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We tackle a nonlinear optimal control problem for a stochastic differential equation in Euclidean space and its state-linear counterpart for the Fokker-Planck-Kolmogorov equation in the space of probabilities. Our approach is founded on a…
We introduce an approximation method to solve an optimal control problem via the Lagrange dual of its weak formulation. It is based on a sum-of-squares representation of the Hamiltonian, and extends a previous method from polynomial…
We investigate feedback control for infinite horizon optimal control problems for partial differential equations. The method is based on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is…
We present a semi-real-time algorithm for minimal-time optimal path planning based on optimal control theory, dynamic programming, and Hamilton-Jacobi (HJ) equations. Partial differential equation (PDE) based optimal path planning methods…
We address the optimal control problems arising from partial differential equations with large discrete dimensional control systems. To obtain reduced order models, we find basis elements from the canonical polyadic (CP) decomposition.…
This paper studies the problem of constructing control Lyapunov functions (CLFs) and feedback stabilization strategies for deterministic nonlinear control systems described by ordinary differential equations. Many numerical methods for…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
We introduce a numerical method, based on modified hat functions, for solving a class of fractional optimal control problems. In our scheme, the control and the fractional derivative of the state function are considered as linear…
These notes present preliminary results regarding two different approximations of linear infinite-horizon optimal control problems arising in model predictive control. Input and state trajectories are parametrized with basis functions and a…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…
This paper investigates large-population stochastic control problems in which agents share their state information and cooperate to minimize a convex cost functional. The latter is decomposed into individual and coupling costs, with the…
We study linear-quadratic stochastic optimal control problems with bilinear state dependence for which the underlying stochastic differential equation (SDE) consists of slow and fast degrees of freedom. We show that, in the same way in…
We propose an {\em implementable} numerical scheme for the discretization of linear-quadratic optimal control problems involving SDEs in higher dimensions with {\em control constraint}. For time discretization, we employ the implicit Euler…
We describe a convex programming approach to the calculation of lower bounds on the minimum cost of constrained decentralized control problems with nonclassical information structures. The class of problems we consider entail the…
We consider the problem of discounted optimal state-feedback regulation for general unknown deterministic discrete-time systems. It is well known that open-loop instability of systems, non-quadratic cost functions and complex nonlinear…
In this paper, we aim to solve the high dimensional stochastic optimal control problem from the view of the stochastic maximum principle via deep learning. By introducing the extended Hamiltonian system which is essentially an FBSDE with a…
We revisit the linear programming approach to deterministic, continuous time, infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure…
This paper presents a novel method to synthesize stochastic control Lyapunov functions for a class of nonlinear, stochastic control systems. In this work, the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation is…
This paper presents an efficient numerical method for solving fractional optimal control problems using an operational matrix for a fractional wavelet. Using well-known formulae such as Caputo and Riemann-Liouville operators to determine…
Distributed control problems under some specific information constraints can be formulated as (possibly infinite dimensional) convex optimization problems. The underlying motivation of this work is to develop an understanding of the optimal…