1,721,087 research outputs found
The geometry of the generalized algebraic Riccati equation and of the singular Hamiltonian system
No full textThis paper analyses the properties of the solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. This analysis reveals the presence of a subspace that may provide an appropriate degree of freedom to stabilize the system in the related optimal control problem even in cases where the Riccati equation does not admit a stabilizing solution
On the reduction of the continuous-time generalized algebraic Riccati equation: An effective procedure for solving the singular LQ problem with smooth solutions
No full textThis paper presents a reduction technique for the continuous-time constrained generalized Riccati equation arising in the context of the singular Linear Quadratic (LQ) optimal control problem. This technique allows to express the solutions of the constrained generalized Riccati equation in terms of the solutions of a reduced-order standard Riccati equation. This result is used to provide a solution to the singular LQ problem with closed-loop stability in the case when the allowed controls are restricted to be regular for any initial condition
Multivariable tracking control for MIMO linear systems: An LMI approach
No full textinfo:eu-repo/semantics/publishe
Solvability conditions for the positive real lemma equations in the discrete time
No full textPassivity theory and the positive real lemma have been recognised as two of the cornerstones of modern systems and control theory. As digital control is pervasive in virtually all control applications, developing a general theory on the discrete-time positive real lemma appears to be an important issue. While for minimal realisations the relations between passivity, positive-realness and existence of solutions of the positive real lemma equations is very well understood, it seems fair to say that this is not the case in the discrete-time case, especially when the realisation is non-minimal and no conditions are assumed on left- and/or right-invertibility of the transfer function. The purpose of this study is to present a necessary and sufficient condition for existence of solutions of the positive real equations under the only assumption that the state matrix A is asymptotically stable
On the structure of the solutions of the constrained generalized discrete-time algebraic Riccati equation
No full textThis paper introduces a new decomposition of the constrained generalized discrete-time algebraic Riccati equation arising in linear quadratic optimal control problems into two parts: the first part is an explicit expression which is common to all solutions. The second part can be either a reduced-order discrete-time algebraic Riccati equation with non-singular associated closed-loop matrix, or a symmetric Stein equation
Reduction of discrete algebraic riccati equations: Elimination of generalized eigenvalues on the unit circle
No full textThe purpose of this paper is to introduce a two-stage procedure that can be used to decompose a discrete-time algebraic Riccati equation into a trivial part, a part that is entirely
arbitrary, and a part that can be obtained by computing the set of solutions of a reduced-order Riccati equation whose associated symplectic pencil has no generalized eigenvalues on the unit circle
A discussion on the discrete-time finite-horizon indefinite LQ problem
No full textThe aim of this paper is to compare and discuss some old and new results on the discrete-time finite-horizon linear quadratic (LQ) optimal control problem in the case where the quadratic forms in the performance index are not assumed to be positive semidefinite, but only symmetric. We show in particular that the necessary and sufficient conditions presented in most contributions in the literature for the existence of a solution to this problem are in fact only sufficient. Our aim is to investigate this issue further, by addressing some of the most delicate and counterintuitive issues that arise in this context
On the geometry of the continuous-time generalized algebraic Riccati equation arising in LQ optimal control
Full text linkIn this paper we analyze the properties of the set of solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. In particular, we study the relationship existing between the solutions of the generalized Riccati equation and the output-nulling subspaces of the underlying system. This analysis reveals the presence of a subspace that plays an important role in the solution of the related optimal control problem
Continuous-time singular linear-quadratic control: Necessary and sufficient conditions for the existence of regular solutions
Full text linkThe purpose of this paper is to provide a full understanding of the role that the constrained generalized continuous algebraic Riccati equation plays in singular linear–quadratic (LQ) optimal control. Indeed, in spite of the vast literature on LQ problems, only recently a sufficient condition for the existence of a non-impulsive optimal control has for the first time connected this equation with the singular LQ optimal control problem. In this paper, we establish four equivalent conditions providing a complete picture that connects the singular LQ problem with the constrained generalized continuous algebraic Riccati equation and with the geometric properties of the underlying system
Finite-Horizon Linear-Quadratic Optimal Control with General Boundary Conditions
No full textThe linear-quadratic (LQ) problem is the prototype of a large number of optimal control problems, including the fixed endpoint, the point-to-point, and several H2 control problems, as well as the dual counterparts. In the past 50 years, these problems have been addressed using different techniques, each tailored to their specific structure. It is only in the last 10 years that it was recognized that a unifying framework is available. This framework hinges on formulae that parameterize the solutions of the Hamiltonian differential equation in the continuous-time case and the solutions of the extended symplectic system in the discrete-time case. Whereas traditional techniques involve the solutions of Riccati differential or difference equations, the formulae used here to solve the finite-horizon LQ control problem only rely on solutions of the algebraic Riccati equations. In this entry, aspects of the framework are described within a discrete-time context
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