Triangular form for Euler–Lagrange systems with application to the global output tracking control

Abstract

This paper presents a practical method to solve the problem of global output feedback tracking trajectories for a class of Euler-Lagrange systems when the variables of velocity are the unmeasured part of the state. We exhibited a new output feedback control scheme, which globally exponentially stabilize trajectories. It relies on the determination of a change of coordinates which gives to the systems a triangular form. Results are illustrated on the academic example of the two-link direct drive robot manipulator.

X–Y pedestal: partial quasi-linearization and cascade-based global output feedback tracking control

“…Given the X-Y pedestal system (18)- (20) with q and τ assumed known and v as bounded, our first objective is to design a velocity observer being uniformly globally exponentially convergent. Given a desired trajectory, q d : R ≥0 → R n , twice continuously differentiable and norm-bounded by β d , for the X-Y pedestal system with q assumed measurable, the second objective is to find a dynamic controller with uniform globally asymptotic stability in tracking and estimation errors.…”

“…Such approaches yield interdependent tuning of the observer and the controller gains (see, for instance, [18,[20][21][22][23][24]), and yield complex Lyapunov-based dynamic controller, as proposed in [14,18,20,21]. For instance, the order of the dynamical controllers in [14,20,21] is 3n + 1, 2n, and 2n, respectively, which is high due to their observer's dimension. In [23], Nicosia-Tomei observer is extended to obtain semi-globally exponential stability results for tracking errors and estimation errors.…”

Observers are Unnecessary for Output-Feedback Control of Lagrangian Systems

“…Unfortunately, the extension of the control method in [18] to the case of n-degree-of-freedom systems is stymied by structural properties; a fact well studied in [19]. Interesting exceptions for which appropriate changes of coordinates apply to particular classes of Euler-Lagrange systems include [20], [21] and some references therein.…”

Distributed adaptive tracking backstepping control in networked nonidentical Lagrange systems

“…In recent years, coordinated control of networked Lagrange systems has attracted increasing attention from various fields of science and engineering. This problem arises in many application domains, including the control of multiple robot manipulators, formation control of UAVs, and mobile sensor networks [3,[7][8][9][10][11][12][13][14][15], but its dynamics analysis is still very challenging due to the inherent nonlinearity and strong coupling between its generalized coordinates. Among the existing researches, the synchronization issue of Lagrange network systems possessing a nonlinear inertia matrix is much more involved and difficult.…”

“…Among the existing researches, the synchronization issue of Lagrange network systems possessing a nonlinear inertia matrix is much more involved and difficult. Ren [12] presented the distributed leaderless consensus algorithms for networked Lagrange systems under an undirected graph, Mabrouk [13] considered the global output tracking control for a class of Euler-Lagrange systems via a dynamic control law in the framework of triangular form, Wu and Zhou [8,9] proposed an analysis procedure for impulsive synchronization motion in networked open-loop multi-body systems formulated by Lagrange dynamics. In addition Mei, Ren, and Ma [16] further put forward to the distributed coordinated tracking schemes for undirected networked Lagrange systems with parametric uncertainties.…”