Necessary and sufficient conditions under which an H 2 optimal control problem has a unique solution

A set of necessary and sufficient conditions under which a general H 2-optimal control problem has a unique solution is derived. It is shown that the solution for an H 2-optimal control problem, if it exists, is unique if and only if (i) the transfer function from the control input to the controlled output is left invertible, and (ii) the transfer function from the disturbance to the measurement output is right invertible.

[1]  Maciejowsk.  Multivariable Feedback Design , 1989 .

[2]  Ben M. Chen,et al.  A reduced order observer based controller design for H/sub /spl infin//-optimization , 1994 .

[3]  Pramod P. Khargonekar,et al.  H2-optimal control with an H∞-constraint The state feedback case , 1991, Autom..

[4]  W. Fleming,et al.  Deterministic and Stochastic Optimal Control , 1975 .

[5]  T. Geerts.  All optimal controls for the singular linear-quadratic problem without stability; a new interpretation of the optimal cost , 1989 .

[6]  Johannes Schumacher.  A geometric approach to the singular filtering problem , 1985 .

[7]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[8]  Antonie Arij Stoorvogel.  The singular H2 control problem , 1992, Autom..

[9]  A. Saberi,et al.  Cheap and singular controls for linear quadratic regulators , 1985, 1985 24th IEEE Conference on Decision and Control.

[10]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[11]  J. Doyle.  Synthesis of robust controllers and filters , 1983, The 22nd IEEE Conference on Decision and Control.

[12]  Tutorial solution to the linear quadratic regulator problem using H2 optimal control theory , 1989 .

[13]  Ben M. Chen,et al.  Construction and parameterization of all static and dynamic H2 -optimal state feedback solutions, optimal fixed modes and fixed decoupling zeros , 1993, IEEE Trans. Autom. Control..

[14]  J. Willems,et al.  Singular optimal control: A geometric approach , 1986 .

[15]  Thomas Kailath,et al.  A view of three decades of linear filtering theory , 1974, IEEE Trans. Inf. Theory.

[16]  The disturbance decoupling problem with measurement feedback and stability for systems with direct feedthrough matrices , 1991 .

[17]  Ton Geerts,et al.  Continuity properties of the cheap control problem without stability , 1989 .