Follow the bouncing ball: global results on tracking and state estimation with impacts

in IEEE Transactions on Automatic Control (2013)

In this paper we formulate tracking and state- estimation problems of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set. Due to the discontinuous trajectories ... [more ▼]

In this paper we formulate tracking and state- estimation problems of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set. Due to the discontinuous trajectories arising from the impacts, we use hybrid systems stability analysis tools to establish the results. Using a novel concept of mirrored images of the target mass we prove that 1) a tracking control algorithm, and 2) an observer algorithm guarantee global exponential stability results for specific classes of polyhedral billiards, including rectangles. Moreover, we combine these two algorithms within dynamic controllers that guarantee global output feedback tracking. The results are illustrated via simulations. [less ▲]

Coordinated motion design on Lie groups

in IEEE Transactions on Automatic Control (2010), 55(5), 1047-1058

The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it ... [more ▼]

The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it introduces a precise method to design control laws in fully actuated and underactuated settings with simple integrator dynamics. It thereby shows that coordination can be studied in a systematic way once the Lie group geometry of the configuration space is well characterized. Applying the proposed general methodology to particular examples allows to retrieve control laws that have been proposed in the literature on intuitive grounds. A link with Brockett's double bracket flows is also made. The concepts are illustrated on SO(3) , SE(2) and SE(3). [less ▲]

Robust and Adaptive Observer-Based Partial Stabilization for a Class of Nonlinear Systems

in IEEE Transactions on Automatic Control (2009), 54(7),

The problem of adaptive stabilization with respect to a set for a class of nonlinear sys- tems in the presence of external disturbances is considered. A novel adaptive observer-based solution for the case ... [more ▼]

The problem of adaptive stabilization with respect to a set for a class of nonlinear sys- tems in the presence of external disturbances is considered. A novel adaptive observer-based solution for the case of noisy measurements is proposed. The efficiency of proposed solution is demonstrated via example of swinging a pendulum with unknown parameters. [less ▲]

Stabilization of planar collective motion: All-to-all communication

in IEEE Transactions on Automatic Control (2007), 52(5), 811-824

This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria ... [more ▼]

This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level. [less ▲]

Trading the Stability of Finite Zeros for Global Stabilization of Nonlinear Cascade Systems

in IEEE Transactions on Automatic Control (2002), 47(3), 521-525

This note analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a stable nonlinear system. It is shown that the ... [more ▼]

This note analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a stable nonlinear system. It is shown that the instability of the zeros of the linear system can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term. Below this limit, global stabilization is achieved by smooth static-state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions. [less ▲]

Slow Peaking and Low-Gain Designs for Global Stabilization of Nonlinear Systems

in IEEE Transactions on Automatic Control (2000), 45(3), 453-461

Shape signifiers for throttle control of a low-order compressor model

in IEEE Transactions on Automatic Control (1998), 43(11), 1643-1648

Rotating stall and surge, two instability mechanisms limiting the performance of aeroengines compressors, are studied on the third-order Moore–Greitzer model. The skewness of the compressor characteristic ... [more ▼]

Rotating stall and surge, two instability mechanisms limiting the performance of aeroengines compressors, are studied on the third-order Moore–Greitzer model. The skewness of the compressor characteristic, a single parameter shape signifier, is shown to determine the key qualitative properties of feedback control. [less ▲]