A Convergent Algorithm for the Output Covariance Constraint Control Problem

This paper considers the optimal control problem of minimizing control effort subject to multiple performance constraints on output covariance matrices $Y_i$ of the form $Y_i \leq \overline{Y}_i$, where $\overline{Y}_i$ is given. The contributions of this paper are a set of conditions that characterize global optimality, and an iterative algorithm for finding a solution to the optimality conditions. This iterative algorithm is completely described up to a user-specified parameter. We show that, under suitable assumptions on problem data, the iterative algorithm converges to a solution of the optimality conditions, provided that this parameter is properly chosen. Both discrete- and continuous-time problems are considered.

[1]  R. Skelton,et al.  Minimum energy controllers with inequality constraints on output variances , 1989 .

[2]  Pertti M. Mäkilä,et al.  Computer-aided design procedure for multiobjective LQG control problems , 1989 .

[3]  V. Kučera.  A contribution to matrix quadratic equations , 1972 .

[4]  H. Toivonen.  A multiobjective linear quadratic Gaussian control problem , 1984 .

[5]  Vladimír Kucera,et al.  The discrete Riccati equation of optimal control , 1972, Kybernetika.

[6]  P. Khargonekar,et al.  Multiple objective optimal control of linear systems: the quadratic norm case , 1991 .

[7]  Robert E. Skelton,et al.  Space structure control design by variance assignment , 1985 .

[8]  R. Skelton,et al.  Mixed L2 and L∞ problems by weight selection in quadratic optimal control , 1991 .

[9]  T. Runolfsson,et al.  Output residence time control , 1989 .

[10]  Stephen P. Boyd,et al.  Linear controller design: limits of performance , 1991 .

[11]  Cornelius T. Leondes,et al.  The multiple linear quadratic gaussian problem , 1986 .

[12]  P. Makila.  On multiple criteria stationary linear quadratic control , 1989 .

[13]  Hannu T. Toivonen.  Variance constrained self-tuning control , 1983, Autom..

[14]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[15]  Christopher I. Byrnes,et al.  Algebraic and geometric methods in linear systems theory , 1980 .

[16]  Mario A. Rotea,et al.  The generalized H2 control problem , 1993, Autom..

[17]  D. Wilson.  Convolution and Hankel operator norms for linear systems , 1989 .