The initial value problem for a matrix Riccati differential equation associated with an M -matrix is known to have a global solution X(t) on [0,∞) when X(0) takes values from a suitable set of nonnegative matrices. It is also known, except for the critical case, that as t goes to infinity X(t) converges to the minimal nonnegative solution of the corresponding algebraic Riccati equation. In this...

This paper proposes a sampling based kinodynamic planning technique for planning informative trajectories for a sensing robot in a spatiotemporal environmental field. The robot uses a Kalman-Bucy filter to estimate the spatiotemporal field. The proposed algorithm finds a trajectory for the robot that minimizes a metric on the error covariance matrix of the field estimate. Since the error covari...

In this paper we recall discrete order preserving property related to the Riccati matrix equation. We present results obtained by applying solutions of differential

The Linear-Quadratic (LQ) optimal control problem is studied for a class of first-order hyperbolic partial differential equation models by using a nonlinear infinite-dimensional (distributed parameter) Hilbert state-space description. First the dynamical properties of the linearized model around some equilibrium profile are studied. Next the LQ-feedback operator is computed by using the corresp...

Uncertain differential game investigates interactive decision making of players over time and the system dynamics can be described by an uncertain differential equation. This paper goes further to study the two players zero-sum uncertain differential game. In order to guarantee the saddle-point Nash equilibrium, a Max-Min theorem is provided. Furthermore, when the system dynamics is described b...

This technical report describes three approaches for solving the Differential Riccati Equation (DRE), by means of the Backward Differentiation Formula (BDF) and resolution of the corresponding implicit equation, using Newton's method. These approaches are based on: GMRES method, resolution of Sylvester equation and fixed point method. The role and use of DRE is especially important in optimal c...

Given a particular solution of a one-dimensional stationary Schrödinger equation this equation of second order can be reduced to a first order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or thr...