Almost Automorphy and Riccati Equation

被引:0
作者
Indira Mishra
机构
[1] Univ. de Chile,Depto. Matematicas, Facultad de Ciencias
来源
Differential Equations and Dynamical Systems | 2019年 / 27卷
关键词
Almost automorphic function; Riccati equation; Exact controllability; Evolution equation; Hyperbolic semigroups; Interpolation spaces; 34 K06; 34 A12; 37 L05;
D O I
暂无
中图分类号
学科分类号
摘要
In this paper we first consider a linear time invariant system with almost automorphic forcing term. We propose two new deterministic quadratic control problems motivated by Da-Prato. We make use of a degenerate Riccati equation to solve these control problems. We also study the existence and uniqueness of an almost automorphic solutions of the associated differential equations.
引用
收藏
页码:379 / 394
页数:15
相关论文
共 28 条
[1]  
Bochner S(1964)Continuous mapping of almost automorphic and almost automorphic functions Proc. Nat. Sci. USA. 52 907-910
[2]  
Da Prato G(1987)Optimal control of linear systems with almost periodic inputs Siam. J. Control Optim. 25 1007-1019
[3]  
Ichikawa A(1990)Quadratic control for linear time varying systems Siam. J. Control Optim. 28 359-381
[4]  
Da Prato G(2009)Controllability of semilinear differential systems with nonlocal initial conditions in Banach spaces J. Optim. Theory Appl. 142 267-273
[5]  
Ichikawa A(2014)Almost automorphic functions of order Discrete Dyn. Nat. Soc. 2014 1-13
[6]  
Chang YK(2009) and applications to dynamic equations on time-scale Control Cybern. 38 1393-1410
[7]  
Nieto JJ(2008)On a degenerate Riccati equation Nonlinear Anal. 69 2114-2124
[8]  
Li WS(2010)Almost periodic and almost automorphic solutions to semilenear parabolic boundary differential equations Electron. J. Qual. Theory Differ. Equ. 22 1-26
[9]  
Mophou G(2012)Existence of almost automorphic solutions to some classes of nonautonomous higher-order differential equations Electron. J. Differ. Equ. 2012 1-11
[10]  
N’Guérkata GM(2013)Almost automorphic mild solutions of hyperbolic evolution equations, with Stepanov-like almost automorphic forcing term Ann. Mat. Pura Appl. (4) 192 393-405