Related papers: $\mathcal{H}_2$ optimal model reduction of linear …
We study linear quadratic Gaussian (LQG) control design for linear port-Hamiltonian systems. To this end, we exploit the freedom in choosing the weighting matrices and propose a specific choice which leads to an LQG controller which is…
The main purpose of this article is to prove that, under certain assumptions in a linear prediction setting, optimal methods based upon model reduction and even an optimal predictor can be provided. The optimality is formulated in terms of…
The convergence of policy gradient algorithms hinges on the optimization landscape of the underlying optimal control problem. Theoretical insights into these algorithms can often be acquired from analyzing those of linear quadratic control.…
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes…
A new definition of the $\mathcal{H}_2$ norm for linear switched systems is introduced. It is based on appropriately defined time-domain kernels, or equivalently, on infinite controllability and observability Gramian matrices. Furthermore,…
This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory…
We solve a linear quadratic optimal control problem for sampled-data systems with stochastic delays. The delays are stochastically determined by the last few delays. The proposed optimal controller can be efficiently computed by iteratively…
Policy optimization (PO) is a key ingredient for reinforcement learning (RL). For control design, certain constraints are usually enforced on the policies to optimize, accounting for either the stability, robustness, or safety concerns on…
We study the policy gradient method (PGM) for the linear quadratic Gaussian (LQG) dynamic output-feedback control problem using an input-output-history (IOH) representation of the closed-loop system. First, we show that any dynamic…
This paper is concerned with a backward stochastic linear-quadratic (LQ, for short) optimal control problem with deterministic coefficients. The weighting matrices are allowed to be indefinite, and cross-product terms in the control and…
State-specific thermochemical collisional models are crucial to accurately describe the physics of systems involving nonequilibrium plasmas, but they are also computationally expensive and impractical for large-scale, multi-dimensional…
We propose and study an algorithm for computing a nearest passive system to a given non-passive linear time-invariant system (with much freedom in the choice of the metric defining `nearest', which may be restricted to structured…
The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks, which is an optimization algorithm for finding a local minimum of an objective function. The quantum versions of gradient…
The $H_2$ norm is a commonly used performance metric in the design of estimators. However, $H_2$-optimal estimation of most PDEs is complicated by the lack of transfer function and state-space representations. To address this problem, we…
In this paper we study the linear quadratic regulation (LQR) problem for dynamical systems coupled over large-scale networks and obtain locally computable low-complexity solutions. The underlying large or even infinite networks are…
This paper first presents necessary and sufficient conditions for the solvability of discrete time, mean-field, stochastic linear-quadratic optimal control problems. Then, by introducing several sequences of bounded linear operators, the…
We develop a new method for equality constrained optimization problems based on a sequential cubic programming framework. Each iteration utilizes a step decomposition based on the Jacobian of the constraints into a normal and a tangential…
We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…
We analyse an iterative algorithm to minimize quadratic functions whose Hessian matrix $H$ is the expectation of a random symmetric $d\times d$ matrix. The algorithm is a variant of the stochastic variance reduced gradient (SVRG). In…
We consider the problem of finite-horizon optimal control of a discrete linear time-varying system subject to a stochastic disturbance and fully observable state. The initial state of the system is drawn from a known Gaussian distribution,…