Related papers: Optimal Feedback Law Recovery by Gradient-Augmente…
A learning based method for obtaining feedback laws for nonlinear optimal control problems is proposed. The learning problem is posed such that the open loop value function is its optimal solution. This infinite dimensional, function space,…
We address finding the semi-global solutions to optimal feedback control and the Hamilton--Jacobi--Bellman (HJB) equation. Using the solution of an HJB equation, a feedback optimal control law can be implemented in real-time with minimum…
We propose a variant of consensus-based optimization (CBO) algorithms, controlled-CBO, which introduces a feedback control term to improve convergence towards global minimizers of non-convex functions in multiple dimensions. The feedback…
A learning technique for finite horizon optimal control problems and its approximation based on polynomials is analyzed. It allows to circumvent, in part, the curse dimensionality which is involved when the feedback law is constructed by…
Using a recently introduced representation of the second order adjoint state as the solution of a function-valued backward stochastic partial differential equation (SPDE), we calculate the viscosity super- and subdifferential of the value…
In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost…
This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…
We consider the problem of optimal sparse output feedback controller synthesis for continuous linear time invariant systems when the feedback gain is static and subject to specified structural constraints. Introducing an additional term…
Learning optimal feedback control laws capable of executing optimal trajectories is essential for many robotic applications. Such policies can be learned using reinforcement learning or planned using optimal control. While reinforcement…
This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability…
We present a neural network approach for approximating the value function of high-dimensional stochastic control problems. Our training process simultaneously updates our value function estimate and identifies the part of the state space…
A self-learning approach for optimal feedback gains for finite-horizon nonlinear continuous time control systems is proposed and analysed. It relies on parameter dependent approximations to the optimal value function obtained from a family…
A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated formal differentiation of…
We consider the problem of nonlinear stochastic optimal control. This problem is thought to be fundamentally intractable owing to Bellman's "curse of dimensionality". We present a result that shows that repeatedly solving an open-loop…
A Hamiltonian algorithm, both theoretical and numerical, to obtain the reduced equations implementing Pontryagine's Maximum Principle for singular linear-quadratic optimal control problems is presented. This algorithm is inspired on the…
In high-dimensional statistics, variable selection recovers the latent sparse patterns from all possible covariate combinations. This paper proposes a novel optimization method to solve the exact L0-regularized regression problem, which is…
We propose a neural network approach that yields approximate solutions for high-dimensional optimal control problems and demonstrate its effectiveness using examples from multi-agent path finding. Our approach yields controls in a feedback…
We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…
We derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ODEs and a PDE of Vlasov-type. Such problems arise naturally as ${\Gamma}$-limits of optimal control problems subject to ODE…
We consider the co-design problem of sparse output feedback and row/column-sparse output matrix. A row-sparse (resp. column-sparse) output matrix implies a small number of outputs (resp. sensor measurements). We impose…