Related papers: Solving differential Riccati equations: A nonlinea…
Continuous-time algebraic Riccati equations can be found in many disciplines in different forms. In the case of small-scale dense coefficient matrices, stabilizing solutions can be computed to all possible formulations of the Riccati…
In the present paper, we consider large scale nonsymmetric differential matrix Riccati equations with low rank right hand sides. These matrix equations appear in many applications such as control theory, transport theory, applied…
In the present paper, we consider large-scale continuous-time differential matrix Riccati equations having low rank right-hand sides. These equations are generally solved by Backward Differentiation Formula (BDF) or Rosenbrock methods…
The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially…
Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention…
This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal…
The numerical solution of kinetic equations is challenging due to the high dimensionality of the underlying phase space. In this paper, we develop a dynamical low-rank method based on the projector-splitting integrator in tensor-train (TT)…
This paper proposes a novel lifting method which converts the standard discrete-time linear periodic system to an augmented linear time-invariant system. The linear quadratic optimal control is then based on the solution of the…
This paper proposes an effective low-rank alternating direction doubling algorithm (R-ADDA) for computing numerical low-rank solutions to large-scale sparse continuous-time algebraic Riccati matrix equations. The method is based on the…
Algebraic Riccati equations are encountered in many applications of control and engineering problems, e.g., LQG problems and $H^\infty$ control theory. In this work, we study the properties of one type of discrete-time algebraic Riccati…
Algebraic Riccati equations with indefinite quadratic terms play an important role in applications related to robust controller design. While there are many established approaches to solve these in case of small-scale dense coefficients,…
We consider approximations to the solutions of differential Riccati equations in the context of linear quadratic regulator problems, where the state equation is governed by a multiscale operator. Similarly to elliptic and parabolic…
We study in this paper the linear quadratic optimal control (linear quadratic regulation, LQR for short) for discrete-time complex-valued linear systems, which have shown to have several potential applications in control theory. Firstly, an…
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.…
The differential Riccati equation appears in different fields of applied mathematics like control and system theory. Recently Galerkin methods based on Krylov subspaces were developed for the autonomous differential Riccati equation. These…
We consider the numerical solution of large-scale symmetric differential matrix Riccati equations. Under certain hypotheses on the data, reduced order methods have recently arisen as a promising class of solution strategies, by forming…
In the fields of control theory and machine learning, the dynamic low-rank approximation for large-scale matrices has received substantial attention. Considering large-scale semilinear stiff matrix differential equations, we propose…
This paper presents a numerical framework for the low-rank approximation of the solution to three-dimensional parabolic problems. The key contribution of this work is the tensorization process based on a tensor-train reformulation of the…
We study the time-inconsistent linear quadratic optimal control problem for forward-backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research…
The numerical solution of the algebraic Riccati equation is a challenging task especially for very large problem dimensions. In this paper we present a new algorithm that combines the very appealing computational features of projection…