The linear quadratic (LQ) optimal control problem is studied for a partial differential equation model of a time-varying plug flow tubular reactor. First some properties of the linearized model around a specific equilibrium profile are studied. Next, an LQ-control feedback is computed by using the corresponding operator Riccati differential equation, whose solution can be obtained via a related...

the extended homogeneous balance method is used to construct exacttraveling wave solutions of the maccari system, in which thehomogeneous balance method is applied to solve the riccati equationand the reduced nonlinear ordinary differential equation. many exacttraveling wave solutions of the maccari system equation aresuccessfully obtained.

in this paper, we introduce a family of fractional-order chebyshev functions based on the classical chebyshev polynomials. we calculate and derive the operational matrix of derivative of fractional order $gamma$ in the caputo sense using the fractional-order chebyshev functions. this matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

In this present study analytical method based on Riccati Equation as for converting the Nonlinear Lakshmanan-Porsezian-Daniel (LPD) equation into the nonlinear ODE and finding soliton solutions of this sustem discused. Obtaining solutions are new and obtained from wave transformation. The obtained results show that the presented method is effective and appropriate for solving nonlinear differen...

This paper presents a new characterization of stabilizability via Riccati equation for linear time-varying (LTV) systems. An equivalence is given between the global null-controllability, complete stabilizability and the existence of the solution of some appropriate Riccati differential equation.

The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furtherm...

Both linear time-invariant (LTI) and linear time-varying (LTV) systems are addressed. They are placed in a unified conceptual framework. The characteristic equation for each subclass is formulated as a Riccati equation. Where LTI-systems lead to algebraic Riccati equations, the LTV-case generalizes this result to differential Riccati equations.

This paper presents a simple and efficient method for determining the solution of Riccati differential equation with coefficients rational. In case the differential Galois group of the differential equation (E l) : y = ry, r ∈ C(x) is reducible, we look for the rational solutions of Riccati differential equation θ + θ 2 = r, by reducing the number of check to be made and by accelerating the sea...