Journal ArticleDOI
A new fundamental solution for differential Riccati equations arising in control
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TLDR
In this article, the authors considered the matrix differential Riccati equation (DRE) as a finite-dimensional solution to a deterministic linear/quadratic control problem and proposed a semiconvex dual of the associated semigroup.About:
This article is published in Automatica.The article was published on 2008-04-01. It has received 44 citations till now. The article focuses on the topics: Riccati equation & Matrix (mathematics).read more
Citations
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Nonlinear Markov Processes and Kinetic Equations
TL;DR: In this article, the authors developed the interplay between probability and analysis in nonlinear Markov evolution, and used probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior.
Journal ArticleDOI
Linear-Quadratic-Gaussian Mixed Games with Continuum-Parametrized Minor Players
Son Luu Nguyen,Minyi Huang +1 more
TL;DR: A mean field linear-quadratic-Gaussian game with a major player and a large number of minor players parametrized by a continuum set has an $\varepsilon$-Nash equilibrium property when applied to the large but finite population model.
Journal ArticleDOI
Improved precise integration method for differential Riccati equation
TL;DR: An improved precise integration method (IPIM) for solving the differential Riccati equation (DRE) is presented and the criterion for choosing two parameters of the PIM is given.
Journal ArticleDOI
On the solution of the Riccati differential equation arising from the LQ optimal control problem
TL;DR: The matrix Riccati differential equation (RDE) that arises from linear-quadratic optimal control problems is considered and explicit closed formulae for the solution of the RDE with a terminal condition using particular solutions of the associated algebraic RicCati equation are established.
Journal ArticleDOI
A Max-plus Dual Space Fundamental Solution for a Class of Operator Differential Riccati Equations
TL;DR: It is demonstrated that this semigroup of max-plus integral operators can be used to propagate all solutions of the operator differential Riccati equation that are initialized from a specified class of initial conditions.
References
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Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control
TL;DR: In this paper, a model problem is formulated for optimal control of semiconcave functions with exit time with the objective of minimizing the cost of the control problem with respect to the exit time.
Book
Idempotent Analysis and Its Applications
TL;DR: In this article, a generalized solution of Bellman's Differential Equation and multiplicative additive asymptotics is presented, which is based on the Maslov Optimziation Theory.
Journal ArticleDOI
Duality and separation theorems in idempotent semimodules
TL;DR: In this article, a nonlinear projection on subsemimodules is introduced, where the projection of a point is the maximal approximation from below of the point in the sub-semimmodule.