Boundary Observer Design for Coupled ODEs–Hyperbolic PDEs Systems

Ferrante, Francesco; Cristofaro, Andrea

doi:10.23919/ecc.2019.8795767

Cited by 10 publications

(17 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where the matrix Ω is given by (9). In conclusion we have y, Ay H ≤ 0, and thus A is dissipative, as long as He(Ω) = Ω + Ω 0.…”

Section: Exponential Stabilizationmentioning

confidence: 88%

“…The dynamics of this class of systems are typically governed by a combination of high-order partial differential equations (PDEs), ordinary differential equations (ODEs) and a set of static boundary conditions. Coupled systems of first and second order PDEs with ODEs have been largely investigated in the literature, and tackled with different approaches, such as backstepping [8,10], Lyapunov methods [22,1] and matrix inequalities [4,9]. However, the research on high order PDEs systems is more fragmentary.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Boundary stabilization of systems of high order PDEs arising from flexible robotics

Cristofaro¹,

Ferrante²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

The problem of stabilization of a system of coupled PDEs of the forthorder by means of boundary control is investigated. The considered setup arises from the classical Euler-Bernoulli beam model, and constitutes a generalization of flexible mechanical systems. A linear feedback controller is proposed, and using an abstract formulation based on operator semigroup theory, we are able to prove the well-posedness and the stability of the closed-loop system. The performances of the proposed controller are illustrated by means of numerical simulations.

show abstract

“…where the matrix Ω is given by (9). In conclusion we have y, Ay H ≤ 0, and thus A is dissipative, as long as He(Ω) = Ω + Ω 0.…”

Section: Exponential Stabilizationmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Boundary stabilization of systems of high order PDEs arising from flexible robotics

Cristofaro¹,

Ferrante²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…A preliminary version of this work has been presented in the conference paper [16]. While in [16] the design of the observer is based on the solution to some bilinear matrix inequalities, the present paper proposes a design algorithm based on the solution to some LMIs coupled to a two-dimensional line search. In addition, this paper contains full proofs of the main results.…”

Section: Contributionmentioning

confidence: 99%

“…and observe that the matrix on the lefthand side of (11b) corresponds to Ξ(1). Using (16), for all t ∈ int I, one has:…”

Section: Stability Analysis Of the Error Dynamicsmentioning

confidence: 99%

Boundary observer design for cascaded ODE — Hyperbolic PDE systems: A matrix inequalities approach

2020

Self Cite

View full text Add to dashboard Cite

Boundary observer design for a system of ODEs in cascade with hyperbolic PDEs is studied. An infinite dimensional observer is used to solve the state estimation problem. The interconnection of the observer and the system is written in estimation error coordinates and analyzed as an abstract dynamical system. The design of the observer is performed to achieve global exponential stability of the estimation error with respect to a suitable norm and with a tunable convergence rate. Sufficient conditions in the form matrix inequalities are given for the design of the observer. The effectiveness of the approach is shown in a numerical example.

show abstract

“…These systems are characterized by a distributed parameter nature, and their dynamics are typically governed by a combination of highorder partial differential equations (PDEs), ordinary differential equations (ODEs) and a set of static boundary conditions. Coupled systems of first and second order PDEs with ODEs have been largely investigated in the literature, and tackled with different approaches, such as backstepping [3], [4] or Lyapunov methods [5], [6], [7].…”

Section: Introductionmentioning

confidence: 99%

Linear-Quadratic Optimal Boundary Control of a One-Link Flexible Arm

Cristofaro

Luca

Lanari

2021

IEEE Control Syst. Lett.

Self Cite

View full text Add to dashboard Cite

A linear-quadratic optimal control problem is considered for the infinite-dimensional model of a one-link flexible arm. Two boundary inputs are assumed to be available, namely the joint torque at the link base and a transverse force at the tip of the link. The problem is formulated and solved using semigroup theory and duality arguments. Simulation results are provided to support the theoretical findings, comparing the proposed optimal LQ law with a more conventional PD/state feedback controller in terms of cost and transient performance.

show abstract

Boundary Observer Design for Coupled ODEs–Hyperbolic PDEs Systems

Cited by 10 publications

References 23 publications

Boundary stabilization of systems of high order PDEs arising from flexible robotics

Boundary stabilization of systems of high order PDEs arising from flexible robotics

Boundary observer design for cascaded ODE — Hyperbolic PDE systems: A matrix inequalities approach

Linear-Quadratic Optimal Boundary Control of a One-Link Flexible Arm

Contact Info

Product

Resources

About