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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  
Here we show a constructive procedure to obviate the solution of the PDE, through the well-known cart and pendulum system.  ...  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].  ...  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

Orbital Stabilization of Nonlinear Systems via the Immersion and Invariance Technique [article]

Romeo Ortega, Bowen Yi, Jose Guadalupe Romero, Alessandro Astolfi
2019 arXiv   pre-print
Immersion and Invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems.  ...  Motivated by some modern applications we show that the technique can also be used to solve the problem of orbital stabilization, where the final objective is to generate periodic solutions that are attractive  ...  (B7), if 2 = 0 then lim →∞ ( ) = ∞; and for the case 2 ∈ (0, 0 ) the system (B7) has finite escape time.  ... 
arXiv:1810.00601v2 fatcat:npewjpegdvbf3e3ri4ilpxybbq

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  ...  It is shown that structural knowledge from the solution of the IDA-PBC energy shaping problem can be exploited to find an immersion map for I&I.  ...  (b) A further investigation of systems with different structure, like the Cart-Pendulum system would be a topic of interest.  ... 
doi:10.1016/j.ejcon.2013.09.008 fatcat:imol7od23rconfng5cqplsccze

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

Huseyin Alpaslan Yildiz, Leyla Goren-Sumer
2020 arXiv   pre-print
To demonstrate the success of the proposed method, the stability problem of the inverted pendulum on a cart is considered.  ...  In this paper, a method is proposed to obtain an approximate solution of these matching conditions for a class of under-actuated EL systems.  ...  stabilizing cart and pendulum shown in Fig. 1 .  ... 
arXiv:2007.01649v1 fatcat:tnfsehqqu5ggffqbq7xw33te6q

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  
The new result is applied to obtain an (almost) globally stabilizing scheme for the vertical takeoff and landing aircraft with strong input coupling, and a controller for the pendulum in a cart that can  ...  swing-up the pendulum from any position in the upper half plane and stop the cart at any desired location.  ...  ACKNOWLEDGMENT The authors would like to thank two anonymous reviewers for their valuable comments. The second author would also like to thank E. Panteley and G.  ... 
doi:10.1109/tac.2005.860292 fatcat:z2kchwfdc5hd3pglmzjwdwt24a

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.  ...  Our interest is centered on systems that can be rendered linear in the velocities via a (partial) change of coordinates.  ...  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

A globally exponentially stable speed observer for a class of mechanical systems: experimental and simulation comparison with high-gain and sliding mode designs

S. Aranovskiy, R. Ortega, J. G. Romero, D. Sokolov
2017 International Journal of Control  
It is shown in the paper that the problem of speed observation for mechanical systems that are partially linearisable via coordinate changes admits a very simple and robust (exponentially stable) solution  ...  This result should be contrasted with the very complicated observers based on immersion and invariance reported in the literature.  ...  Acknowledgment The authors are grateful to Frederic Mazenc for help in the proof of Proposition 4.1 and Elena Panteley for some clarifications on PE and stability of the system (13) that significantly  ... 
doi:10.1080/00207179.2017.1404130 fatcat:u7kcval6hbh2dcpqwihw73xz4e

Combining Trajectory Optimization, Supervised Machine Learning, and Model Structure for Mitigating the Curse of Dimensionality in the Control of Bipedal Robots [article]

Xingye Da, Jessy Grizzle
2017 arXiv   pre-print
The design procedure is first developed for ordinary differential equations and illustrated on a simple model.  ...  The process begins with trajectory optimization to design an open-loop periodic walking motion of the high-dimensional model and then adding to this solution, a carefully selected set of additional open-loop  ...  Acknowledgements The optimization and gait generation for the 3D walking and  ... 
arXiv:1711.02223v1 fatcat:za63vkgejfhajost5mfdwxdfny

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

Mutaz Ryalat, Dina Shona Laila
2016 European Journal of Control  
The parametrization accounts for kinetic energy shaping, which is then used to simplify the potential energy PDEs and their solution that is used for the potential energy shaping.  ...  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

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.  ...  Inverted Pendulum on a Cart [6] The inertia matrix M of the well-known inverted pendulum on a cart system and its corresponding lower triangular Cholesky factorization, T T = M −1 are given as, M = 1 *  ... 
doi:10.1109/cdc.2008.4738912 dblp:conf/cdc/VenkatramanOSS08 fatcat:jnzlyw3k35hzpfitmjgtew3tmu

A control algorithm for nonlinear offshore structural dynamical systems

R. Manikandan, Nilanjan Saha
2015 Proceedings of the Royal Society A  
This results in a control law which may either be partial or full rank for the dynamical system depending on measurable states. The performance of the controller is compared with conventional NQR.  ...  By doing so, the system becomes conditioned only on the present state and therefore one needs to solve only an algebraic statedependent Riccati problem.  ...  The authors also gratefully acknowledge partial financial support given by the Earth Systems Science Organization, Ministry of Earth Sciences, Government of India through National Institute of Ocean Technology  ... 
doi:10.1098/rspa.2015.0605 fatcat:5axqpamtlfbshnmi735kkjecoi

Energy Shaping of Port-Hamiltonian Systems by Using Alternate Passive Input-Output Pairs

Aneesh Venkatraman, Arjan van der Schaft
2010 European Journal of Control  
Inverted Pendulum on a Cart [24], [81] We construct a velocity observer for the inverted pendulum on a cart system whose inertia matrix is given in (1.6) and the lower triangular Cholesky factor in (3.29  ...  For the construction of the velocity observer, we use the Immersion and Invariance technique with dynamic scaling, recently proposed in [44] for a special class of nonlinear systems and later extended  ...  for port-Hamiltonian systems with dissipation (PHSD) by following a constructive approach.  ... 
doi:10.3166/ejc.16.665-677 fatcat:ypquninoifdxxo7ejujs5aeevy

Reduced-Order Nonlinear Observers via Contraction Analysis and Convex Optimization [article]

Bowen Yi, Ruigang Wang, Ian R. Manchester
2021 arXiv   pre-print
In this paper, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization.  ...  Despite the fact that contraction is a concept naturally suitable for state estimation, the existing solutions are either local or relatively conservative when applying to physical systems.  ...  ACKNOWLEDGEMENT The authors would like to express their gratitude to three reviewers for their careful reading of our manuscript, and many thoughtful comments that helped improve its clarity.  ... 
arXiv:2012.06158v2 fatcat:wqi6jlobqvdzfnzuj5pgx44ltq

Quantum Algorithm of Imperfect KB Self-organization Pt I: Smart Control-Information-Thermodynamic Bounds

Sergey Victorovich Ulyanov
2021 Artificial Intelligence Advances  
Quantum genetic algorithm applied on line for the quantum correlation's type searching between unknown solutions in quantum superposition of imperfect knowledge bases of intelligent controllers designed  ...  Background of the model is a new model of quantum inference based on quantum genetic algorithm.  ...  pendulum (a) and simulation & experimental results comparison for unpredicted control situation in cases of PID-controller, fuzzy controller and QFI-controller for "cart -pole" system and 7 Dof redundant  ... 
doi:10.30564/aia.v3i2.3171 fatcat:k6arll5t6rgvtcueomdxfanomi

Portable Motion-Analysis Device for Upper-Limb Research, Assessment and Rehabilitation in Non-Laboratory Settings

Won Joon Sohn, Rifat Sipahi, Terence D. Sanger, Dagmar Sternad
2019 IEEE Journal of Translational Engineering in Health and Medicine  
The device meets key needs for clinical practice: 1) a portable solution for quantitative motor assessment for upper-limb movement disorders at non-laboratory clinical settings, 2) a low-cost rehabilitation  ...  systems are difficult to use.  ...  ACKNOWLEDGMENT The authors would like to thank Robert Bottomly, Pauline Maurice, Eric Penchansky, and Jim Papadopoulos for assisting in the initial design of the hardware of the MAGIC Table.  ... 
doi:10.1109/jtehm.2019.2953257 pmid:32166053 pmcid:PMC6889943 fatcat:ojxmfdtw65bc7n5snuacybt7oq
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