork = [ featureInputLayer(numObs,'Normalization','none','Name','observation') fullyConnectedLayer(400,'Name','ActorFC1') reluLayer('Name','ActorRelu1') fullyConnectedLayer(300,'Name',“ActorFC2”) reluLayer('Name','ActorRelu2') fullyConnectedLayer(1,'Name','ActorFC3') tanhLayer('Name','ActorTanh') scalingLayer('Name','ActorScaling','Scale',max(actInfo.UpperLimit))]; actorNetwork = dlnetwork(actorNetwork); actorOpts = rlOptimizerOptions(“LearnRate”,1e-04,'GradientThreshold',1); actor = rlContinuousDeterministicActor(actorNetwork,obsInfo,actInfo);

To create the DDPG agent, first specify the DDPG agent options usingrlDDPGAgentOptions.

agentOpts = rlDDPGAgentOptions(...'SampleTime',Ts,...'CriticOptimizerOptions',criticOpts,...'ActorOptimizerOptions',actorOpts,...'ExperienceBufferLength',1e6,...'DiscountFactor',0.99,...'MiniBatchSize',128); agentOpts.NoiseOptions.Variance = 0.6; agentOpts.NoiseOptions.VarianceDecayRate = 1e-5;

Then create the DDPG agent using the specified actor representation, critic representation, and agent options. For more information, seerlDDPGAgent.

agent = rlDDPGAgent(actor,critic,agentOpts);

Train Agent

To train the agent, first specify the training options. For this example, use the following options.

Run training for at most 50000 episodes, with each episode lasting at mostceil(Tf/Ts)time steps.
Display the training progress in the Episode Manager dialog box (set thePlotsoption) and disable the command line display (set theVerboseoption tofalse).
Stop training when the agent receives an average cumulative reward greater than –740 over five consecutive episodes. At this point, the agent can quickly balance the pendulum in the upright position using minimal control effort.
Save a copy of the agent for each episode where the cumulative reward is greater than –740.

For more information, seerlTrainingOptions.

maxepisodes = 5000; maxsteps = ceil(Tf/Ts); trainOpts = rlTrainingOptions(...'MaxEpisodes',maxepisodes,...'MaxStepsPerEpisode',maxsteps,...'ScoreAveragingWindowLength',5,...'Verbose',false,...“阴谋”,'training-progress',...'StopTrainingCriteria','AverageReward',...'StopTrainingValue',-740,...'SaveAgentCriteria','EpisodeReward',...'SaveAgentValue',-740);

Train the agent using thetrainfunction. Training this agent is a computationally intensive process that takes several hours to complete. To save time while running this example, load a pretrained agent by settingdoTrainingtofalse. To train the agent yourself, setdoTrainingtotrue.

doTraining = false;ifdoTraining% Train the agent.trainingStats = train(agent,env,trainOpts);else% Load the pretrained agent for the example.load('SimulinkPendulumDDPG.mat','agent')end

Simulate DDPG Agent

To validate the performance of the trained agent, simulate it within the pendulum environment. For more information on agent simulation, seerlSimulationOptionsandsim.

simOptions = rlSimulationOptions('MaxSteps',500); experience = sim(env,agent,simOptions);

Figure Simple Pendulum Visualizer contains an axes object. The axes object contains 2 objects of type line, rectangle.