Reduced-order modeling using Dynamic Mode Decomposition and Least Angle Regression

Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model selection algorithm from statistics and machine learning known as Least Angle Regression (LARS). We modify LARS to be complex-valued and utilize LARS to select DMD modes. We refer to the resulting algorithm as Least Angle Regression for Dynamic Mode Decomposition (LARS4DMD). Sparsity-Promoting Dynamic Mode Decomposition (DMDSP), a popular mode-selection algorithm, serves as a benchmark for comparison. Numerical results from a Poiseuille flow test problem show that LARS4DMD yields reduced-order models that have comparable performance to DMDSP. LARS4DMD has the added benefit that the regularization weighting parameter required for DMDSP is not needed.Comment: 14 pages, 2 Figures, Submitted to AIAA Aviation Conference 201

Dynamic Instability of Follower Forced Euler Bernoulli Cantilever Beam With Tip Mass

This work focuses on the stability analysis of an Euler Bernoulli cantilever beam with a tip mass at the free end, subject to a follower force. This can serve as a viable model for analysis of elastic instability occurring due to fluid-structure interaction of structural components submerged in fluids and gases. A linear model with appropriate boundary conditions is developed using the energy formulation. The characteristic equation of the linear model establishes the relationship between the pulsation of the beam and the magnitude of applied follower force. The evolution of temporal eigenvalues with respect to the magnitude of the follower force helps in evaluation of the critical follower forces responsible for different modes of instability. The presented model demonstrates the existence of only dynamic instability in the system. Furthermore, the model predicts that both types of the dynamic instability i.e., flutter and divergence, are possible in the system

Minimum Time Control of a Gantry Crane System with Rate Constraints

This paper focuses on the development of minimum time control profiles for point-to-point motion of a gantry crane system in the presence of uncertainties in modal parameters. Assuming that the velocity of the trolley of the crane can be commanded and is subject to limits, an optimal control problem is posed to determine the bang-off-bang control profile to transition the system from a point of rest to the terminal states with no residual vibrations. Both undamped and underdamped systems are considered and the variation of the structure of the optimal control profiles as a function of the final displacement is studied. As the magnitude of the rigid body displacement is increased, the collapse and birthing of switches in the optimal control profile are observed and explained. Robustness to uncertainties in modal parameters is accounted for by forcing the state sensitivities at the terminal time to zero. The observation that the time-optimal control profile merges with the robust time-optimal control is noted for specific terminal displacements and the migration of zeros of the time-delay filter parameterizing the optimal control profile are used to explain this counter intuitive result. A two degree of freedom gantry crane system is used to experimentally validate the observations of the numerical studies and the tradeoff of increase in maneuver time to the reduction of residual vibrations is experimentally illustrated

Time-Optimal Output Transition for Minimum-Phase Systems

The time-optimal output transition control problem for stable or marginally stable systems with minimum-phase zeros is discussed in this paper. A double integrator system with a real left-half plane zero is used to illustrate the development of the time-optimal output transition controller. It is shown that an exponentially decaying postactuation control profile is necessary to maintain the output at the desired final location. It is shown that the resulting solution to the output transition time-optimal control profile can be generated by a time-delay filter whose zeros and poles cancels the poles and zeros of the system to be controlled. The design of the time-optimal output transition problem is generalized and illustrated on the benchmark floating oscillator problem

Research Opportunities in Contextualized Fusion Systems. The Harbor Surveillance Case

Proceedings of: International Workshop of Intelligent Systems for Context-Based Information Fusion (ISCIF 2011) associated to 11th International Work-Conference on Artificial Neural Networks, IWANN, Torremolinos-Málaga, Spain, June 8-10, 2011.The design of modern Information Fusion (IF) systems involves a complex process to achieve the requirements in the selected applications, especially in domains with a high degree of customization. In general, an advanced fusion system is required to show robust, context-sensitive behavior and efficient performance in real time. It is necessary to exploit all potentially relevant sensor and contextual information in the most appropriate way. Among modern applications for IF technology is the case of surveillance of complex harbor environments that are comprised of large numbers of surface vessels, high-value and dangerous facilities, and many people. The particular conditions and open needs in the harbor scenario are reviewed in this paper, highlighting research opportunities to explore in the development of fusion systems in this area.This work was supported in part by Projects CICYT TIN2008-06742-C02-02/TSI, CICYT TEC2008-06732-C02-02/TEC and CAM CONTEXTS S2009/TIC-1485.Publicad