Switching rules for stabilization of linear systems of conservation laws

International audienceIn this paper, the exponential convergence in L 2-norm is analyzed for a class of switched linear systems of conservation laws. The boundary conditions are subject to switches. We investigate the problem of synthesizing stabilizing switching controllers. By means of Lyapunov techniques, three control strategies are developed based on steepest descent selection, possibly combined with a hysteresis and a low-pass filter. For the first strategy we show the global exponential stabilizability, but no result for the existence and uniqueness of trajectories can be stated. For the other ones, the problem is shown to be well posed and global exponential convergence can be obtained. Moreover, we consider the robustness issues for these switching rules in presence of measurement noise. Some numerical examples illustrate our approach and show the merits of the proposed strategies. Particularly, we have developped a model for a network of open channels, with switching controllers in the gate operations

Scaling properties of noise-induced switching in a bistable tunnel diode circuit

Noise-induced switching between coexisting metastable states occurs in a wide range of far-from-equilibrium systems including micro-mechanical oscillators, epidemiological and climate change models, and nonlinear electronic transport in tunneling structures such as semiconductor superlattices and tunnel diodes. In the case of tunnel diode circuits, noise-induced switching behavior is associated with negative differential resistance in the static current-voltage characteristics and bistability, i.e., the existence of two macroscopic current states for a given applied voltage. Noise effects are particularly strong near the onset and offset of bistable current behavior, corresponding to bifurcation points in the associated dynamical system. In this paper, we show that the tunnel diode system provides an excellent experimental platform for the precision measurement of scaling properties of mean switching times versus applied voltage near bifurcation points. More specifically, experimental data confirm that the mean switching time scales logarithmically as the 3/2 power of voltage difference over an exceptionally wide range of time scales and noise intensities.Comment: 9 pages, 9 figures, accepted manuscript for publication in the European Physical Journal B, Topical Issue: Non-Linear and Complex Dynamics in Semiconductors and Related Material

The dynamics and optimal control of spinning spacecraft and movable telescoping appendages, part A

The problem of optimal control with a minimum time criterion as applied to a single boom system for achieving two axis control is discussed. The special case where the initial conditions are such that the system can be driven to the equilibrium state with only a single switching maneuver in the bang-bang optimal sequence is analyzed. The system responses are presented. Application of the linear regulator problem for the optimal control of the telescoping system is extended to consider the effects of measurement and plant noises. The noise uncertainties are included with an application of the estimator - Kalman filter problem. Different schemes for measuring the components of the angular velocity are considered. Analytical results are obtained for special cases, and numerical results are presented for the general case

Switching Quantum Dynamics for Fast Stabilization

Control strategies for dissipative preparation of target quantum states, both pure and mixed, and subspaces are obtained by switching between a set of available semigroup generators. We show that the class of problems of interest can be recast, from a control--theoretic perspective, into a switched-stabilization problem for linear dynamics. This is attained by a suitable affine transformation of the coherence-vector representation. In particular, we propose and compare stabilizing time-based and state-based switching rules for entangled state preparation, showing that the latter not only ensure faster convergence with respect to non-switching methods, but can designed so that they retain robustness with respect to initialization, as long as the target is a pure state or a subspace.Comment: 15 pages, 4 figure

Multi-physics phenomena influencing the performance of the car horn

Usually cars are equipped with disk horns. In these devices electromagnetic energy is converted into mechanical energy of two nuclei that vibrate and impact each other \u2013 the impacts excite the disk that radiates sound. This paper aims at understanding the results of acoustic tests carried out on horns with different excitation voltages and different mounting brackets. Since many non-linear phenomena are inherent in the vibrations of the nuclei, a detailed model of the electromechanical system is developed. Results show the dependence of operating frequency on the input voltage and the role played by the various mechanical and electrical parameters on the dynamics of the horn. Particular nonlinear effects, like sub-harmonic excitation, are presented and discussed. A general agreement between experimental results and numerical simulations is found

Dynamics of Simple Balancing Models with State Dependent Switching Control

Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by either a connected movable cart or an applied torque for which the control is turned off when the pendulum is located within certain regions of phase space. Without applying a small angle approximation for deviations about the vertical position, we see structurally stable periodic orbits which may be attracting or repelling. Due to the nonsmooth nature of the control, these periodic orbits are born in various discontinuity-induced bifurcations. Also we show that a coincidence of switching events can produce complicated periodic and aperiodic solutions.Comment: 36 pages, 12 figure

Switching Control for Parameter Identifiability of Uncertain Systems

This paper considers the problem of identifying the parameters of an uncertain linear system by means of feedback control. The problem is approached by considering time-varying controllers. It is shown that even when the uncertainty set is not finite, parameter identifiability can be generically ensured by switching among a finite number of linear time-invariant controllers. The results are shown to have several implications, ranging from fault detection and isolation to adaptive and supervisory control. Practical aspects of the problem are also discussed in details

Effects of low-frequency noise cross-correlations in coupled superconducting qubits

We study the effects of correlated low frequency noise sources acting on a two qubit gate in a fixed coupling scheme. A phenomenological model for the spatial and cross-talk correlations is introduced. The decoherence inside the SWAP subspace is analysed by combining analytic results based on the adiabatic approximation and numerical simulations. Results critically depend on amplitude of the low frequency noise with respect to the qubits coupling strength. Correlations between noise sources induce qualitative different behaviors depending on the values of the above parameters. The possibility to reduce dephasing due to correlated low frequency noise by a recalibration protocol is discussed.Comment: 18 pages, 7 figure