Related papers: Penalized Weighted Trace Minimization for Optimal …
This paper studies the linear-quadratic (LQ) optimal control problem of a class of systems governed by the first-order hyperbolic partial differential equations (PDEs) with final state constraints. The main contribution is to present the…
We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…
This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
This paper is concerned with a discrete-time mean-field stochastic linear-quadratic optimal control problem arose from financial application. Through matrix dynamical optimization method, a group of linear feedback controls is investigated.…
This work is concerned with a class of optimal control problems governed by a partial differential equation that are motivated by an application in radiotherapy treatment planning, where the primary design objective is to minimize the…
We propose a computational framework for replacing the repeated numerical solution of differential Riccati equations in finite-horizon Linear Quadratic Regulator (LQR) problems by a learned operator surrogate. Instead of solving a nonlinear…
The purpose of this paper is to investigate the role that the continuous-time generalised Riccati equation plays within the context of singular linear-quadratic optimal control. This equation has been defined following the analogy with the…
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…
A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with quadratic cost functional. A notion of equilibrium control is introduced, which can be regarded as a…
We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…
We study sparse solutions of optimal control problems governed by PDEs with uncertain coefficients. We propose two formulations, one where the solution is a deterministic control optimizing the mean objective, and a formulation aiming at…
This paper presents a pioneering approach to solving the linear quadratic regulation (LQR) and linear quadratic tracking (LQT) problems with constrained inputs using a novel off-policy continuous-time Q-learning framework. The proposed…
Hybrid optimal control problems are studied for a general class of hybrid systems where autonomous and controlled state jumps are allowed at the switching instants and in addition to terminal and running costs switching between discrete…
In this paper we study the quadratic regulator problem for a process governed by a Volterra integral equation in ${\mathbb R}^n$. Our main goal is the proof that it is possible to associate a Riccati differential equation to this quadratic…
This paper is concerned with optimal control problems for control systems in continuous time, and interacting particle system methods designed to construct approximate control solutions. Particular attention is given to the linear quadratic…
The second part of our study is devoted to an analysis of the exactness of penalty functions for optimal control problems with terminal and pointwise state constraints. We demonstrate that with the use of the exact penalty function method…
Different from most of the previous works, this paper provides a thorough solution to the fundamental problems of linear-quadratic (LQ) control and stabilization for discrete-time mean-field systems under basic assumptions. Firstly, the…
This paper addresses the problem of computing optimal impedance schedules for legged locomotion tasks involving complex contact interactions. We formulate the problem of impedance regulation as a trade-off between disturbance rejection and…
In this work we recast parametrized time dependent optimal control problems governed by partial differential equations in a saddle point formulation and we propose reduced order methods as an effective strategy to solve them. Indeed, on one…