Related papers: Solving Linear-Quadratic Stochastic Control Proble…
The Linear Quadratic Gaussian (LQG) problem is a classic and widely studied model in optimal control, providing a fundamental framework for designing controllers for linear systems subject to process and observation noises. In recent years,…
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…
We consider the problem of stochastic optimal control in the presence of an unknown disturbance. We characterize the disturbance via empirical characteristic functions, and employ a chance constrained approach. By exploiting properties of…
This work proposes a method for solving linear stochastic optimal control (SOC) problems using sum of squares and semidefinite programming. Previous work had used polynomial optimization to approximate the value function, requiring a high…
The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…
We consider some certain nonlinear perturbations of the stochastic linear-quadratic optimization problems and study the connections between their solutions and the corresponding Markovian backward stochastic diferential equations (BSDEs).…
This paper studies the stochastic optimal control problem for systems with unknown dynamics. First, an open-loop deterministic trajectory optimization problem is solved without knowing the explicit form of the dynamical system. Next, a…
In this paper, we consider a linear quadratic (LQ) optimal control problem in both finite and infinite dimensions. We derive an asymptotic expansion of the value function as the fixed time horizon T tends to infinity. The leading term in…
Many real world stochastic control problems suffer from the "curse of dimensionality". To overcome this difficulty, we develop a deep learning approach that directly solves high-dimensional stochastic control problems based on Monte-Carlo…
This paper revisits the classical Linear Quadratic Gaussian (LQG) control from a modern optimization perspective. We analyze two aspects of the optimization landscape of the LQG problem: 1) connectivity of the set of stabilizing controllers…
In this paper, we present an equivalent convex optimization formulation for discrete-time stochastic linear systems subject to linear chance constraints, alongside a tight convex relaxation for quadratic chance constraints. By lifting the…
Control of linear dynamics with multiplicative noise naturally introduces robustness against dynamical uncertainty. Moreover, many physical systems are subject to multiplicative disturbances. In this work we show how these dynamics can be…
It is a longstanding unsolved problem to characterize the optimal feedbacks for general SLQs (i.e., stochastic linear quadratic control problems) with random coefficients in infinite dimensions; while the same problem but in finite…
This paper considers a risk-sensitive optimal control problem for a field-mediated interconnection of a quantum plant with a coherent (measurement-free) quantum controller. The plant and the controller are multimode open quantum harmonic…
We study the sample efficiency of domain randomization and robust control for the benchmark problem of learning the linear quadratic regulator (LQR). Domain randomization, which synthesizes controllers by minimizing average performance over…
Domain randomization is a simple, effective, and flexible scheme for obtaining robust feedback policies aimed at reducing the sim-to-real gap due to model mismatch. While domain randomization methods have yielded impressive demonstrations…
We consider a linear stochastic differential equation with stochastic drift and multiplicative noise. We study the problem of approximating its solution with the process that solves the equation where the possibly stochastic drift is…
This paper studies the data-driven synthesis of linear quadratic integral (LQI) controllers for continuous-time systems. The objective is to achieve optimal state-feedback control with integral action for reference tracking using only…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…