Mesh Independence of Kleinman--Newton Iterations for Riccati Equations in Hilbert Space
نویسندگان
چکیده
In this paper we consider the convergence of the infinite dimensional version of the Kleinman–Newton algorithm for solving the algebraic Riccati operator equation associated with the linear quadratic regulator problem in a Hilbert space. We establish mesh independence for this algorithm and apply the result to systems governed by delay equations. Numerical examples are presented to illustrate the results.
منابع مشابه
Inexact Kleinman-Newton Method for Riccati Equations
In this paper we consider the numerical solution of the algebraic Riccati equation using Newton's method. We propose an inexact variant which allows one control the number of the inner iterates used in an iterative solver for each Newton step. Conditions are given under which the monotonicity and global convergence result of Kleinman also hold for the inexact Newton iterates. Numerical results ...
متن کاملA mesh independent superlinear algorithm for some nonlinear nonsymmetric elliptic systems
Nonlinear elliptic transport systems arise in various problems in applied mathematics, most often leading to large-scale problems owing to the huge number of equations, see e.g. [14, 17, 18]. For large-scale elliptic problems, iterative processes are the most widespread solution methods, which often rely on Hilbert space theory when mesh independence is desired. (See e.g. [7, 11, 12] and the au...
متن کاملA Multi - Level Technique for the Approximate Solution of Operator Lyapunov andAlgebraic Riccati
We consider multi-grid, or more appropriately, multi-level techniques for the numerical solution of operator Lyapunov and algebraic Riccati equations. The Riccati equation, which is quadratic, plays an essential role in the solution of linear-quadratic optimal control problems. The linear Lyapunov equation is important in the stability theory for linear systems and its solution is the primary s...
متن کاملA Multi-level Technique for the Approximate Solution of Opertaor Lyapunov and Riccati Equations
We consider multi-grid, or more appropriately, multi-level techniques for the numerical solution of operator Lyapunov and algebraic Riccati equations. The Riccati equation, which is quadratic, plays an essential role in the solution of linear-quadratic optimal control problems. The linear Lyapunov equation is important in the stability theory for linear systems and its solution is the primary s...
متن کاملA revised Kleinman algorithm to solve algebraic Riccati equation of singularly perturbed systems
In this paper, we show that the Kleinman algorithm can be used well to solve the algebraic Riccati equation (ARE) of singularly perturbed systems, where the quadratic term of the ARE may be inde1nite. The quadratic convergence property of the Kleinman algorithm is proved by using the Newton–Kantorovich theorem when the initial condition is chosen appropriately. In addition, the numerical method...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Control and Optimization
دوره 47 شماره
صفحات -
تاریخ انتشار 2008