Wenjian Hao

Wenjian Hao, Zehui Lu, Devesh Upadhyay et al.

This paper proposes a distributed data-driven framework for dynamics learning, termed distributed deep Koopman learning using partial trajectories (DDKL-PT). In this framework, each agent in a multi-agent system is assigned a partial trajectory offline and locally approximates the unknown dynamics using a deep neural network within the Koopman operator framework. By exchanging local estimated dynamics rather than training data, agents achieve consensus on a global dynamics model without sharing their private training trajectories. Simulation studies on a surface vehicle demonstrate that DDKL-PT achieves consensus on the learned dynamics, and each agent attains reasonably small approximation errors on the testing dataset. Furthermore, a model predictive control scheme is developed by integrating the learned Koopman dynamics with known kinematic relations. Results on a reference-tracking task indicate that the distributedly learned dynamics are sufficiently accurate for model-based optimal control.

Wenjian Hao, Yuxuan Fang, Zehui Lu et al.

This paper presents a model-based reinforcement learning (RL) framework for optimal closed-loop control of nonlinear robotic systems. The proposed approach learns linear lifted dynamics through Koopman operator theory and integrates the resulting model into an actor-critic architecture for policy optimization, where the policy represents a parameterized closed-loop controller. To reduce computational cost and mitigate model rollout errors, policy gradients are estimated using one-step predictions of the learned dynamics rather than multi-step propagation. This leads to an online mini-batch policy gradient framework that enables policy improvement from streamed interaction data. The proposed framework is evaluated on several simulated nonlinear control benchmarks and two real-world hardware platforms, including a Kinova Gen3 robotic arm and a Unitree Go1 quadruped. Experimental results demonstrate improved sample efficiency over model-free RL baselines, superior control performance relative to model-based RL baselines, and control performance comparable to classical model-based methods that rely on exact system dynamics.

Wenjian Hao, Devesh Upadhyay, Shaoshuai Mou

This paper proposes a data-driven framework to learn a finite-dimensional approximation of a Koopman operator for approximating the state evolution of a dynamical system under noisy observations. To this end, our proposed solution has two main advantages. First, the proposed method only requires the measurement noise to be bounded. Second, the proposed method modifies the existing deep Koopman operator formulations by characterizing the effect of the measurement noise on the Koopman operator learning and then mitigating it by updating the tunable parameter of the observable functions of the Koopman operator, making it easy to implement. The performance of the proposed method is demonstrated on several standard benchmarks. We then compare the presented method with similar methods proposed in the latest literature on Koopman learning.

Wenjian Hao, Bowen Huang, Wei Pan et al.

This paper presents a data-driven approach to approximate the dynamics of a nonlinear time-varying system (NTVS) by a linear time-varying system (LTVS), which is resulted from the Koopman operator and deep neural networks. Analysis of the approximation error between states of the NTVS and the resulting LTVS is presented. Simulations on a representative NTVS show that the proposed method achieves small approximation errors, even when the system changes rapidly. Furthermore, simulations in an example of quadcopters demonstrate the computational efficiency of the proposed approach.

Wenjian Hao, Zehui Lu, Zihao Liang et al.

This paper develops a policy learning method for tuning a pre-trained policy to adapt to additional tasks without altering the original task. A method named Adaptive Policy Gradient (APG) is proposed in this paper, which combines Bellman's principle of optimality with the policy gradient approach to improve the convergence rate. This paper provides theoretical analysis which guarantees the convergence rate and sample complexity of $\mathcal{O}(1/T)$ and $\mathcal{O}(1/ε)$, respectively, where $T$ denotes the number of iterations and $ε$ denotes the accuracy of the resulting stationary policy. Furthermore, several challenging numerical simulations, including cartpole, lunar lander, and robot arm, are provided to show that APG obtains similar performance compared to existing deterministic policy gradient methods while utilizing much less data and converging at a faster rate.

Wenjian Hao, Paulo C. Heredia, Shaoshuai Mou

This paper presents a data-driven method to find a closed-loop optimal controller, which minimizes a specified infinite-horizon cost function for systems with unknown dynamics. Suppose the closed-loop optimal controller can be parameterized by a given class of functions, hereafter referred to as the policy. The proposed method introduces a novel gradient estimation framework, which approximates the gradient of the cost function with respect to the policy parameters via integrating the Koopman operator with the classical concept of actor-critic. This enables the policy parameters to be tuned iteratively using gradient descent to achieve an optimal controller, leveraging the linearity of the Koopman operator. The convergence analysis of the proposed framework is provided. The control performance of the proposed method is evaluated through simulations compared with classical optimal control methods that usually assume the dynamics are known.

Yiqiang Han, Wenjian Hao, Umesh Vaidya

We develop a data-driven, model-free approach for the optimal control of the dynamical system. The proposed approach relies on the Deep Neural Network (DNN) based learning of Koopman operator for the purpose of control. In particular, DNN is employed for the data-driven identification of basis function used in the linear lifting of nonlinear control system dynamics. The controller synthesis is purely data-driven and does not rely on a priori domain knowledge. The OpenAI Gym environment, employed for Reinforcement Learning-based control design, is used for data generation and learning of Koopman operator in control setting. The method is applied to two classic dynamical systems on OpenAI Gym environment to demonstrate the capability.

Wenjian Hao, Rongyao Wang, Alexander Krolicki et al.

Proper path planning is the first step of robust and efficient autonomous navigation for mobile robots. Meanwhile, it is still challenging for robots to work in a complex environment without complete prior information. This paper presents an extension to the A* search algorithm and its variants to make the path planning stable with less computational burden while handling long-distance tasks. The implemented algorithm is capable of online searching for a collision-free and smooth path when heading to the defined goal position. This paper deploys the algorithm on the autonomous drone platform and implements it on a remote control car for algorithm efficiency validation.

Wenjian Hao, Yiqiang Han

This paper compares two different types of data-driven control methods, representing model-based and model-free approaches. One is a recently proposed method - Deep Koopman Representation for Control (DKRC), which utilizes a deep neural network to map an unknown nonlinear dynamical system to a high-dimensional linear system, which allows for employing state-of-the-art control strategy. The other one is a classic model-free control method based on an actor-critic architecture - Deep Deterministic Policy Gradient (DDPG), which has been proved to be effective in various dynamical systems. The comparison is carried out in OpenAI Gym, which provides multiple control environments for benchmark purposes. Two examples are provided for comparison, i.e., classic Inverted Pendulum and Lunar Lander Continuous Control. From the results of the experiments, we compare these two methods in terms of control strategies and the effectiveness under various initialization conditions. We also examine the learned dynamic model from DKRC with the analytical model derived from the Euler-Lagrange Linearization method, which demonstrates the accuracy in the learned model for unknown dynamics from a data-driven sample-efficient approach.