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The framework of deep operator network (DeepONet) has been widely exploited thanks to its capability of solving high dimensional partial differential equations. In this paper, we incorporate DeepONet with a recently developed policy…
In this paper, previous works on the Model Predictive Control (MPC) and the Divergent Component of Motion (DCM) for bipedal walking control are extended. To this end, we employ a single MPC which uses a combination of Center of Pressure…
Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-Jacobi-Bellman equations. Building on recent machine learning inspired approaches towards high-dimensional PDEs, we investigate the…
Impedance-based control represents a prevalent strategy in the powered trans femoral prostheses because of its ability to reproduce natural walking. However, most existing studies have developed impedance-based prosthesis controllers for…
Stochastic optimal control problems governed by delay equations with delay in the control are usually more difficult to study than the the ones when the delay appears only in the state. This is particularly true when we look at the…
This paper explores a class of fully coupled nonlinear forward-backward stochastic difference equations (FBS$\Delta$Es). Building on insights from linear quadratic optimal control problems, we introduce a more relaxed framework of…
In this paper a Feynman-type path integral control approach is used for a recursive formulation of a health objective function subject to a fatigue dynamics, a forward-looking stochastic multi-risk susceptible-infective-recovered (SIR)…
This paper presents a safety-critical locomotion control framework for quadrupedal robots. Our goal is to enable quadrupedal robots to safely navigate in cluttered environments. To tackle this, we introduce exponential Discrete Control…
In this paper, we study the solvability of a class of multi-dimensional forward backward stochastic differential equations (FBSDEs) with oblique reflection and unbounded stopping time. Under some mild assumptions on the coefficients in such…
We deal with a new maximum principle-based stochastic control model for river management through operating a dam and reservoir system. The model is based on coupled forward-backward stochastic differential equations (FBSDEs) derived from…
We successfully evolved a neural network controller that produces dynamic walking in a simulated bipedal robot with compliant actuators, a difficult control problem. The evolutionary evaluation uses a detailed software simulation of a…
We tackle the problem of perceptive locomotion in dynamic environments. In this problem, a quadrupedal robot must exhibit robust and agile walking behaviors in response to environmental clutter and moving obstacles. We present a…
In this work, we propose a learning approach for 3D dynamic bipedal walking when footsteps are constrained to stepping stones. While recent work has shown progress on this problem, real-world demonstrations have been limited to relatively…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
This work studies the deep learning-based numerical algorithms for optimal hedging problems in markets with general convex transaction costs on the trading rates, focusing on their scalability of trading time horizon. Based on the…
Robust closed-loop locomotion remains challenging for soft quadruped robots due to high-dimensional dynamics, actuator hysteresis, and difficult-to-model contact interactions, while conventional proprioception provides limited information…
This paper is concerned with optimal control of stochastic fully coupled forward-backward linear quadratic (FBLQ) problems with indefinite control weight costs. In order to obtain the state feedback representation of the optimal control, we…
In this paper, we study the maximum principle for stochastic optimal control problems of forward-backward stochastic difference systems (FBS{\Delta}Ss) where the uncertainty is modeled by a discrete time, finite state process, rather than…
This paper studies open-loop equilibriums for a general class of time-inconsistent stochastic control problems under jump-diffusion SDEs with deterministic coefficients. Inspired by the idea of Four-Step-Scheme for forward-backward…
For continuous systems modeled by dynamical equations such as ODEs and SDEs, Bellman's Principle of Optimality takes the form of the Hamilton-Jacobi-Bellman (HJB) equation, which provides the theoretical target of reinforcement learning…