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.

A new truncation in Painleve analysis

Abstract: The author observes that when the expansion variable in Painleve analysis satisfies a system of Riccati equations, truncation at a level higher than constant level is allowed. This extends the range of exact solutions to nonlinear partial differential equations that one is able to obtain using truncated Painleve expansions.

A new method for suboptimal control of a class of non‐linear systems

Abstract: In this paper, a new non-linear control synthesis technique (θ–D approximation) is discussed. This approach achieves suboptimal solutions to a class of non-linear optimal control problems characterized by a quadratic cost function and a plant model that is affine in control. An approximate solution to the Hamilton–Jacobi–Bellman (HJB) equation is sought by adding perturbations to the cost function. By manipulating the perturbation terms both semi-global asymptotic stability and suboptimality properties are obtained. The new technique overcomes the large-control-for-large-initial-states problem that occurs in some other Taylor series expansion based methods. Also this method does not require excessive online computations like the recently popular state dependent Riccati equation (SDRE) technique. Furthermore, it provides a closed-form non-linear feedback controller if finite number of terms are taken in the series expansion. A scalar problem and a 2-D benchmark problem are investigated to demonstrate the effectiveness of this new technique. Both stability and convergence proofs are given. Copyright © 2004 John Wiley & Sons, Ltd.

Linear-quadratic optimal control problems for mean-field stochastic differential equations — time-consistent solutions

Abstract: Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. Time-inconsistency feature of the problems is carefully investigated. Both open-loop and closed-loop equilibrium solutions are presented for such kind of problems. Open-loop solutions are presented by means of variational method with decoupling of forward-backward stochastic differential equations, which lead to a Riccati equation system lack of symmetry. Closed-loop solutions are presented by means of multi-person differential games, the limit of which leads to a Riccati equation system with a symmetric structure.

Optimal control of stable weakly regular linear systems

Abstract: The paper extends quadratic optimal control theory to weakly regular linear systems, a rather broad class of infinite-dimensional systems with unbounded control and observation operators. We assume that the system is stable (in a sense to be defined) and that the associated Popov function is bounded from below. We study the properties of the optimally controlled system, of the optimal cost operatorX, and the various Riccati equations which are satisfied byX. We introduce the concept of an optimal state feedback operator, which is an observation operator for the open-loop system, and which produces the optimal feedback system when its output is connected to the input of the system. We show that if the spectral factors of the Popov function are regular, then a (unique) optimal state feedback operator exists, and we give its formula in terms ofX. Most of the formulas are quite reminiscent of the classical formulas from the finite-dimensional theory. However, an unexpected factor appears both in the formula of the optimal state feedback operator as well as in the main Riccati equation. We apply our theory to an extensive example.