Abstract

The necessity to deal with partial differential equations (PDEs) and the dissipation condition are the mainadversities in the application of Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC). Recently,an algebraic solution of IDA-PBC has been explored for a class of affine polynomial systems by using sum of squares(SOS) and semidefinite programming (SDP). In this work, we extend the previous method by incorporating actuatorsaturation (AS) and two minimization objectives in the SDP. Our results are validated on two polynomial systems.

Highlights

  • The first depends on the solution of partial differential equations (PDEs) and the second together with zero state detectability (ZSD) of the closed-loop guarantees asymptotic stability

  • With the objective to completely avoid PDEs, the following leading methods have been proposed: constructive procedures (Donaire et al, 2016a; Borja et al, 2016; Romero et al, 2017), implicit port-Hamiltonian representation (Macchelli, 2014; Castaños and Gromov, 2016) and an algebraic approach (Fujimoto and Sugie, 2001; Batlle et al, 2007; Nunna et al, 2015). It has been shown in (Batlle et al, 2007; Donaire et al, 2016b) that a two step Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) may be restrictive in some cases, introducing a single step procedure (SIDAPBC)

  • To the best knowledge of the authors there is no definitive solution to the actuator saturation (AS) controller design problem with IDA-PBC

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Summary

INTRODUCTION

Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) has experienced increasing practice due its wide applicability (Petrovicet al., 2001; Batlle et al, 2004, 2007; Ortega and García-Canseco, 2004; Li et al, 2010; Astolfi and Ortega, 2001; Fujimoto et al, 2001; Renton et al, 2012; Li et al, 2013; Astolfi et al, 2002a; Xue and Zhiyong, 2017). With the objective to completely avoid PDEs, the following leading methods have been proposed: constructive procedures (Donaire et al, 2016a; Borja et al, 2016; Romero et al, 2017), implicit port-Hamiltonian representation (Macchelli, 2014; Castaños and Gromov, 2016) and an algebraic approach (Fujimoto and Sugie, 2001; Batlle et al, 2007; Nunna et al, 2015) It has been shown in (Batlle et al, 2007; Donaire et al, 2016b) that a two step IDA-PBC may be restrictive in some cases, introducing a single step procedure (SIDAPBC).

IDA-PBC FOR POLYNOMIAL SYSTEMS
Algebraic IDA-PBC
IDA-PBC FOR AFFINE NONLINEAR SYSTEMS
MAIN RESULT
Optimization Objectives in SDP
SIMULATIONS
Third Order Multiple Input System with AS
CONCLUSION

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