The Experts below are selected from a list of 288 Experts worldwide ranked by ideXlab platform
Lorenzo Ntogramatzidis - One of the best experts on this subject based on the ideXlab platform.
-
the geometry of the generalized algebraic Riccati Equation and of the singular hamiltonian system
Linear & Multilinear Algebra, 2019Co-Authors: Lorenzo Ntogramatzidis, Augusto FerranteAbstract:This 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 ...
-
on the reduction of the continuous time generalized algebraic Riccati Equation an effective procedure for solving the singular lq problem with smooth solutions
Automatica, 2018Co-Authors: Augusto Ferrante, Lorenzo NtogramatzidisAbstract:Abstract This 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.
-
the geometry of the generalized algebraic Riccati Equation and of the singular hamiltonian system
arXiv: Optimization and Control, 2017Co-Authors: Lorenzo Ntogramatzidis, Augusto FerranteAbstract:This paper analyzes 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.
-
the discrete time generalized algebraic Riccati Equation order reduction and solutions structure
Systems & Control Letters, 2015Co-Authors: Lorenzo Ntogramatzidis, Augusto FerranteAbstract:Abstract In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati Equation arising in optimal control and optimal filtering problems into two parts corresponding to an additive decomposition X = X 0 + Δ of each solution X : The first part is trivial, in the sense that it is an explicit expression of the addend X 0 which is common to all solutions, so that it does not depend on the particular X . The second part can be–depending on the structure of the considered generalized Riccati Equation–either a reduced-order discrete-time regular algebraic Riccati Equation whose associated closed-loop matrix is non-singular, or a symmetric Stein Equation. The proposed reduction is explicit, so that it can be easily implemented in a software package that uses only standard linear algebra procedures.
-
the discrete time generalized algebraic Riccati Equation order reduction and solutions structure
arXiv: Optimization and Control, 2014Co-Authors: Lorenzo Ntogramatzidis, Augusto FerranteAbstract:In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati Equation arising in optimal control and optimal filtering problems into two parts corresponding to an additive decomposition X=X0+D of each solution X: The first part is an explicit expression of the addend X0 which is common to all solutions, and does not depend on the particular X. The second part can be either a reduced-order discrete-time regular algebraic Riccati Equation whose associated closed-loop matrix is non-singular, or a symmetric Stein Equation.
Augusto Ferrante - One of the best experts on this subject based on the ideXlab platform.
-
the geometry of the generalized algebraic Riccati Equation and of the singular hamiltonian system
Linear & Multilinear Algebra, 2019Co-Authors: Lorenzo Ntogramatzidis, Augusto FerranteAbstract:This 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 ...
-
on the reduction of the continuous time generalized algebraic Riccati Equation an effective procedure for solving the singular lq problem with smooth solutions
Automatica, 2018Co-Authors: Augusto Ferrante, Lorenzo NtogramatzidisAbstract:Abstract This 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.
-
the geometry of the generalized algebraic Riccati Equation and of the singular hamiltonian system
arXiv: Optimization and Control, 2017Co-Authors: Lorenzo Ntogramatzidis, Augusto FerranteAbstract:This paper analyzes 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.
-
the discrete time generalized algebraic Riccati Equation order reduction and solutions structure
Systems & Control Letters, 2015Co-Authors: Lorenzo Ntogramatzidis, Augusto FerranteAbstract:Abstract In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati Equation arising in optimal control and optimal filtering problems into two parts corresponding to an additive decomposition X = X 0 + Δ of each solution X : The first part is trivial, in the sense that it is an explicit expression of the addend X 0 which is common to all solutions, so that it does not depend on the particular X . The second part can be–depending on the structure of the considered generalized Riccati Equation–either a reduced-order discrete-time regular algebraic Riccati Equation whose associated closed-loop matrix is non-singular, or a symmetric Stein Equation. The proposed reduction is explicit, so that it can be easily implemented in a software package that uses only standard linear algebra procedures.
-
the discrete time generalized algebraic Riccati Equation order reduction and solutions structure
arXiv: Optimization and Control, 2014Co-Authors: Lorenzo Ntogramatzidis, Augusto FerranteAbstract:In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati Equation arising in optimal control and optimal filtering problems into two parts corresponding to an additive decomposition X=X0+D of each solution X: The first part is an explicit expression of the addend X0 which is common to all solutions, and does not depend on the particular X. The second part can be either a reduced-order discrete-time regular algebraic Riccati Equation whose associated closed-loop matrix is non-singular, or a symmetric Stein Equation.
Xuemin Shen - One of the best experts on this subject based on the ideXlab platform.
-
solution of the singularly perturbed matrix difference Riccati Equation
International Journal of Systems Science, 1992Co-Authors: Xuemin ShenAbstract:Abstract A new method is introduced to obtain the solution of the singularly perturbed matrix difference Riccati Equation by solving two reduced order linear Equations. The order reduction is achieved via the use of the Chang's transformation applied to the hamiltonian matrix of a singularly perturbed linear-quadratic control problem. Since the decoupling transformation can be obtained up to an arbitrary degree of accuracy at very low cost, this approach produces an efficient numerical method for solving singularly perturbed difference Riccati Equations. The results are verified through a real world example.
Zoran Gajic - One of the best experts on this subject based on the ideXlab platform.
-
solving the singularly perturbed matrix differential Riccati Equation a lyapunov Equation approach
Advances in Computing and Communications, 2010Co-Authors: Thang Nguyen, Zoran GajicAbstract:In this paper, we study the finite time (horizon) optimal control problem for singularly perturbed systems. The solution is obtained in terms of the corresponding solution of the algebraic Riccati Equation and the decomposition of the singularly perturbed differential Lyapunov Equation into reduced-order differential Lyapunov/Sylvester Equations. An illustrative numerical example is provided to show the efficiency of the proposed approach.
-
exact slow fast decomposition of the singularly perturbed matrix differential Riccati Equation
Applied Mathematics and Computation, 2010Co-Authors: Sarah Koskie, C Coumarbatch, Zoran GajicAbstract:In this paper the Hamiltonian matrix formulation of the Riccati Equation is used to derive the reduced-order pure-slow and pure-fast matrix differential Riccati Equations of singularly perturbed systems. These pure-slow and pure-fast matrix differential Riccati Equations are obtained by decoupling the singularly perturbed matrix differential Riccati Equation of dimension n"1+n"2 into the pure-slow regular matrix differential Riccati Equation of dimension n"1 and the pure-fast stiff matrix differential Riccati Equation of dimension n"2. A formula is derived that produces the solution of the original singularly perturbed matrix differential Riccati Equation in terms of solutions of the pure-slow and pure-fast reduced-order matrix differential Riccati Equations and solutions of two reduced-order initial value problems. In addition to its theoretical importance, the main result of this paper can also be used to implement optimal filtering and control schemes for singularly perturbed linear time-invariant systems independently in pure-slow and pure-fast time scales.
-
solving the matrix differential Riccati Equation a lyapunov Equation approach
IEEE Transactions on Automatic Control, 2010Co-Authors: Thang Nguyen, Zoran GajicAbstract:In this technical note, we investigate a solution of the matrix differential Riccati Equation that plays an important role in the linear quadratic optimal control problem. Unlike many methods in the literature, the approach that we propose employs the negative definite anti-stabilizing solution of the matrix algebraic Riccati Equation and the solution of the matrix differential Lyapunov Equation. An illustrative numerical example is provided to show the efficiency of our approach.
Thang Nguyen - One of the best experts on this subject based on the ideXlab platform.
-
solving the singularly perturbed matrix differential Riccati Equation a lyapunov Equation approach
Advances in Computing and Communications, 2010Co-Authors: Thang Nguyen, Zoran GajicAbstract:In this paper, we study the finite time (horizon) optimal control problem for singularly perturbed systems. The solution is obtained in terms of the corresponding solution of the algebraic Riccati Equation and the decomposition of the singularly perturbed differential Lyapunov Equation into reduced-order differential Lyapunov/Sylvester Equations. An illustrative numerical example is provided to show the efficiency of the proposed approach.
-
solving the matrix differential Riccati Equation a lyapunov Equation approach
IEEE Transactions on Automatic Control, 2010Co-Authors: Thang Nguyen, Zoran GajicAbstract:In this technical note, we investigate a solution of the matrix differential Riccati Equation that plays an important role in the linear quadratic optimal control problem. Unlike many methods in the literature, the approach that we propose employs the negative definite anti-stabilizing solution of the matrix algebraic Riccati Equation and the solution of the matrix differential Lyapunov Equation. An illustrative numerical example is provided to show the efficiency of our approach.
