Related papers: An Efficient Algorithm for Periodic Riccati Equati…
In this paper we consider a class of conjugate discrete-time Riccati equations, arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Under mild and reasonable assumptions, the existence of…
This paper thoroughly investigates stochastic linear-quadratic optimal control problems with the Markovian regime switching system, where the coefficients of the state equation and the weighting matrices of the cost functional are random.…
In this paper, we investigate the minimal time problem for the guidance of a rocket, whose motion is described by its attitude kinematics and dynamics but also by its orbit dynamics. Our approach is based on a refined geometric study of the…
This article explores the discrete-time stochastic optimal LQR control with delay and quadratic constraints. The inclusion of delay, compared to delay-free optimal LQR control with quadratic constraints, significantly increases the…
This article is concerned with the optimal boundary control of the Maxwell system. We consider a Bolza problem, where the quadratic functional to be minimized penalizes the electromagnetic field at a given final time. Since the state is…
In this paper, the open-loop, closed-loop, and weak closed-loop solvability for discrete-time linear-quadratic (LQ) control problem is considered due to the fact that it is always open-loop optimal solvable if the LQ control problem is…
A method is presented for parallelizing the computation of solutions to discrete-time, linear-quadratic, finite-horizon optimal control problems, which we will refer to as LQR problems. This class of problem arises frequently in robotic…
In this article, the focus is mainly on gaining the optimal control for the unstable power system models and stabilizing them through the Riccati-based feedback stabilization process with sparsity-preserving techniques. We are to find the…
We study a stochastic control problem for continuous multidimensional martingales with fixed quadratic variation. In a radially symmetric environment, we are able to find an explicit solution to the control problem and find an optimal…
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the…
A linear-quadratic (LQ, for short) optimal control problem is considered for mean-field stochastic differential equations with constant coefficients in an infinite horizon. The stabilizability of the control system is studied followed by…
In this article, we focus on a periodic resource allocation problem applied to a dynamical system which comes from a biological system. More precisely, we consider a system with $N$ resources and $N$ activities, each activity use the…
In this paper we develop a novel, discrete-time optimal control framework for mechanical systems with uncertain model parameters. We consider finite-horizon problems where the performance index depends on the statistical moments of the…
A study of the linear quadratic (LQ) control problem on a finite time interval for a model equation in Hilbert spaces which comprehends the memory of the inputs was performed recently by the authors. The outcome included a closed-loop…
We propose a simple and original approach for solving linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon pro\-blems, and allow notably some coefficients to be stochastic. Extension to…
We generalize the classical theory on algebraic Riccati equations and optimization to infinite-dimensional well-posed linear systems, thus completing the work of George Weiss, Olof Staffans and others. We show that the optimal control is…
It is well known that conservative mechanical systems exhibit local oscillatory behaviours due to their elastic and gravitational potentials, which completely characterise these periodic motions together with the inertial properties of the…
We present high order explicit geometric integrators to solve linear-quadratic optimal control problems and $N$-player differential games. These problems are described by a system coupled non-linear differential equations with boundary…
This paper presents sufficient conditions for small-time local controllability of a control-affine system that describes the rotational motion of a satellite in a circular orbit. The satellite is modeled as a rigid body subject to…
Optimization of low-thrust trajectories that involve a larger number of orbit revolutions is considered a challenging problem. This paper describes a high-precision symplectic method and optimization techniques to solve the minimum-energy…