Nonlinear output feedback H∞-control of mechanical systems under unilateral constraints

Montano, Oscar; Orlov, Yury; Aoustin, Yannick

doi:10.1016/j.ifacol.2015.09.197

Cited by 7 publications

(8 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, sufficient conditions of a fully actuated hybrid system (formally corresponding to the case k = 0) to possess a solution to the attenuation problem are first recalled from Montano et al (2014Montano et al ( , 2015a. Then, the virtual holonomic constraint approach is presented as well as the concepts of transverse coordinates and transverse linearization are.…”

Section: Background Materialsmentioning

confidence: 99%

“…Theorem 2 (Montano et al, 2014) Let conditions C1), C3) and (19) be satisfied with some γ > 0. Then the closed-loop (5)-(7) system driven by the output feedback…”

Section: H ∞ -Output Feedback Synthesis Under Unilateral Constraintsmentioning

confidence: 99%

“…The H ∞ approach, that has recently been developed by Orlov and Aguilar (2014) towards nonsmooth mechanical applications with hard-to-model friction forces (such as dry or Coulomb friction and backlash effects), and then extended by Montano et al (2014) to fully actuated systems under unilateral constraints, is now generalized to an underactuated mechanical system with collisions. As in the fully actuated case (Montano et al, 2014), a local synthesis of an underactuated system is derived in the presence of unilateral constraints by means of two coupled Riccati equations that appear in solving the H ∞ state feedback and output injection designs for the linearized system viewed beyond the system constraints.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Orbital stabilization of an underactuated bipedal gait via nonlinear $${{\mathcal H}}_{\infty }$$ H ∞ -control using measurement feedback

Montano

Orlov

Aoustin³

et al. 2016

Auton Robot

View full text Add to dashboard Cite

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

show abstract

Section: Background Materialsmentioning

confidence: 99%

“…Theorem 2 (Montano et al, 2014) Let conditions C1), C3) and (19) be satisfied with some γ > 0. Then the closed-loop (5)-(7) system driven by the output feedback…”

Section: H ∞ -Output Feedback Synthesis Under Unilateral Constraintsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Orbital stabilization of an underactuated bipedal gait via nonlinear $${{\mathcal H}}_{\infty }$$ H ∞ -control using measurement feedback

Montano

Orlov

Aoustin³

et al. 2016

Auton Robot

View full text Add to dashboard Cite

show abstract

“…Proof of Theorem 5. The proof is rather technical and it follows the standard arguments of the nonlinear L 2 -gain analysis of Isidori and Astolfi [15] and Van Der Schaft [16], recently extended in Osuna and Orlov [20] to discontinuous (Filippov) vector fields and Montano et al [21] to dynamic systems, operating under unilateral constraints. It is clear that Lemma 1 is applicable both to a proximal solution (x) of the Hamilton-Jacobi inequality (22), viewed on the solutions x( ) of the disturbance-free system (11) beyond the discontinuity manifold (20), and to that of (24), viewed on the solutions of the disturbance-free system (14) when g 0 (x) = 0 along the discontinuity manifold (20).…”

Section: Hamilton-jacobi Inequality and Its Proximal Solutionsmentioning

confidence: 99%

“…Recently, it was demonstrated by Castaños and Fridman [19] that the closed-loop system, driven in the sliding mode, is capable of presenting good performance in the presence of unmatched disturbances as well; however, L 2 -gain analysis of such systems has not been addressed yet. To avoid this shortcoming, L 2 -gain analysis was separately developed for sliding mode systems by Osuna and Orlov [20] and for dynamic systems under unilateral constraints by Montano et al [21].…”

Section: Introductionmentioning

confidence: 99%

NonlinearL2-Gain Analysis of Hybrid Systems in the Presence of Sliding Modes and Impacts

Osuna

Montano

Orlov

2016

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

TheL2-gain analysis is extended towards hybrid mechanical systems, operating under unilateral constraints and admitting both sliding modes and collision phenomena. Sufficient conditions for such a system to be internally asymptotically stable and to possessL2-gain less than ana priorigiven disturbance attenuation level are derived in terms of two independent inequalities which are imposed on continuous-time dynamics and on discrete disturbance factor that occurs at the collision time instants. The former inequality may be viewed as the Hamilton-Jacobi inequality for discontinuous vector fields, and it is separately specified beyond and along sliding modes, which occur in the system between collisions. Thus interpreted, the former inequality should impose the desired integral input-to-state stability (iISS) property on the Filippov dynamics between collisions whereas the latter inequality is invoked to ensure that the impact dynamics (when the state trajectory hits the unilateral constraint) are input-to-state stable (ISS). These inequalities, being coupled together, form the constructive procedure, effectiveness of which is supported by the numerical study made for an impacting double integrator, driven by a sliding mode controller. Desired disturbance attenuation level is shown to satisfactorily be achieved under external disturbances during the collision-free phase and in the presence of uncertainties in the transition phase.

show abstract

Trajectory planning and tracking control for 6‐DOF Stanford manipulator based on adaptive sliding mode multi‐stage switching control

Zhang

2021

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

This article intends to investigate the trajectory planning and tracking control for six‐degrees‐of‐freedom (6‐DOF) Stanford manipulator consisting of 3‐DOF mechanical arm and 3‐DOF spherical wrist. By using Denavit–Hartenberg (DH) method, the Euler–Lagrange equations of motion of mechanical arm subsystem and spherical wrist subsystem are established, respectively. A new version of backstepping‐based adaptive sliding mode controller is proposed for trajectory tracking of each subsystem. In order to grasp an object from one point to another, a special smooth continuous trajectory is planned by inverse kinematics analysis which transforms the position of the end‐effector in the task space to the joint position in the joint space. After that, a multi‐stage switching control strategy is proposed to achieve trajectory tracking control. Simulation results are provided to demonstrate the performance of the proposed control strategy.

show abstract

Nonlinear output feedback H∞-control of mechanical systems under unilateral constraints

Cited by 7 publications

References 9 publications

Orbital stabilization of an underactuated bipedal gait via nonlinear $${{\mathcal H}}_{\infty }$$ H ∞ -control using measurement feedback

Orbital stabilization of an underactuated bipedal gait via nonlinear $${{\mathcal H}}_{\infty }$$ H ∞ -control using measurement feedback

NonlinearL2-Gain Analysis of Hybrid Systems in the Presence of Sliding Modes and Impacts

Trajectory planning and tracking control for 6‐DOF Stanford manipulator based on adaptive sliding mode multi‐stage switching control

Contact Info

Product

Resources

About