Minimal complexity control law synthesis, part 2: problem solution via H2/H∞ optimal static output feedback

In part 1 of this two-part paper [1] it was shown that a large class of fixed-structure control laws can be recast as static output feedback controllers for a suitably modified plant. Accordingly, we develop here a comprehensive theory for designing static output feedback controllers. Our results go beyond earlier work by addressing both H<inf>2</inf> and H<sub>∞</sub> performance criteria and by accounting fully for all of the singularities in the problem formulation. The results are applied to the fixed-order problem (FoP) [1] to obtain a major unification of prior results, namely: the Bernstein-Haddad H<sub>2</sub>/H<sub>∞</sub> fixed-order dynamic compensator theory, the Glover-Doyle full-order H<sub>∞</sub> dynamic compensator theory, the Hyland-Bernstein H<sub>2</sub> fixed-order dynamic compensator (optimal projection) theory, and the classical LQG theory.

[1]  A. Bryson,et al.  Linear filtering for time-varying systems using measurements containing colored noise , 1965 .

[2]  Sven Axsäter,et al.  Sub-optimal Time-variable Feedback Control of Linear Dynamic Systems with Random Inputs† , 1966 .

[3]  R. Kosut.  Suboptimal control of linear time-invariant systems subject to control structure constraints , 1970 .

[4]  M. Athans,et al.  On the determination of the optimal constant output feedback gains for linear multivariable systems , 1970 .

[5]  M. Athans,et al.  Optimal limited state variable feedback controllers for linear systems , 1971 .

[6]  B. Friedland.  Limiting Forms of Optimum Stochastic Linear Regulators , 1971 .

[7]  Yu-Chi Ho,et al.  Linear stochastic singular control problems , 1972 .

[8]  C. Knapp,et al.  On optimal output feedback , 1972 .

[9]  H. Kwatny.  Minimal order observers and certain singular problems of optimal estimation and control , 1974 .

[10]  H. Horisberger,et al.  Solution of the optimal constant output feedback problem by conjugate gradients , 1974 .

[11]  H. Kimura.  Pole assignment by gain output feedback , 1975 .

[12]  B. Anderson,et al.  Output feedback stabilization and related problems-solution via decision methods , 1975 .

[13]  P. N. Paraskevopoulos,et al.  A general solution to the output feedback eigenvalue-assignment problem , 1976 .

[14]  H. Kimura.  A further result on the problem of pole assignment by output feedback , 1977 .

[15]  Hidenori Kimura,et al.  On pole assignment by output feedback , 1978 .

[16]  K. Glover,et al.  Bounded peaking in the optimal linear regulator with cheap control , 1978 .

[17]  B. Francis.  The optimal linear-quadratic time-invariant regulator with cheap control , 1979 .

[18]  Richard W. Longman,et al.  Exact pole assignment using direct or dynamic output feedback , 1982 .

[19]  The Singular Steady State Linear Regulator , 1982 .

[20]  Peddapullaiah Sannuti,et al.  Direct singular perturbation analysis of high-gain and cheap control problems , 1983, Autom..

[21]  S. Richter,et al.  Continuation methods: Theory and applications , 1983 .

[22]  J. O'Reilly.  Partial cheap control of the time-invariant regulator , 1983 .

[23]  L. Silverman,et al.  System structure and singular control , 1983 .

[24]  D. Bernstein,et al.  The optimal projection equations for fixed-order dynamic compensation , 1984 .

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

[26]  Ian R. Petersen,et al.  Disturbance Attenuation: A Design Method Based on the Algebraic Riccati Equation , 1986 .

[27]  Dennis S. Bernstein,et al.  The Optimal Projection Equations for Reduced-Order State Estimation: The Singular Measurement Noise Case , 1987, 1987 American Control Conference.

[28]  D. Bernstein.  The optimal projection equations for static and dynamic output feedback: The singular case , 1987 .

[29]  Y. Halevi.  Limiting forms of optimal observers , 1988 .

[30]  D. Bernstein,et al.  LQG control with an H/sup infinity / performance bound: a Riccati equation approach , 1989 .

[31]  D. Bernstein,et al.  A Riccati Equation Approach to the Singular LQG Problem , 1989 .

[32]  Yoram Halevi,et al.  The optimal reduced-order estimator for systems with singular measurement noise , 1989 .