Related papers: The Riccati Characteristic Equation
We study the $T$-periodic solutions of the real Riccati differential equation $x' = x^2 + \gamma(t),$ where $x=x(t)$ and $\gamma$ is a $T$-periodic function. Our goal is to define a real-valued discriminant $\Delta_{\gamma}$ that determines…
We propose a new algorithm for a broad class of periodic time-varying Stochastic Game-Theoretic Riccati Differential Equations arising in Zero-Sum Linear-Quadratic Stochastic Differential Games. The algorithm is constructed via dual-layer…
The Riccati equation method is used to establish three new oscillatory criteria for the second order linear ordinary differential equations in the marginal, sub extremal and extremal cases.We show that the first of these criteria implies…
Comparing and recognizing metrics can be extraordinarily difficult because of the group of diffeomorphisms. Two metrics, that could even be the same, could look completely different in different coordinates. This is the gauge problem. The…
Analytic interpolation problems with rationality and derivative constraints are ubiquitous in systems and control. This paper provides a new method for such problems, both in the scalar and matrix case, based on a non-standard Riccati-type…
We consider Homogeneous Algebraic Riccati Equations in the general situation when the matrix of the dynamics can be "mixed". We show that in this case the equation may have infinitely many families of solutions. An analysis of these…
The Riccati equation method is used to establish some global solvability criteria for some classes of second order nonlinear ordinary differential equations. Two oscillation theorems are proved. The results are applied to the Emden - Fowler…
A detailed analysis of the invariant point transformations for the first four partial differential equations which belong to the Complex Burgers` Hierarchy is performed. Moreover, a detailed application of the reduction process through the…
In this paper, we investigate a class of time-inconsistent discrete-time stochastic linear-quadratic optimal control problems, whose time-consistent solutions consist of an open-loop equilibrium control and a linear feedback equilibrium…
Recurrence plots (RPs) are powerful tools for visualizing time series dynamics; however, traditional Recurrence Quantification Analysis (RQA) often relies on global metrics, such as line counting, that can overlook system-specific,…
The main point of this paper is to present a class of equations over integers that one can check if they have a solution by checking a set of inequalities. The prototype of such equations is the equations appearing in the well-known…
We model the behaviour of a relativistic spherically symmetric shearing fluid undergoing gravitational collapse with heat flux. It is demonstrated that the governing equation for the gravitational behaviour is a Riccati equation. We show…
Applying the resolution-scale relativity principle to develop a mechanics of non-differentiable dynamical paths, we find that, in one dimension, stationary motion corresponds to an Ito process driven by the solutions of a Riccati equation.…
A method is presented for parallelizing the computation of solutions to discrete-time, linear-quadratic, finite-horizon optimal control problems, which we will refer to as LQR problems. This class of problem arises frequently in robotic…
Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…
We describe some monotone properties of solutions to second order linear difference equations with real constant coefficients. As an application, we give a characterization of the Fibonacci numbers.
The paper derived differential equations which solve the problem of restoration the motion parameters for a rigid reference frame from the known proper acceleration and angular velocity of its origin as functions of proper time. These…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
We establish a consistency result by comparing two independent notions of generalised solutions to a large class of linear hyperbolic first order PDE systems with constant coefficients, showing that they eventually coincide. The first is…
This paper investigates the properties of the solutions of the generalised discrete algebraic Riccati equation arising from the solution of the classic infinite-horizon linear quadratic control problem. In particular, a geometric analysis…