The generalised discrete algebraic Riccati equation in linear-quadratic optimal control

The generalised discrete algebraic Riccati equation in linear-quadratic optimal control

This paper investigates the properties of the solutions of the generalised discrete algebraic Riccati equation arising from the classic infinitehorizon linear quadratic (LQ) control problem. In particular, a geometric analysis is used to study the relationship existing between the solutions of the generalised Riccati equation and the output-nulling subspaces of the underlying system and the cor...

The discrete Riccati equation of optimal control

Indefinite Stochastic Linear Quadratic Control and Generalized Differential Riccati Equation

We consider a stochastic linear–quadratic (LQ) problem with possible indefinite cost weighting matrices for the state and the control. An outstanding open problem is to identify an appropriate Riccati-type equation whose solvability is equivalent to the solvability of this possibly indefinite LQ problem. In this paper we introduce a new type of differential Riccati equation, called the generali...

Differential-algebraic Riccati Decoupling for Linear-quadratic Optimal Control Problems for Semi-explicit Index-2 DAEs

We investigate existence and structure of solutions to quadratic control problems with semi-explicit differential algebraic constraints. By means of an equivalent index-1 formulation we identify conditions for the unique existence of optimal solutions. Knowing of the existence of an optimal input we provide a representation of the associated feedback-law via a Riccatilike decoupling that is for...

A characterization of solutions of the discrete-time algebraic Riccati equation based on quadratic difference forms

This paper is concerned with a characterization of all symmetric solutions to the discrete-time algebraic Riccati equation (DARE). Dissipation theory and quadratic difference forms from the behavioral approach play a central role in this paper. Along the line of the continuous-time results due to Trentelman and Rapisarda [H.L. Trentelman, P. Rapisarda, Pick matrix conditions for sign-definite s...