Global asymptotic and finite-gain L&lt;inf&gt;2&lt;/inf&gt; stabilization of port-controlled Hamiltonian systems subject to actuator saturation

Sun, Weiwei; Lin, Zongli; Wang, Yuzhen

doi:10.1109/acc.2009.5160232

Cited by 17 publications

(7 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the experimental section of the paper, we show that our method is also robust to unmodeled nonlinearities, such as control input saturation. Control input saturation in PBC for PH systems has been addressed explicitly in the literature [10], [11], [12], [13], [14], [15], [16]. We show that our approach solves the problem of control input saturation on the learning side without the need of augmenting the model-based PBC.…”

Section: Reinforcement Learning For Port-hamiltonian Systemsmentioning

confidence: 82%

Reinforcement Learning for Port-Hamiltonian Systems

Sprangers

Babuška

Nageshrao

et al. 2015

IEEE Trans. Cybern.

View full text Add to dashboard Cite

Abstract-Passivity-based control (PBC) for port-Hamiltonian systems provides an intuitive way of achieving stabilization by rendering a system passive with respect to a desired storage function. However, in most instances the control law is obtained without any performance considerations and it has to be calculated by solving a complex partial differential equation (PDE). In order to address these issues we introduce a reinforcement learning approach into the energy-balancing passivity-based control (EB-PBC) method, which is a form of PBC in which the closed-loop energy is equal to the difference between the stored and supplied energies. We propose a technique to parameterize EB-PBC that preserves the systems's PDE matching conditions, does not require the specification of a global desired Hamiltonian, includes performance criteria, and is robust to extra non-linearities such as control input saturation. The parameters of the control law are found using actor-critic reinforcement learning, enabling learning near-optimal control policies satisfying a desired closedloop energy landscape. The advantages are that near-optimal controllers can be generated using standard energy shaping techniques and that the solutions learned can be interpreted in terms of energy shaping and damping injection, which makes it possible to numerically assess stability using passivity theory. From the reinforcement learning perspective, our proposal allows for the class of port-Hamiltonian systems to be incorporated in the actor-critic framework, speeding up the learning thanks to the resulting parameterization of the policy. The method has been successfully applied to the pendulum swing-up problem in simulations and real-life experiments.

show abstract

Section: Reinforcement Learning For Port-hamiltonian Systemsmentioning

confidence: 82%

Reinforcement Learning for Port-Hamiltonian Systems

Sprangers

Babuška

Nageshrao

et al. 2015

IEEE Trans. Cybern.

View full text Add to dashboard Cite

show abstract

“…In this context, Åström et al (2008); Escobar et al (1999) have studied PBC with AS on two specific systems. Sun et al (2009); Wei and Yuzhen (2010) analyze stability for saturation in the damping injection term. A variable structure approach to energy shaping for a class of Port-Hamiltonians system is developed in (Macchelli, 2002;Macchelli et al, 2003).…”

Section: Introductionmentioning

confidence: 99%

Algebraic IDA-PBC for Polynomial Systems with Input Saturation: An SOS-based Approach

Cieza

Reger

2019

View full text Add to dashboard Cite

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.

show abstract

“…Recently, the PSS problem was investigated in for Hamiltonian systems, and some interesting results were obtained for the existence of PSS controllers of a set of Hamiltonian systems. However, there are, to the authors’ best knowledge, few results except for nonlinear Hamiltonian systems that are subject to AS. Particularly, very few works have been developed on the adaptive parallel simultaneous stabilization (APSS) for nonlinear Hamiltonian systems subject to AS and parameter uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Adaptive parallel simultaneous stabilization of a set of uncertain port‐controlled hamiltonian systems subject to actuator saturation

Wei

Wang

2013

Adaptive Control & Signal

Self Cite

View full text Add to dashboard Cite

This paper investigates adaptive parallel simultaneous stabilization (APSS) of a set of uncertain nonlinear port-controlled Hamiltonian (PCH) systems subject to actuator saturation and proposes a number of results on the design of the APSS controllers. First, the case of two PCH systems is studied. Using both the dissipative Hamiltonian structural and saturated actuator properties, the two systems are combined to generate an augmented PCH system, with which, some results on the control designs are then obtained. When there are external disturbances in the two systems, an H 1 APSS controller is designed for the systems. Second, the case of more than two uncertain PCH systems subject to actuator saturation is investigated, and several new results are proposed for the APSS problem. Finally, an illustrative example is presented to show that the adaptive stabilization controllers obtained in this paper work very well.

show abstract

Global asymptotic and finite-gain L<inf>2</inf> stabilization of port-controlled Hamiltonian systems subject to actuator saturation

Cited by 17 publications

References 15 publications

Reinforcement Learning for Port-Hamiltonian Systems

Reinforcement Learning for Port-Hamiltonian Systems

Algebraic IDA-PBC for Polynomial Systems with Input Saturation: An SOS-based Approach

Adaptive parallel simultaneous stabilization of a set of uncertain port‐controlled hamiltonian systems subject to actuator saturation

Contact Info

Product

Resources

About