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Numerical error bound of optimal control for homogeneous linear systems

Daraghmeh Adnan, Qatanani Naji

Archives of Control Sciences

2019

Vol. 29, No. 2

323--337

In this article we focus on the balanced truncation linear quadratic regulator (LQR) with constrained states and inputs. For closed-loop, we want to use the LQR to find an optimal control that minimizes the objective function which called "the quadratic cost function” with respect to the constraints on the states and the control input. In order to do that we have used formal asymptotes for the Pontryagin maximum principle (PMP) and we introduce an approach using the so called The Hamiltonian Function and the underlying algebraic Riccati equation. The theoretical results are validated numerically to show that the model order reduction based on open-loop balancing can also give good closed-loop performance.

Characteristic Impedance of Power Lines with Ground Wires

Rizzo R., Andreotti A., Pierno A., Assante D.

Przegląd Elektrotechniczny

2013

R. 89, nr 5

11-14

In the paper the characteristic impedance of a power line equipped with shield wires is analysed. The solution to the problem is found by means of a non-symmetric algebraic Riccati equation. Solutions are presented for practical line configurations.

W artykule przedstawiono analizę impedancji charakterystycznej linii elektroenergetycznej z ekranowanymi kablami w praktycznym zastosowaniu konfiguracyjnym. W analizie wykorzystano niesymetryczne równanie Riccatiego.

On a degenerate Riccati equation

Kesavan S., Raymond J. P.

Control and Cybernetics

2009

Vol. 38, no 4B

1393-1410

In this paper, we study the existence of solutions to a degenerate algebraic Riccati equation associated to an optimal control problem with infinite time horizon. Under some assumptions on the control system, we can select a solution to this Riccati equation providing a feedback control law able to stabilize the system.

Matrix Quadratic Equations, Column/row Reduced Factorizations and an Inertia Theorem for Matrix Polynomials

Karelin I., Lerer L.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 6

1285-1310

It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial G(lambda) (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of G(lambda). The proof of these results depends heavily on a new inertia theorem for matrix polynomials which is also one of the main results in this paper.