Linear quadratic optimal control, dissipativity, and para-Hermitian matrix polynomials
نویسنده
چکیده
In this paper we will look at two results in which a special para-Hermitian matrix polynomial appears in linear quadratic systems theory. The first result constitutes the first step in a dissipativity check. The second result shows that dissipativity is equivalent to the solvability of the infinitehorizon linear quadratic optimal control problem and that its solutions are given by the behavior specified by the special para-Hermitian matrix polynomial. The results can be used to derive efficient eigenvalue methods for linear first-order statespace systems.
منابع مشابه
Turnpike properties and strict dissipativity for discrete time linear quadratic optimal control problems
We investigate turnpike behaviour of discrete time optimal control problems with linear dynamics and linear-quadratic cost functions including state and control constraints. We give necessary and sufficient conditions in terms of spectral criteria and matrix inequalities. As important tools we use the concepts of strict dissipativity and a new property called strict pre-dissipativity of a syste...
متن کاملNumerical Solution of Eigenvalue Problems for Alternating Matrix Polynomials and Their Application in Control Problems for Descriptor Systems
Numerical methods for eigenvalue problems associated to alternating matrix pencils and polynomials are discussed. These problems arise in a large number of control applications for differential-algebraic equations ranging from regular and singular linear-quadratic optimal and robust control to dissipativity checking. We present a survey of several of these applications and give a systematic ove...
متن کاملHaar Matrix Equations for Solving Time-Variant Linear-Quadratic Optimal Control Problems
In this paper, Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems. Firstly, using necessary conditions for optimality, the problem is changed into a two-boundary value problem (TBVP). Next, Haar wavelets are applied for converting the TBVP, as a system of differential equations, in to a system of matrix algebraic equations...
متن کاملThe Numerical Solution of Some Optimal Control Systems with Constant and Pantograph Delays via Bernstein Polynomials
In this paper, we present a numerical method based on Bernstein polynomials to solve optimal control systems with constant and pantograph delays. Constant or pantograph delays may appear in state-control or both. We derive delay operational matrix and pantograph operational matrix for Bernstein polynomials then, these are utilized to reduce the solution of optimal control with constant...
متن کاملConvergence Properties of Hermitian and Skew Hermitian Splitting Methods
In this paper we consider the solutions of linear systems of saddle point problems. By using the spectrum of a quadratic matrix polynomial, we study the eigenvalues of the iterative matrix of the Hermitian and skew Hermitian splitting method.
متن کامل