Optimal periodic output feedback control: a continuous-time approach and a case study

This article deals with the problem of optimal static output feedback control of linear periodic systems in continuous time, for which a continuous-time approach, which allows to deal with both stable and unstable open loop systems, is presented. The proposed approach is tested on the problem of designing attitude control laws for a Low-Earth Orbit (LEO) satellite on the basis of feedback from a triaxial magnetometer and a set of high-precision gyros. Simulation results are used to demonstrate the feasibility of the proposed strategy and to evaluate its performance.

[1]  A. Laub,et al.  Numerical solution of the discrete-time periodic Riccati equation , 1994, IEEE Trans. Autom. Control..

[2]  Alessandro Astolfi,et al.  Hankel/Toeplitz matrices and the static output feedback stabilization problem , 2005, Math. Control. Signals Syst..

[3]  Kurt Lust,et al.  Improved numerical Floquet Multipliers , 2001, Int. J. Bifurc. Chaos.

[4]  Sven Hammarling.  Numerical solution of the discrete-time, convergent, non-negative definite Lyapunov equation , 1991 .

[5]  Chaouki T. Abdallah,et al.  Static output feedback: a survey , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[6]  Dimitri Peaucelle,et al.  RESILIENT STATIC OUTPUT FEEDBACK STABILIZATION OF LINEAR PERIODIC SYSTEMS , 2006 .

[7]  Andreas Varga,et al.  A PERIODIC SYSTEMS TOOLBOX FOR MATLAB , 2005 .

[8]  James R. Wertz,et al.  Spacecraft attitude determination and control , 1978 .

[9]  Vladimir B. Larin,et al.  On static output-feedback stabilization of a periodic system , 2006 .

[10]  B. Marin.  Overview of Recent Developments , 1987 .

[11]  Rafal Wisniewski.  Linear Time-Varying Approach to Satellite Attitude Control Using Only Electromagnetic Actuation , 2000 .

[12]  P. Kabamba,et al.  Simultaneous pole assignment in linear periodic systems by constrained structure feedback , 1989 .

[13]  Dimitri Peaucelle,et al.  Robust H 2 performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs , 2005 .

[14]  Robert E. Skelton,et al.  Static output feedback controllers: stability and convexity , 1998, IEEE Trans. Autom. Control..

[15]  S. Bittanti,et al.  Periodic Systems: Filtering and Control , 2008 .

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

[17]  Min-Shin Chen,et al.  Static output feedback control for periodically time-varying systems , 1999, IEEE Trans. Autom. Control..

[18]  Dimitri Peaucelle,et al.  LMI Formulation For The Resilient Dynamic Output Feedback Stabilization of Linear Periodic Systems , 2006 .

[19]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[20]  P. Makila,et al.  Computational methods for parametric LQ problems--A survey , 1987 .

[21]  Marco Lovera,et al.  Magnetic spacecraft attitude control: a survey and some new results , 2005 .

[22]  A. Astolfi,et al.  Global magnetic attitude control of spacecraft in the presence of gravity gradient , 2003, IEEE Transactions on Aerospace and Electronic Systems.

[23]  Marco Lovera,et al.  On the Role of Zeros in Rotorcraft Aeromechanics , 2004 .

[24]  András Varga,et al.  Gradient-Based Approach to Solve Optimal Periodic Output Feedback Control Problems , 1998, Autom..

[25]  Alessandro Astolfi,et al.  A note on asymptotic stabilization of linear systems by periodic, piecewise constant, output feedback , 2004, Proceedings of the 2004 American Control Conference.

[26]  Mark J. Balas,et al.  Full-State Feedback Control of a Variable-Speed Wind Turbine: A Comparison of Periodic and Constant Gains , 2001 .

[27]  Anthony J. Calise,et al.  Optimal Output Feedback for Linear Time-Periodic Systems , 1992 .

[28]  A. Schubert.  Autonomous Orbit Control for Spacecraft on Elliptical Orbits Using a Non-Inertial Coordinate Frame , 2001 .

[29]  P. Colaneri,et al.  Output stabilizability of periodic systems: necessary and sufficient conditions , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[30]  Stephen J. Wright,et al.  Numerical Optimization (Springer Series in Operations Research and Financial Engineering) , 2000 .

[31]  A. Varga.  Periodic Lyapunov equations: Some applications and new algorithms , 1997 .

[32]  Genshiro Kitagawa,et al.  An algorithm for solving the matrix equation X = FXF T + S , 1977 .

[33]  Daniel Graupe,et al.  Analysis of optimal-cost sensitivity to parameter changes , 1971 .

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

[35]  A. Barraud.  ' An algorithm for solving the matrix equation X=FXFT + S' , 1978 .

[36]  Adam W. Bojanczyk,et al.  Periodic Schur decomposition: algorithms and applications , 1992, Optics & Photonics.

[37]  Dirk Aeyels,et al.  Pole assignment for linear periodic second order systems by means of periodic memoryless output feedback , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[38]  A. Varga.  On solving periodic differential matrix equations with applications to periodic system norms computation , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[39]  Marco Lovera,et al.  Optimal discrete-time design of magnetic attitude control laws , 2005 .

[40]  G. Hulot,et al.  Swarm- The Earth's Magnetic Field and Environment Explorers , 2004 .

[41]  Christopher Geyer.  The Attitude Control Problem , 2022 .

[42]  András Varga,et al.  An overview of recent developments in computational methods for periodic systems , 2007, PSYCO.

[43]  Marco Lovera,et al.  Closed-Loop Aeromechanical Stability of Hingeless Rotor Helicopters with Higher Harmonic Control , 2006 .

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

[45]  András Varga,et al.  On solving periodic Riccati equations , 2008, Numer. Linear Algebra Appl..