Francis equations vs invariant subspace algorithm for hybrid output regulation

In this paper, we deal with the output regulation problem for linear hybrid systems in the presence of unpredictable (time-driven) jumps, hence with arbitrary time domains. In particular we provide necessary and sufficient conditions for the solvability of the hybrid regulation problem, which non-trivially extend the classical conditions of regulation for LTI non-hybrid systems. Interestingly, differently from the latter, the former conditions are intrinsically nonlinear, since the dynamics of the interconnected system restricted to the error-zeroing invariant subspace may not be limited, as in the non-hybrid case, to those of the exosystem E. Then, we explore the relation between the discussed necessary and sufficient conditions and the constructive approach provided by the subspace invariant algorithm.

[1]  Laura Menini,et al.  Output Regulation of Hybrid Linear Systems with Unpredictable Jumps , 2014 .

[2]  Morten Lauge Pedersen,et al.  Encyclopedia of Life Support Systems (EOLSS) , 2005 .

[3]  Bernard Brogliato,et al.  Trajectory Tracking Control of Multiconstraint Complementarity Lagrangian Systems , 2010, IEEE Transactions on Automatic Control.

[4]  S. Ge,et al.  Switched Linear Systems: Control and Design , 2005 .

[5]  Lorenzo Marconi,et al.  A note about hybrid linear regulation , 2010, 49th IEEE Conference on Decision and Control (CDC).

[6]  Nathan van de Wouw,et al.  Tracking Control for Hybrid Systems With State-Triggered Jumps , 2013, IEEE Transactions on Automatic Control.

[7]  Shuzhi Sam Ge,et al.  Switched Linear Systems , 2005 .

[8]  Mario Sassano,et al.  On semiclassical solutions of hybrid regulator equations , 2013, 21st Mediterranean Conference on Control and Automation.

[9]  Lorenzo Marconi,et al.  Hybrid output regulation for minimum phase linear systems , 2011, Proceedings of the 2011 American Control Conference.

[10]  Lorenzo Marconi,et al.  Internal Model Principle for Linear Systems With Periodic State Jumps , 2013, IEEE Transactions on Automatic Control.

[11]  Mario Sassano,et al.  Necessary and sufficient conditions for output regulation in a class of hybrid linear systems , 2013, 52nd IEEE Conference on Decision and Control.

[12]  Lorenzo Marconi,et al.  Hybrid output regulation with unmeasured clock , 2011, IEEE Conference on Decision and Control and European Control Conference.

[13]  Boris M. Miller,et al.  Dynamical systems with active singularities: Input/state/output modeling and control , 2008, Autom..

[14]  R. Sanfelice,et al.  Hybrid dynamical systems , 2009, IEEE Control Systems.

[15]  Ricardo G. Sanfelice,et al.  Hybrid Dynamical Systems: Modeling, Stability, and Robustness , 2012 .

[16]  Laura Menini,et al.  Output regulation for a class of linear hybrid systems. Part 2: stabilization , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[17]  N. Wouw,et al.  An embedding approach for the design of state‐feedback tracking controllers for references with jumps , 2014 .

[18]  Laura Menini,et al.  Output regulation for a class of linear hybrid systems. Part 1: trajectory generation , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[19]  Laura Menini,et al.  A case study for hybrid regulation: Output tracking for a spinning and bouncing disk , 2013, 21st Mediterranean Conference on Control and Automation.

[20]  L. Menini,et al.  Trajectory tracking in linear hybrid systems: An internal model principle approach , 2008, 2008 American Control Conference.

[21]  G. Basile,et al.  Controlled and conditioned invariants in linear system theory , 1992 .

[22]  Lorenzo Marconi,et al.  Hybrid internal models for robust spline tracking , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[23]  Laura Menini,et al.  Robust Trajectory Tracking for a Class of Hybrid Systems: An Internal Model Principle Approach , 2012, IEEE Transactions on Automatic Control.

[24]  Laura Menini,et al.  Trajectory tracking for a particle in elliptical billiards , 2008, Int. J. Control.