An Approximation Theorem for the Algebraic Riccati Equation
نویسندگان
چکیده
منابع مشابه
An Approximation Theorem for the Algebraic Riccati Equation
For an infinite-dimensional linear quadratic control problem in Hilbert space, approximation of the solution of the algebraic Riccati operator equation in the strong operator topology is considered under conditions weaker than uniform exponential stability of the approximating systems. As an application, strong convergence of the approximating Riccati operators in case of a previously developed...
متن کاملAn exponential spline for solving the fractional riccati differential equation
In this Article, proposes an approximation for the solution of the Riccati equation based on the use of exponential spline functions. Then the exponential spline equations are obtained and the differential equation of the fractional Riccati is discretized. The effect of performing this mathematical operation is obtained from an algebraic system of equations. To illustrate the benefits of the me...
متن کاملAn efficient algorithm for the discrete-time algebraic Riccati equation
In this paper the authors develop a new algorithm to solve the standard discrete-time algebraic Riccati equation by using a skewHamiltonian transformation and the square-root method. The algorithm is structure-preserving and efficient because the Hamiltonian structure is fully exploited and only orthogonal transformations are used. The efficiency and stability of the algorithm are analyzed. Num...
متن کاملAnalysis of an Iteration Method for the Algebraic Riccati Equation
We consider a recently published method for solving algebraic Riccati equations. We present a new perspective on this method in terms of the underlying linear-quadratic optimal control problem: we prove that the matrix obtained by this method expresses the optimal cost for a projected optimal control problem. The projection is determined by the so-called shift parameters of the method. Our repr...
متن کاملReduced Basis Approximation for the Discrete-time Parametric Algebraic Riccati Equation
In this work we study the application of the reduced basis (RB) approximation method for parametric discrete-time algebraic Riccati equations (DARE). The DARE is very challenging to solve in large dimensions and parametric problems for large-scale applications are therefore often infeasible. We thus propose to apply the low-rank factor greedy (LRFG) algorithm to build a suitable low-dimensional...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Control and Optimization
سال: 1990
ISSN: 0363-0129,1095-7138
DOI: 10.1137/0328061