Showing results 101 to 120 of 130
  Collective Motion: Bistability and Trajectory Tracking; ; Sepulchre, Rodolphe  in Proceedings of the 43rd IEEE Conference on Decision and Control (2004, December) This paper presents analysis and application of steering control laws for a network of self-propelled, planar particles. We explore together the two stably controlled group motions, parallel motion and ... [more ▼] This paper presents analysis and application of steering control laws for a network of self-propelled, planar particles. We explore together the two stably controlled group motions, parallel motion and circular motion, for modeling and design purposes. We show that a previously considered control law simultaneously stabilizes both parallel and circular group motion, leading to bistability and hysteresis. We also present behavior primitives that enable piecewise-linear network trajectory tracking. [less ▲] Detailed reference viewed: 2 (0 ULg)STABILIZATION THROUGH WEAK AND OCCASIONAL INTERACTIONS : A BILLIARD BENCHMARK; Sepulchre, Rodolphe in Proceedings of the 6th IFAC Symposium on Nonlinear Control Systems (2004, September) The paper addresses the stabilization of periodic orbits in a wedge billiard with actuated edges. It is shown how the rich dynamical properties of the open-loop dynamics, e.g. ergodicity properties and ... [more ▼] The paper addresses the stabilization of periodic orbits in a wedge billiard with actuated edges. It is shown how the rich dynamical properties of the open-loop dynamics, e.g. ergodicity properties and KAM curves, can be exploited to design robust stabilizing feedbacks with large basins of attraction. [less ▲] Detailed reference viewed: 37 (1 ULg)OPEN-LOOP STABILIZATION OF 2D IMPACT JUGGLING; ; Sepulchre, Rodolphe in Proceedings of 6th IFAC Symposium on Nonlinear Control Systems (2004, September) The paper studies the properties of a sinusoidally vibrating wedge billiard as a model for 2D impact juggling. It is shown that some periodic orbits that are unstable in the elastic xed wedge become ... [more ▼] The paper studies the properties of a sinusoidally vibrating wedge billiard as a model for 2D impact juggling. It is shown that some periodic orbits that are unstable in the elastic xed wedge become exponentially stable in the (non-)elastic vibrating wedge. These orbits are linked with some classical juggling patterns, providing an interesting benchmark for the study of the frequency-locking properties in human rhythmic tasks. [less ▲] Detailed reference viewed: 2 (0 ULg)Continuous dynamical systems that realize discrete optimization on the hypercube; Sepulchre, Rodolphe in Systems & Control Letters (2004), 52(3-4), 297-304 We study the problem of finding a local minimum of a multilinear function E over the discrete set {0, 1}(n). The search is achieved by a gradient-like system in [0, 1](n) with cost function E. Under mild ... [more ▼] We study the problem of finding a local minimum of a multilinear function E over the discrete set {0, 1}(n). The search is achieved by a gradient-like system in [0, 1](n) with cost function E. Under mild restrictions on the metric, the stable attractors of the gradient-like system are shown to produce solutions of the problem, even when they are not in the vicinity of the discrete set {0, 1}(n). Moreover, the gradient-like system connects with interior point methods for linear programming and with the analog neural network studied by Vidyasagar (IEEE Trans. Automat. Control 40 (8) (1995) 1359), in the same context. (C) 2004 Elsevier B.V. All rights reserved. [less ▲] Detailed reference viewed: 17 (5 ULg)DISSIPATIVITY AND GLOBAL ANALYSIS OF LIMIT CYCLES IN NETWORKS OF OSCILLATORS; Sepulchre, Rodolphe in Proceedings of the 16th Symposium on Mathematical Theory of Networks and Systems (2004, July) This paper is concerned with the global analysis of synchrone oscillations in special networks of oscillators. In previous work, we de ned a class of highdimensional, parameter-dependent nonlinear systems ... [more ▼] This paper is concerned with the global analysis of synchrone oscillations in special networks of oscillators. In previous work, we de ned a class of highdimensional, parameter-dependent nonlinear systems exhibiting almost globally asymptotically stable limit cycle oscillations. In this paper, we show how (incremental) dissipativity may be used to extend the global analysis of limit cycle oscillations to networks of coupled identical systems. [less ▲] Detailed reference viewed: 5 (1 ULg)Riemannian geometry of Grassmann manifolds with a view on algorithmic computation; ; Sepulchre, Rodolphe in Acta Applicandae Mathematicae (2004), 80(2), 199-220 We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in R-n. In these ... [more ▼] We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in R-n. In these formulas, p-planes are represented as the column space of n x p matrices. The Newton method on abstract Riemannian manifolds proposed by Smith is made explicit on the Grassmann manifold. Two applications - computing an invariant subspace of a matrix and the mean of subspaces - are worked out. [less ▲] Detailed reference viewed: 38 (5 ULg)Cubically convergent iterations for invariant subspace computation; Sepulchre, Rodolphe ; et alin SIAM Journal on Matrix Analysis and Applications (2004), 26(1), 70-96 We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of R-n and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is ... [more ▼] We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of R-n and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in terms of numerical cost and global behavior with three other methods that display the same property of cubic convergence. Moreover, we consider heuristics that greatly improve the global behavior of the iterations. [less ▲] Detailed reference viewed: 30 (2 ULg)Stabilization of periodic orbits in a wedge billiardSepulchre, Rodolphe ; in Proceedings of the 42nd IEEE Conference on Decision and Control (2003, December) This paper introduces a stabilization problem for an elementary impact control system in the plane. The rich dynamical properties of the wedge billiard, combined to the relevance of the associated ... [more ▼] This paper introduces a stabilization problem for an elementary impact control system in the plane. The rich dynamical properties of the wedge billiard, combined to the relevance of the associated stabilization problem for feedback control issues in legged robotics make it a valuable benchmark for energy-based stabilization of impact control systems. [less ▲] Detailed reference viewed: 3 (0 ULg)A Grassmann-Rayleigh quotient iteration for computing invariant subspaces; ; Sepulchre, Rodolphe et alin SIAM Review (2002), 44(1), 57-73 The classical Rayleigh quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQl which computes a p ... [more ▼] The classical Rayleigh quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQl which computes a p-dimensional invariant subspace of A. Cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature. [less ▲] Detailed reference viewed: 24 (7 ULg)Trading the Stability of Finite Zeros for Global Stabilization of Nonlinear Cascade SystemsSepulchre, Rodolphe ; ; 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 ▲] Detailed reference viewed: 4 (0 ULg)A duality principle for homogeneous vector fields with applications; ; et al in Systems & Control Letters (2002), 47(1), 37-46 We introduce a duality principle for homogeneous vectorfields. As an application of this duality principle, stability and boundedness results for negative order homogeneous differential equations are ... [more ▼] We introduce a duality principle for homogeneous vectorfields. As an application of this duality principle, stability and boundedness results for negative order homogeneous differential equations are obtained, starting form known results for positive order homogeneous differential equations. [less ▲] Detailed reference viewed: 14 (0 ULg)Improving the performance of low-gain designs for bounded control of linear systems; Sepulchre, Rodolphe ; in Automatica (2002), 38(11), 1777-1782 Detailed reference viewed: 6 (0 ULg)Global analysis of a continuous-time flow whith computes time-optimal switchings; Sepulchre, Rodolphe in Proceedings of the 40th IEEE Conference on Decision and Control (2001, December) The minimum-time bounded control of linear systems is generically bang-bang and the number of switchings does not exceed the dimension of the system if the eigenvalues of the system matrix are real. This ... [more ▼] The minimum-time bounded control of linear systems is generically bang-bang and the number of switchings does not exceed the dimension of the system if the eigenvalues of the system matrix are real. This paper proposes a synthesis method for such problems based on dynamical systems that "compute" the optimal sequence of switching times. [less ▲] Detailed reference viewed: 5 (0 ULg)Robust global state feedback stabilization of cement mills; ; et al in IEEE Transactions on Automatic Control (2001), 46(4), 618-623 Plugging is well known to be a major cause of instability in industrial cement mills. A simple nonlinear model able to simulate the plugging phenomenon is presented. It is shown how a nonlinear robust ... [more ▼] Plugging is well known to be a major cause of instability in industrial cement mills. A simple nonlinear model able to simulate the plugging phenomenon is presented. It is shown how a nonlinear robust controller can be designed in order to fully prevent the mill from plugging [less ▲] Detailed reference viewed: 9 (1 ULg)Stability of perturbed functional differential equations and stabilization of nonlinear cascades; Sepulchre, Rodolphe ; in SIAM Journal on Control & Optimization (2001), 40 In this paper the effect of bounded input perturbation on the stability of nonlinear globally asymptotically stable delay differential equations is analyzed. We investigate under which conditions global ... [more ▼] In this paper the effect of bounded input perturbation on the stability of nonlinear globally asymptotically stable delay differential equations is analyzed. We investigate under which conditions global stability in preserved and if not, whether semi-global stabilization is possible by controlling the size or shape of the perturbation. This results in a general framework, in which the stabilization of partial linear cascade systems using partial state feedback can be treated systematically. [less ▲] Detailed reference viewed: 10 (1 ULg)Slow Peaking and Low-Gain Designs for Global Stabilization of Nonlinear SystemsSepulchre, Rodolphe in IEEE Transactions on Automatic Control (2000), 45(3), 453-461 Detailed reference viewed: 7 (0 ULg)Boundedness properties for time-varying nonlinear systems; ; Sepulchre, Rodolphe in SIAM Journal on Control & Optimization (2000), 39(5), 1408-1422 Detailed reference viewed: 6 (1 ULg)Delayed control of axial compressors; Sepulchre, Rodolphe ; in International Journal of Bifurcation & Chaos in Applied Sciences & Engineering (2000), 10(5), Detailed reference viewed: 10 (2 ULg)Nonlinear analysis of cardiac rythm fluctuations using DFA method; Sepulchre, Rodolphe ; et alin Physica A: Statistical Mechanics and its Applications (1999), 272 Detailed reference viewed: 5 (0 ULg)Global stabilization of feedforward systems with exponentially unstable Jacobian linearization; Sepulchre, Rodolphe ; in Systems & Control Letters (1999), 37(2), 107-115 The global stabilization of a class of feedforward systems having an exponentially unstable Jacobian linearization is achieved by a high gain feedback saturated at a low level. The control law forces the ... [more ▼] The global stabilization of a class of feedforward systems having an exponentially unstable Jacobian linearization is achieved by a high gain feedback saturated at a low level. The control law forces the derivatives of the state variables to small values along the closed loop trajectories. This “slow control” design is illustrated with a benchmark example and its limitations are emphasized. [less ▲] Detailed reference viewed: 12 (1 ULg) |
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