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We present a neural network approach for closed-loop deep brain stimulation (DBS). We cast the problem of finding an optimal neurostimulation strategy as a control problem. In this setting, control policies aim to optimize therapeutic…
In this paper, we study the following nonlinear backward stochastic integral partial differential equation with jumps \begin{equation*} \left\{ \begin{split} -d V(t,x) =&\displaystyle\inf_{u\in U}\bigg\{H(t,x,u, DV(t,x),D \Phi(t,x), D^2…
We introduce the deep multi-FBSDE method for robust approximation of coupled forward-backward stochastic differential equations (FBSDEs), focusing on cases where the deep BSDE method of Han, Jentzen, and E (2018) fails to converge. To…
This paper introduces a new formulation for stochastic optimal control and stochastic dynamic optimization that ensures safety with respect to state and control constraints. The proposed methodology brings together concepts such as…
One of the fundamental challenges in realizing the potential of legged robots is generating plans to traverse challenging terrains. Control actions must be carefully selected so the robot will not crash or slip. The high dimensionality of…
In this paper, we consider the fully coupled forward-backward stochastic functional differential equations (FBSFDEs) with stochastic functional differential equations as the forward equations and the generalized anticipated backward…
In this note, we study a class of indefinite stochastic McKean-Vlasov linear-quadratic (LQ in short) control problem under the control taking nonnegative values. In contrast to the conventional issue, both the classical dynamic programming…
This paper presents a layered control approach for real-time trajectory planning and control of robust cooperative locomotion by two holonomically constrained quadrupedal robots. A novel interconnected network of reduced-order models, based…
Quadrupedal robots excel in mobility, navigating complex terrains with agility. However, their complex control systems present challenges that are still far from being fully addressed. In this paper, we introduce the use of Sample-Based…
Humanoid robots are made to resemble humans but their locomotion abilities are far from ours in terms of agility and versatility. When humans walk on complex terrains, or face external disturbances, they combine a set of strategies,…
Locomotion on dynamic rigid surface (i.e., rigid surface accelerating in an inertial frame) presents complex challenges for controller design, which are essential for deploying humanoid robots in dynamic real-world environments such as…
This paper studies a new class of linear-quadratic mean field games and teams problem, where the large-population system satisfies a class of $N$ weakly coupled linear backward stochastic differential equations (BSDEs), and $z_i$ (a part of…
This paper is concerned with a Stackelberg game of backward stochastic differential equations (BSDEs), where the coefficients of the backward system and the cost functionals are deterministic, and the control domain is convex. Necessary and…
To achieve high-accuracy manipulation in the presence of unknown disturbances, we propose two novel efficient and robust motion control schemes for high-dimensional robot manipulators. Both controllers incorporate an unknown system dynamics…
We present an advanced and novel control method to enable actuated Spring Loaded Inverted Pendulum model to walk over rough and challenging terrains. The high-level philosophy is the decoupling of the controls of the vertical and horizontal…
Robots operating in human environments need various skills, like slow and fast walking, turning, side-stepping, and many more. However, building robot controllers that can exhibit such a large range of behaviors is a challenging problem…
In this work, we present a second-order numerical scheme to address the solution of optimal control problems constrained by the evolution of nonlinear Fokker-Planck equations arising from socio-economic dynamics. In order to design an…
In this paper, we focus on a class of time-inconsistent stochastic control problems, where the objective function includes the mean and several higher-order central moments of the terminal value of state. To tackle the time-inconsistency,…
This study proposes a novel planning framework based on a model predictive control formulation that incorporates signal temporal logic (STL) specifications for task completion guarantees and robustness quantification. This marks the…
In this paper we make a survey on the so called randomization method, a recent methodology to study stochastic optimization problems. It allows to represent the value function of an optimal control problem by a suitable backward stochastic…