Related papers: Optimal Convergence Rate in Feed Forward Neural Ne…
This paper studies an optimal dividend problem with a drawdown constraint in a Brownian motion model, requiring the dividend payout rate to remain above a fixed proportion of its historical maximum. This leads to a path-dependent stochastic…
This paper studies the infinite-horizon optimal consumption with a path-dependent reference under exponential utility. The performance is measured by the difference between the nonnegative consumption rate and a fraction of the historical…
We propose a novel formulation for approximating reachable sets through a minimum discounted reward optimal control problem. The formulation yields a continuous solution that can be obtained by solving a Hamilton-Jacobi equation.…
The ergodic control problem for a non-degenerate controlled diffusion controlled through its drift is considered under a uniform stability condition that ensures the well-posedness of the associated Hamilton-Jacobi-Bellman (HJB) equation. A…
Feedforward neural networks with error backpropagation (FFBP) are widely applied to pattern recognition. One general problem encountered with this type of neural networks is the uncertainty, whether the minimization procedure has converged…
Recent research reveals that deep learning is an effective way of solving high dimensional Hamilton-Jacobi-Bellman equations. The resulting feedback control law in the form of a neural network is computationally efficient for real-time…
In this paper we propose a new computational method for designing optimal regulators for high-dimensional nonlinear systems. The proposed approach leverages physics-informed machine learning to solve high-dimensional Hamilton-Jacobi-Bellman…
Microgrids have more operational flexibilities as well as uncertainties than conventional power grids, especially when renewable energy resources are utilized. An energy storage based feedback controller can compensate undesired dynamics of…
We provide a novel uniform convergence guarantee for DeepReach, a deep learning-based method for solving Hamilton-Jacobi-Isaacs (HJI) equations associated with reachability analysis. Specifically, we show that the DeepReach algorithm, as…
Artificial neural networks have successfully tackled a large variety of problems by training extremely deep networks via back-propagation. A direct application of back-propagation to spiking neural networks contains biologically implausible…
For pricing American options, %after suitable discretization in space and time, a sequence of discrete linear complementarity problems (LCPs) or equivalently Hamilton-Jacobi-Bellman (HJB) equations need to be solved in a sequential…
This paper presents a two-stage framework for constrained near-optimal feedback control of input-affine nonlinear systems. An approximate value function for the unconstrained control problem is computed offline by solving the…
In this work, we propose a class of numerical schemes for solving semilinear Hamilton-Jacobi-Bellman-Isaacs (HJBI) boundary value problems which arise naturally from exit time problems of diffusion processes with controlled drift. We…
This paper studies the consensus problem of heterogeneous multi-agent systems by the feedforward control and linear quadratic (LQ) optimal control theory. Different from the existing consensus control algorithms, which require to design an…
We present a partial-differential-equation-based optimal path-planning framework for curvature constrained motion, with application to vehicles in 2- and 3-spatial-dimensions. This formulation relies on optimal control theory, dynamic…
An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is…
This paper considers consumption and portfolio optimization problems with recursive preferences in both infinite and finite time regions. Specially, the financial market consists of a risk-free asset and a risky asset that follows a general…
In this paper infinite horizon optimal control problems for nonlinear high-dimensional dynamical systems are studied. Nonlinear feedback laws can be computed via the value function characterized as the unique viscosity solution to the…
We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential…
Backpropagation algorithm has driven the remarkable success of deep neural networks, but its lack of biological plausibility and high computational costs have motivated the ongoing search for alternative training methods. Hebbian learning…