Slow peaking and low-gain designs for global stabilization of nonlinear systems

This paper presents an analysis of the slow-peaking phenomenon, a pitfall of low-gain designs that imposes basic limitations to large regions of attraction in nonlinear control systems. The phenomenon is best understood on a chain of integrators perturbed by a vector field up(x, u) that satisfies p(x, 0) = 0. Because small controls (or low-gain designs) are sufficient to stabilize the unperturbed chain of integrators, it may seem that smaller controls, which attenuate the perturbation up(x, u) in a large compact set, can be employed to achieve larger regions of attraction. This intuition is false, however, and peaking may cause a loss of global controllability unless severe growth restrictions are imposed on p(x, u). These growth restrictions are expressed as a higher order condition with respect to a particular weighted dilation related to the peaking exponents of the nominal system. When this higher order condition is satisfied, an explicit control law is derived that achieves global asymptotic stability of x = 0. This stabilization result is extended to more general cascade nonlinear systems in which the perturbation p(x, v) v, v = (ξ, u) T, contains the state ξ and the control u of a stabilizable subsystem ξ = a(ξ, u). As an illustration, a control law is derived that achieves global stabilization of the frictionless ball-and-beam model.

On the two classes of global primary modal instability in laminar separation bubbles

The self-excited global instability mechanisms existing in flat-plate laminar separation bubbles are studied here, in order to shed light on the causes of unsteadiness and three- dimensionality of unforced, nominally two-dimensional separated flows. The presence of two known linear global mechanisms, namely an oscillator behavior driven by local regions of absolute inflectional instability and a centrifugal instability giving rise to a steady three- dimensionalization of the bubble, is studied in a series of model separation bubbles. Present results indicate that absolute instability, and consequently a global oscillator behavior, does not exist for two-dimensional bubbles with a peak reversed-flow velocity below 12% of the free-stream velocity. However, the three-dimensional instability becomes active for recirculation levels as low as urev ≈ 7%. These findings suggest a route to the three-dimensionality and unsteadiness observed in experiments and simulations substantially different from that usually found in the literature, in which two-dimensional vortex shedding is followed by three-dimensionalization.

Output disturbance rejection using parallel model predictive control

The solution time of the online optimization problems inherent to Model Predictive Control (MPC) can become a critical limitation when working in embedded systems. One proposed approach to reduce the solution time is to split the optimization problem into a number of reduced order problems, solve such reduced order problems in parallel and selecting the solution which minimises a global cost function. This approach is known as Parallel MPC. The potential capabilities of disturbance rejection are introduced using a simulation example. The algorithm is implemented in a linearised model of a Boeing 747-200 under nominal flight conditions and with an induced wind disturbance. Under significant output disturbances Parallel MPC provides a significant improvement in performance when compared to Multiplexed MPC (MMPC) and Linear Quadratic Synchronous MPC (SMPC). © 2013 IEEE.

Comparison of moment-curvature models for fiber-reinforced polymer plate-end debonding studies using global energy balance approach

This paper compares a number of different moment-curvature models for cracked concrete sections that contain both steel and external fiber-reinforced polymer (FRP) reinforcement. The question of whether to use a whole-section analysis or one that considers the FRP separately is discussed. Five existing and three new models are compared with test data for moment-curvature or load deflection behavior, and five models are compared with test results for plate-end debonding using a global energy balance approach (GEBA). A proposal is made for the use of one of the simplified models. The availability of a simplified model opens the way to the production of design aids so that the GEBA can be made available to practicing engineers through design guides and parametric studies. Copyright © 2014, American Concrete Institute.

Predictive entropy search for efficient global optimization of black-box functions

We propose a novel information-theoretic approach for Bayesian optimization called Predictive Entropy Search (PES). At each iteration, PES selects the next evaluation point that maximizes the expected information gained with respect to the global maximum. PES codifies this intractable acquisition function in terms of the expected reduction in the differential entropy of the predictive distribution. This reformulation allows PES to obtain approximations that are both more accurate and efficient than other alternatives such as Entropy Search (ES). Furthermore, PES can easily perform a fully Bayesian treatment of the model hyperparameters while ES cannot. We evaluate PES in both synthetic and real-world applications, including optimization problems in machine learning, finance, biotechnology, and robotics. We show that the increased accuracy of PES leads to significant gains in optimization performance.