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Constructive immersion and invariance stabilization for a class of underactuated mechanical systems

I. Sarras, J.Á. Acosta, R. Ortega, A.D. Mahindrakar
2013 Automatica  
In this paper a constructive approach to the stabilization of a desired equilibrium for a class of underactuated mechanical systems via the Immersion & Invariance methodology (I&I) is proposed.  ...  This work generalizes the results recently reported by the authors, where an approach to obviate the solution of the corresponding PDEs for a class of nonlinear systems was proposed.  ...  We consider the class of underactuated mechanical systems where G = G(q) ∈ R n×m has constant rank m < n.  ... 
doi:10.1016/j.automatica.2013.01.059 fatcat:vb3mht4tsbb3rkql3fudvodjbe

Path following of a class of underactuated mechanical systems via immersion and invariance-based orbital stabilization [article]

Bowen Yi, Romeo Ortega, Ian R. Manchester, Houria Siguerdidjane
2020 arXiv   pre-print
This paper aims to provide a new problem formulation of path following for mechanical systems without time parameterization nor guidance laws, namely, we express the control objective as an orbital stabilization  ...  It is shown that, it is possible to adapt the immersion and invariance technique to design static state-feedback controllers that solve the problem.  ...  CONCLUDING REMARKS In this paper, we address the PFP of a class of underactuated mechanical systems, which is reformulated as orbital stabilization.  ... 
arXiv:2001.10325v1 fatcat:3bwl5hxzrbdqbeag3v3i4lti74

Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one

J.A. Acosta, R. Ortega, A. Astolfi, A.D. Mahindrakar
2005 IEEE Transactions on Automatic Control  
We prove in this paper that for a class of mechanical systems with underactuation degree one the partial differential equations can be explicitly solved.  ...  Interconnection and damping assignment passivity-based control is a new controller design methodology developed for (asymptotic) stabilization of nonlinear systems that does not rely on, sometimes unnatural  ...  Viola for their reading of the original manuscript.  ... 
doi:10.1109/tac.2005.860292 fatcat:z2kchwfdc5hd3pglmzjwdwt24a

On the equivalence of two nonlinear control approaches: Immersion and invariance and IDA-PBC

Paul Kotyczka, Ioannis Sarras
2013 European Journal of Control  
Keywords: Underactuated mechanical systems, port-Hamiltonian systems, passivity based control, Immersion and Invariance. the energy function which is constructed in the course of the design process analytically  ...  In this note, the focus is on another underactuated mechanical system, the so-called Acrobot, see e. g. [19] for a description of the system and the model.  ...  In Subsection 4.2, direct equivalences of the IDA-PBC and I&I equations for a more general class of linear mechanical systems have become obvious.  ... 
doi:10.1016/j.ejcon.2013.09.008 fatcat:imol7od23rconfng5cqplsccze

Discrete-Time IDA-PBC for Underactuated Mechanical Systems with Input-Delay and Matched Disturbances

Enrico Franco
2018 2018 26th Mediterranean Conference on Control and Automation (MED)  
This work investigates the control problem of discrete-time underactuated mechanical systems with fixed input-delay and matched disturbances.  ...  Numerical simulations for the ball-on-beam system and for the Acrobot system demonstrate the effectiveness of the proposed approach.  ...  Although interconnection-and-damping-assignment passivity-basedcontrol (IDA-PBC) is an effective strategy for equilibrium stabilization of underactuated mechanical systems [5] , only a limited number  ... 
doi:10.1109/med.2018.8442979 dblp:conf/med/Franco18 fatcat:ikmij3b7crbrfgx2ww57ijmjcq

Speed Observation and Position Feedback Stabilization of Partially Linearizable Mechanical Systems

Aneesh Venkatraman, Romeo Ortega, Ioannis Sarras, Arjan van der Schaft
2010 IEEE Transactions on Automatic Control  
A reduced order globally exponentially stable observer, constructed using the immersion and invariance methodology, is proposed.  ...  Index Terms-Output feedback and observers, underactuated mechanical systems.  ...  Kokkonen for his careful and patient explanation of the beautiful concepts of Lie group theory, and the reviewers, for their careful reading and their numerous constructive remarks.  ... 
doi:10.1109/tac.2010.2042010 fatcat:pe7fu32hpnhpxiximfqlona33y

Stabilization of a Relative Equilibrium for an Underactuated AUV With Disturbances Rejection

Hongjiao Niu, Zhiyong Geng
2019 IEEE Access  
This paper addresses the robust stabilization of a relative equilibrium for an underactuated autonomous underwater vehicle (AUV) with disturbances rejection.  ...  The unmatched disturbances and the uncertain damping that make the realization of the system stabilization become more challenging.  ...  for Turbulence and Complex Systems and the Department of Mechanics and Engineering Science.  ... 
doi:10.1109/access.2018.2889836 fatcat:eqrgizsx5rc5lffh57kgk25nuq

Stabilizing of a Class of Underactuated Euler Lagrange System Using an Approximate Model [article]

Huseyin Alpaslan Yildiz, Leyla Goren-Sumer
2020 arXiv   pre-print
In this paper, a method is proposed to obtain an approximate solution of these matching conditions for a class of under-actuated EL systems.  ...  So the assignable potential energy function and the controlled inertia matrix, both are constructed as a common solution of these PDEs.  ...  In this study, this approach is modified and expanded to a class of underactuated EL systems. To the best of our knowledge, no similar approach is available in the literature.  ... 
arXiv:2007.01649v1 fatcat:tnfsehqqu5ggffqbq7xw33te6q

Control Problems of Hydrodynamic Type

P.S. Krishnaprasad, Vikram Manikonda
1998 IFAC Proceedings Volumes  
Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently  ...  the data needed, and completing and reviewing the collection of information.  ...  INTRODUCTION In this paper we present results related to the controllability and stabilization of a class of underactuated mechanical systems with symmetry.  ... 
doi:10.1016/s1474-6670(17)40324-7 fatcat:uienntvc2jdfzl6bbxtlcrtygy

Control of underactuated mechanical systems: Observer design and position feedback stabilization

Aneesh Venkatraman, Romeo Ortega, Ioannis Sarras, Arjan van der Schaft
2008 2008 47th IEEE Conference on Decision and Control  
IMMERSION AND INVARIANCE OBSERVERS: GENERAL CONSTRUCTIVE PROCEDURE A.  ...  CONCLUDING REMARKS AND FUTURE WORK We have identified in this paper a class of mechanical systems for which a globally exponentially stable reduced order observer can be designed.  ... 
doi:10.1109/cdc.2008.4738912 dblp:conf/cdc/VenkatramanOSS08 fatcat:jnzlyw3k35hzpfitmjgtew3tmu

A Stopping Algorithm for Mechanical Systems [chapter]

Jason Nightingale, Richard Hind, Bill Goodwine
2009 Springer Tracts in Advanced Robotics  
Analysis and control of underactuated mechanical systems in the nonzero velocity setting remains a challenging problem.  ...  The generalized eigenvalues and eigenvectors associated with the symmetric form are used to determine control inputs that will drive a class of mechanical systems underactuated by one control to rest from  ...  The main contribution of this paper is a stopping algorithm for mechanical systems underactuated by one control.  ... 
doi:10.1007/978-3-642-00312-7_11 fatcat:bqbwdbq4zbafpguszk6ho5p5gy

A simplified IDA-PBC design for underactuated mechanical systems with applications

Mutaz Ryalat, Dina Shona Laila
2016 European Journal of Control  
We develop a method to simplify the partial differential equations (PDEs) associated to the potential energy for interconnection and damping assignment passivity based control (IDA-PBC) of a class of underactuated  ...  global stabilization of these systems can be achieved.  ...  A constructive stabilization method for a class of UMSs based on a newly developed immersion and invariance (I&I) technique has been proposed in [30] , and a comparison between the IDA-PBC and I&I methods  ... 
doi:10.1016/j.ejcon.2015.12.001 fatcat:tphynx2de5dhnov5xdlkun4usm

Constructive Invariant Manifolds to Stabilize Pendulum–like systems Via Immersion and Invariance

J.Á. Acosta, R. Ortega, A. Astolfi, I. Sarras
2008 IFAC Proceedings Volumes  
The Immersion and Invariance control technique (I&I), is a method to design asymptotically stabilizing control laws for nonlinear systems, proposed in Astolfi and Ortega [2003].  ...  The three design steps of I&I are: the definition of a target dynamics; the construction of an invariant manifold; and the design of a control law.  ...  INTRODUCTION TO IMMERSION AND INVARIANCE The method of I&I for stabilization of nonlinear systems originated in Astolfi and Ortega [2003] and was further developed in a series of publications that have  ... 
doi:10.3182/20080706-5-kr-1001.00809 fatcat:zw4jcyjvlfbrbfg6cv34onr6vm

Adaptive IDA-PBC for underactuated mechanical systems with constant disturbances

Enrico Franco
2018 International Journal of Adaptive Control and Signal Processing  
This work investigates the control of nonlinear underactuated mechanical systems with matched and unmatched constant disturbances.  ...  In particular, the disturbances are estimated adaptively and then accounted for in the control law employing a new matching condition of algebraic nature.  ...  Assumption 2 restricts the study to constant disturbance, which are the focus of this work. This is a specific class of disturbances that has practical relevance for underactuated systems [18] .  ... 
doi:10.1002/acs.2947 fatcat:ou5tkzyplbhizbocgx2szl3cmi

2007 Index IEEE Transactions on Automatic Control Vol. 52

2007 IEEE Transactions on Automatic Control  
., and Berman, N., H Control and Estimation of Retarded State-Multiplicative Stochastic Systems; TAC Sept. 1773Sept.  ...  ., Approximation Metrics for Discrete and Continuous Systems; TAC May 2007 782-798 Giua, A., see Basile, F., TAC Feb. 2007 306-311 Giua, A., Seatzu, C., and Corona, C., Oct. 2007 Oct.  ...  ., +, TAC Oct. 2007 1948-1951 MIMO systems A Simple Nonlinear Observer for a Class of Uncertain Mechanical Systems.  ... 
doi:10.1109/tac.2007.913948 fatcat:vpztpth7jnhk7b5o5bt2nyrrdm
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