Topic
Riccati equation
About: Riccati equation is a research topic. Over the lifetime, 10428 publications have been published within this topic receiving 210015 citations. The topic is also known as: Riccati's differential equation.
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TL;DR: The existence, uniqueness, and parametrization of Lagrangian invariant subspaces for Hamiltonian matrices is studied and some necessary and sufficient conditions for the existence of Hermitian solutions of algebraic Riccati equations follow as simple corollaries.
Abstract: The existence, uniqueness, and parametrization of Lagrangian invariant subspaces for Hamiltonian matrices is studied. Necessary and sufficient conditions and a complete parametrization are given.
Some necessary and sufficient conditions for the existence of Hermitian solutions of algebraic Riccati equations follow as simple corollaries.
63 citations
TL;DR: A sequence of Lyapunov algebraic equations, whose solutions converge to the solutions of the coupled algebraic Riccati equations of the optimal control problem for jump linear systems are constructed.
Abstract: In this paper we construct a sequence of Lyapunov algebraic equations,whose solutions converge to the solutions of the coupled algebraic Riccati equations of the optimal control problem for jump linear systems. The obtained solutions are positive semidefinite, stabilizing, and unique. The proposed algorithm is extremely efficient from the numerical point of view since it operates only on the reduced-order decoupled Lyapunov equations, Several examples are included to demonstrate the procedure. >
63 citations
TL;DR: In this article, a linear program for an ordinary differential equation is presented, of which a feasible solution defines a continuous piecewise affine linear Lyapunov function for the differential equation.
Abstract: An algorithm that derives a linear program for an ordinary differential equation is presented, of which a feasible solution defines a continuous piecewise affine linear Lyapunov function for the differential equation. The linear program can be generated for an arbitrary region containing an equilibrium of the differential equation. The domain of the Lyapunov function is the region used in the generation of the linear program. The Lyapunov function secures the asymptotic stability of the equilibrium and gives a lower bound on its region of attraction.
63 citations
TL;DR: In this article, the authors considered the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional, where the coefficients of the system and the weigh-ting matrices in the cost functional are adapted processes with respect to the common noise filtration.
Abstract: We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes with respect to the common noise filtration. Semi closed-loop strategies are introduced, and following the dynamic programming approach in [32], we solve the problem and characterize time-consistent optimal control by means of a system of decoupled backward stochastic Riccati differential equations. We present several financial applications with explicit solutions, and revisit in particular optimal tracking problems with price impact, and the conditional mean-variance portfolio selection in incomplete market model.
62 citations
TL;DR: In this paper, a method for the numerical solution of ordinary differential equations is analyzed that is explicit and yet can conserve the quadratic quantities conserved by the equations, which can be a useful alternative to the usual leapfrog technique, in that it does not suffer from the occurrence of blowup phenomena.
62 citations