Riccati Equations Associated Withnon - Admissible Linear Control Systemsin Hilbert
نویسندگان
چکیده
The linear quadratic regulator problem for the second order evolution system with boundary controls is studied. Case that the input-to-state map is non-admissible is treated assuming that the system is exponentially stabilizable by the passive feedback. It is shown that the optimal control is of feedback form in terms of solution to the operator Riccati equation.
منابع مشابه
Generalized H Optimization Problem for Linear Differential Equations in Hilbert Space
In this paper the state-space solution to H optimization problem for linear time-invariant infinite-horizon differential equation in Hilbert space and sign-indefinite cost function is proposed. The necessary and sufficient conditions as well as the parametrization of all admissible controllers are derived in terms of the stabilizing solutions of two Riccati equations
متن کاملGeneralized Discrete-Time H Optimization Problem for Linear Difference Equations in Hilbert Space
In this paper the state-space solution to discretetime H optimization problem for linear timeinvariant infinite-horizon difference equations in Hilbert space and sign-indefinite cost function is proposed. The necessary and sufficient conditions as well as the parametrization of all admissible controllers are derived in terms of the stabilizing solution to the Riccati equation.
متن کاملMesh Independence of Kleinman--Newton Iterations for Riccati Equations in Hilbert Space
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 t...
متن کاملLqg Optimal Control Arising in Mean Field Decision Problems
Abstract. We consider a linear-quadratic-Gaussian (LQG) optimal control problem where the generalized state space is the product of an Euclidian space and an infinite dimensional function space. This model originates from a mean field LQG game with a major player and a large number of minor players, and has importance in designing decentralized strategies in the game. We show that the underlyin...
متن کاملRiccati equations and optimal control of well-posed linear systems
We generalize the classical theory on algebraic Riccati equations and optimization to infinite-dimensional well-posed linear systems, thus completing the work of George Weiss, Olof Staffans and others. We show that the optimal control is given by the stabilizing solution of an integral Riccati equation. If the input operator is not maximally unbounded, then this integral Riccati equation is equ...
متن کامل