Lihan Lian

Lihan Lian

Robotics enthusiast. Passionate about optimal control and deep learning.

Posts by Tags

(Deep) Q-learning

From Q-Learning to Deep Q-Learning and Deep Deterministic Policy Gradient (DDPG) Permalink

16 minute read

Published:

Q-learning, an off-policy reinforcement learning algorithm, uses the Bellman equation to iteratively update state-action values, helping an agent determine the best actions to maximize cumulative rewards. Deep Q-learning improves upon Q-learning by leveraging deep Q network (DQN) to approximate Q-values, enabling it to handle continuous state spaces but it is still only suitable for discrete action spaces. Further advancement, Deep Deterministic Policy Gradient (DDPG), combines Q-learning’s principles with policy gradients, making it also suitable for continuous action spaces. This blog starts by discussing the basic components of reinforcement learning and gradually explore how Q-learning evolves into DQN and DDPG, with application for solving the cartpole environment in Isaac Gym simulator. Corresponding code can be found at this repository.

Algebraic Riccati Equation

From Control Hamiltonian to Algebraic Riccati Equation and Pontryagin’s Maximum Principle Permalink

30 minute read

Published:

Inspired by the Hamiltonian of classical mechanics, Lev Pontryagin introduced the Control Hamiltonian and formulated his celebrated Pontragin’s Maximum Principle (PMP). This blog will first discuss general cases of optimal control problems, including scenarios with both free final time and final states. Then, the derivation of Algebraic Riccati Equation (ARE) in the context of Continuous Linear Qudratic Regulator (LQR) from the perspective of the Control Hamiltonian will be introduced. It will then explain the PMP, finally followed by the example problem of Constrained Continous LQR.

Calculus of Variations

From Control Hamiltonian to Algebraic Riccati Equation and Pontryagin’s Maximum Principle Permalink

30 minute read

Published:

Inspired by the Hamiltonian of classical mechanics, Lev Pontryagin introduced the Control Hamiltonian and formulated his celebrated Pontragin’s Maximum Principle (PMP). This blog will first discuss general cases of optimal control problems, including scenarios with both free final time and final states. Then, the derivation of Algebraic Riccati Equation (ARE) in the context of Continuous Linear Qudratic Regulator (LQR) from the perspective of the Control Hamiltonian will be introduced. It will then explain the PMP, finally followed by the example problem of Constrained Continous LQR.

Classical Mechanics

On Derivation of Hamilton-Jacobi-Bellman Equation and Its Application Permalink

13 minute read

Published:

The Hamilton-Jacobi-Bellman (HJB) equation is arguably one of the most important cornerstones of optimal control theory and reinforcement learning. In this blog, we will first introduce the Hamilton-Jacobi Equation and Bellman’s Principle of Optimality. We will then delve into the derivation of the HJB equation. Finally, we will conclude with an example that shows the derivation of the famous Algebraic Riccati equation (ARE) from this perspective.

Computer Vision

Implementation Details of Basic-and-Fast-Neural-Style-Transfer Permalink

7 minute read

Published:

Neural style transfer (NST) serves as an essential starting point those interested in deep learning, incorporating critical components or techniques such as convolutional neural networks (CNNs), VGG network, residual networks, upsampling and normalization. The basic neural style transfer method captures and manipulates image features using CNNs and the VGG network directly over the input image. In contrast, the fast neural style transfer method employs a dataset to train an inference neural network that can be used for real-time style transfer. This blogs provides the explanation of the implementation of both methods. Corresponding repository can be found here.

Deep Deterministic Policy Gradient

From Q-Learning to Deep Q-Learning and Deep Deterministic Policy Gradient (DDPG) Permalink

16 minute read

Published:

Q-learning, an off-policy reinforcement learning algorithm, uses the Bellman equation to iteratively update state-action values, helping an agent determine the best actions to maximize cumulative rewards. Deep Q-learning improves upon Q-learning by leveraging deep Q network (DQN) to approximate Q-values, enabling it to handle continuous state spaces but it is still only suitable for discrete action spaces. Further advancement, Deep Deterministic Policy Gradient (DDPG), combines Q-learning’s principles with policy gradients, making it also suitable for continuous action spaces. This blog starts by discussing the basic components of reinforcement learning and gradually explore how Q-learning evolves into DQN and DDPG, with application for solving the cartpole environment in Isaac Gym simulator. Corresponding code can be found at this repository.

Deep Learning

Implementation Details of Basic-and-Fast-Neural-Style-Transfer Permalink

7 minute read

Published:

Neural style transfer (NST) serves as an essential starting point those interested in deep learning, incorporating critical components or techniques such as convolutional neural networks (CNNs), VGG network, residual networks, upsampling and normalization. The basic neural style transfer method captures and manipulates image features using CNNs and the VGG network directly over the input image. In contrast, the fast neural style transfer method employs a dataset to train an inference neural network that can be used for real-time style transfer. This blogs provides the explanation of the implementation of both methods. Corresponding repository can be found here.

Dynamic Programming

Dwell on Differential Dynamic Programming (DDP) and Iterative Linear Quadratic Regulator (iLQR) Permalink

6 minute read

Published:

Although optimal control and reinforcement learning appear to be distinct field, they are, in fact closely related. Differential Dynamic Programming (DDP) and Iterative Linear Quadratic Regulator (iLQR), two powerful algorithms commonly utilized in trajectory optimizations, exemplify how model-based reinforcement learning can bridge the gap between these domains. This blog begins by discussing the fundational principles, including Newton’s method and Bellman Equation. It then delves into the specifics of the DDP and iLQR algorithms, illustrating their application through the classical problem of double pendulum swing-up control.

On Derivation of Hamilton-Jacobi-Bellman Equation and Its Application Permalink

13 minute read

Published:

The Hamilton-Jacobi-Bellman (HJB) equation is arguably one of the most important cornerstones of optimal control theory and reinforcement learning. In this blog, we will first introduce the Hamilton-Jacobi Equation and Bellman’s Principle of Optimality. We will then delve into the derivation of the HJB equation. Finally, we will conclude with an example that shows the derivation of the famous Algebraic Riccati equation (ARE) from this perspective.

Euler-Largrange Equation

On Derivation of Euluer-Lagrange Equation and Its Application Permalink

11 minute read

Published:

Euler-Lagrange equation plays an essential role in calculus of variations and classical mechanics. Beyond its applications in deriving equations of motion, Euler-Lagrange equation is ubiquitous in the filed of trajectory optimization, serving as a critical stepping stone for many powerful optimal control techniques, such as Pontrygain’s Maximum Principle. In this blog, derivation of the Euler-Lagrange equation and two simple cases of its application are introduced.

Functional Analysis

On Derivation of Euluer-Lagrange Equation and Its Application Permalink

11 minute read

Published:

Euler-Lagrange equation plays an essential role in calculus of variations and classical mechanics. Beyond its applications in deriving equations of motion, Euler-Lagrange equation is ubiquitous in the filed of trajectory optimization, serving as a critical stepping stone for many powerful optimal control techniques, such as Pontrygain’s Maximum Principle. In this blog, derivation of the Euler-Lagrange equation and two simple cases of its application are introduced.

Lagrangian Mechanics

On Derivation of Euluer-Lagrange Equation and Its Application Permalink

11 minute read

Published:

Euler-Lagrange equation plays an essential role in calculus of variations and classical mechanics. Beyond its applications in deriving equations of motion, Euler-Lagrange equation is ubiquitous in the filed of trajectory optimization, serving as a critical stepping stone for many powerful optimal control techniques, such as Pontrygain’s Maximum Principle. In this blog, derivation of the Euler-Lagrange equation and two simple cases of its application are introduced.

Linear Qudratic Regulator

From Control Hamiltonian to Algebraic Riccati Equation and Pontryagin’s Maximum Principle Permalink

30 minute read

Published:

Inspired by the Hamiltonian of classical mechanics, Lev Pontryagin introduced the Control Hamiltonian and formulated his celebrated Pontragin’s Maximum Principle (PMP). This blog will first discuss general cases of optimal control problems, including scenarios with both free final time and final states. Then, the derivation of Algebraic Riccati Equation (ARE) in the context of Continuous Linear Qudratic Regulator (LQR) from the perspective of the Control Hamiltonian will be introduced. It will then explain the PMP, finally followed by the example problem of Constrained Continous LQR.

Neural Style Transfer

Implementation Details of Basic-and-Fast-Neural-Style-Transfer Permalink

7 minute read

Published:

Neural style transfer (NST) serves as an essential starting point those interested in deep learning, incorporating critical components or techniques such as convolutional neural networks (CNNs), VGG network, residual networks, upsampling and normalization. The basic neural style transfer method captures and manipulates image features using CNNs and the VGG network directly over the input image. In contrast, the fast neural style transfer method employs a dataset to train an inference neural network that can be used for real-time style transfer. This blogs provides the explanation of the implementation of both methods. Corresponding repository can be found here.

Optimal Control

On Derivation of Hamilton-Jacobi-Bellman Equation and Its Application Permalink

13 minute read

Published:

The Hamilton-Jacobi-Bellman (HJB) equation is arguably one of the most important cornerstones of optimal control theory and reinforcement learning. In this blog, we will first introduce the Hamilton-Jacobi Equation and Bellman’s Principle of Optimality. We will then delve into the derivation of the HJB equation. Finally, we will conclude with an example that shows the derivation of the famous Algebraic Riccati equation (ARE) from this perspective.

Policy Gradient

Shed Some Light on Proximal Policy Optimization (PPO) and Its Application Permalink

1 minute read

Published:

Proximal Policy Optimization (PPO) is a reinforcement learning algorithm that refines policy gradient methods like REINFORCE using importance sampling and a clipped surrogate objective to stabilize updates. PPO-Penalty explicitly penalizes KL divergence in the objective function, and PPO-Clip instead uses clipping to prevent large policy updates. In many robotics tasks, PPO is first used to train a base policy (potentially with privileged information). Then, a deployable controller is learned from this base policy using imitation learning, distillation, or other techniques. This blog explores PPO’s core principle, with code available at repo1 and repo2.

Proximal Policy Optimization

Shed Some Light on Proximal Policy Optimization (PPO) and Its Application Permalink

1 minute read

Published:

Proximal Policy Optimization (PPO) is a reinforcement learning algorithm that refines policy gradient methods like REINFORCE using importance sampling and a clipped surrogate objective to stabilize updates. PPO-Penalty explicitly penalizes KL divergence in the objective function, and PPO-Clip instead uses clipping to prevent large policy updates. In many robotics tasks, PPO is first used to train a base policy (potentially with privileged information). Then, a deployable controller is learned from this base policy using imitation learning, distillation, or other techniques. This blog explores PPO’s core principle, with code available at repo1 and repo2.

Reinforcement Learning

Shed Some Light on Proximal Policy Optimization (PPO) and Its Application Permalink

1 minute read

Published:

Proximal Policy Optimization (PPO) is a reinforcement learning algorithm that refines policy gradient methods like REINFORCE using importance sampling and a clipped surrogate objective to stabilize updates. PPO-Penalty explicitly penalizes KL divergence in the objective function, and PPO-Clip instead uses clipping to prevent large policy updates. In many robotics tasks, PPO is first used to train a base policy (potentially with privileged information). Then, a deployable controller is learned from this base policy using imitation learning, distillation, or other techniques. This blog explores PPO’s core principle, with code available at repo1 and repo2.

From Q-Learning to Deep Q-Learning and Deep Deterministic Policy Gradient (DDPG) Permalink

16 minute read

Published:

Q-learning, an off-policy reinforcement learning algorithm, uses the Bellman equation to iteratively update state-action values, helping an agent determine the best actions to maximize cumulative rewards. Deep Q-learning improves upon Q-learning by leveraging deep Q network (DQN) to approximate Q-values, enabling it to handle continuous state spaces but it is still only suitable for discrete action spaces. Further advancement, Deep Deterministic Policy Gradient (DDPG), combines Q-learning’s principles with policy gradients, making it also suitable for continuous action spaces. This blog starts by discussing the basic components of reinforcement learning and gradually explore how Q-learning evolves into DQN and DDPG, with application for solving the cartpole environment in Isaac Gym simulator. Corresponding code can be found at this repository.

Dwell on Differential Dynamic Programming (DDP) and Iterative Linear Quadratic Regulator (iLQR) Permalink

6 minute read

Published:

Although optimal control and reinforcement learning appear to be distinct field, they are, in fact closely related. Differential Dynamic Programming (DDP) and Iterative Linear Quadratic Regulator (iLQR), two powerful algorithms commonly utilized in trajectory optimizations, exemplify how model-based reinforcement learning can bridge the gap between these domains. This blog begins by discussing the fundational principles, including Newton’s method and Bellman Equation. It then delves into the specifics of the DDP and iLQR algorithms, illustrating their application through the classical problem of double pendulum swing-up control.

On Derivation of Hamilton-Jacobi-Bellman Equation and Its Application Permalink

13 minute read

Published:

The Hamilton-Jacobi-Bellman (HJB) equation is arguably one of the most important cornerstones of optimal control theory and reinforcement learning. In this blog, we will first introduce the Hamilton-Jacobi Equation and Bellman’s Principle of Optimality. We will then delve into the derivation of the HJB equation. Finally, we will conclude with an example that shows the derivation of the famous Algebraic Riccati equation (ARE) from this perspective.

Trajectory Optimization

Dwell on Differential Dynamic Programming (DDP) and Iterative Linear Quadratic Regulator (iLQR) Permalink

6 minute read

Published:

Although optimal control and reinforcement learning appear to be distinct field, they are, in fact closely related. Differential Dynamic Programming (DDP) and Iterative Linear Quadratic Regulator (iLQR), two powerful algorithms commonly utilized in trajectory optimizations, exemplify how model-based reinforcement learning can bridge the gap between these domains. This blog begins by discussing the fundational principles, including Newton’s method and Bellman Equation. It then delves into the specifics of the DDP and iLQR algorithms, illustrating their application through the classical problem of double pendulum swing-up control.