Related papers: Numerical Method for a Class of Algebraic Riccati …
Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in various control theory applications. This work demonstrates that when the matrix coefficients of the equation are quasiseparable, the solution…
Considering infinite-horizon, discrete-time, linear quadratic, N-player dynamic games with scalar dynamics, a graphical representation of feedback Nash equilibrium solutions is provided. This representation is utilised to derive conditions…
The work is devoted to the development of numerical methods for computing "formal solutions" of interval systems of linear algebraic equations. These solutions are found in Kaucher interval arithmetic, which extends and completes the…
This paper is concerned with the closed-loop solvability of one kind of linear-quadratic Stackelberg stochastic differential game, where the coefficients are deterministic. The notion of the closed-loop solvability is introduced, which…
Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
There has been significant recent progress in algorithms for approximation of Nash equilibrium in large two-player zero-sum imperfect-information games and exact computation of Nash equilibrium in multiplayer strategic-form games. While…
We are concerned with efficient numerical methods for stochastic continuous-time algebraic Riccati equations (SCARE). Such equations frequently arise from the state-dependent Riccati equation approach which is perhaps the only systematic…
We consider a class of Wasserstein distributionally robust Nash equilibrium problems, where agents construct heterogeneous data-driven Wasserstein ambiguity sets using private samples and radii, in line with their individual risk-averse…
In this note, we study a class of deterministic finite-horizon linear-quadratic difference games with coupled affine inequality constraints involving both state and control variables. We show that the necessary conditions for the existence…
In this paper, we first address a linear quadratic mean-field game problem with a leader-follower structure. By adopting a Riccati-type approach, we show how one can obtain a state-feedback representation of the pairs of strategies which…
We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and…
Differential algebraic Riccati equations are at the heart of many applications in control theory. They are time-depent, matrix-valued, and in particular nonlinear equations that require special methods for their solution. Low-rank methods…
We propose a framework to compute approximate Nash equilibria in integer programming games with nonlinear payoffs, i.e., simultaneous and non-cooperative games where each player solves a parametrized mixed-integer nonlinear program. We…
In this paper we present a numerical scheme for the resolution of matrix Riccati equation, usualy used in control problems. The scheme is unconditionnaly stable and the solution is definite positive at each time step of the resolution. We…
We present an efficient algorithm to compute the explicit open-loop solution to both finite and infinite-horizon dynamic games subject to state and input constraints. Our approach relies on a multiparametric affine variational inequality…
We study Markov perfect equilibria in continuous-time dynamic games with finitely many symmetric players. The corresponding Nash system reduces to the Nash-Lasry-Lions equation for the common value function, also known as the master…
In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati equation arising in optimal control and optimal filtering problems into two parts corresponding to an additive decomposition X=X0+D of…
Stochastic algebraic Riccati equations, also known as rational algebraic Riccati equations, arising in linear-quadratic optimal control for stochastic linear time-invariant systems, were considered to be not easy to solve. The-state-of-art…
We prove a conjecture about the minimal nonnegative solutions of algebraic Riccati equations associated with reducible singular M-matrices. The result enhances our understanding of the behaviour of doubling algorithms for finding the…