Robust variable horizon MPC with move blocking

This paper introduces a new formulation of variable horizon model predictive control (VH-MPC) that utilises move blocking for reducing computational complexity. Various results pertaining to move blocking are derived, following which, a generalised blocked VH-MPC controller is formulated for linear discrete-time systems. Robustness to bounded disturbances is ensured through the use of tightened constraints. The resulting time-varying control scheme is shown to guarantee robust recursive feasibility and finite-time completion. An example is then presented for a particular choice of blocking regime, as would be applicable to vehicle manœuvring problems. Simulations demonstrate the efficacy of the formulation. © 2012 Elsevier B.V. All rights reserved.

Bayesian interpolation in a dynamic sinusoidal model with application to packet-loss concealment

In this paper, we consider Bayesian interpolation and parameter estimation in a dynamic sinusoidal model. This model is more flexible than the static sinusoidal model since it enables the amplitudes and phases of the sinusoids to be time-varying. For the dynamic sinusoidal model, we derive a Bayesian inference scheme for the missing observations, hidden states and model parameters of the dynamic model. The inference scheme is based on a Markov chain Monte Carlo method known as Gibbs sampler. We illustrate the performance of the inference scheme to the application of packet-loss concealment of lost audio and speech packets. © EURASIP, 2010.

The Gaussian mixture MCMC particle algorithm for dynamic cluster tracking

We present a novel filtering algorithm for tracking multiple clusters of coordinated objects. Based on a Markov chain Monte Carlo (MCMC) mechanism, the new algorithm propagates a discrete approximation of the underlying filtering density. A dynamic Gaussian mixture model is utilized for representing the time-varying clustering structure. This involves point process formulations of typical behavioral moves such as birth and death of clusters as well as merging and splitting. For handling complex, possibly large scale scenarios, the sampling efficiency of the basic MCMC scheme is enhanced via the use of a Metropolis within Gibbs particle refinement step. As the proposed methodology essentially involves random set representations, a new type of estimator, termed the probability hypothesis density surface (PHDS), is derived for computing point estimates. It is further proved that this estimator is optimal in the sense of the mean relative entropy. Finally, the algorithm's performance is assessed and demonstrated in both synthetic and realistic tracking scenarios. © 2012 Elsevier Ltd. All rights reserved.

Effects of nonuniform reactant stoichiometry on combustion instability

This paper analyzes the forced response of swirl-stabilized lean-premixed flames to acoustic forcing in a laboratory-scale stratified burner. The double-swirler, double-channel annular burner was specially designed to generate acoustic velocity oscillations and radial fuel stratification at the inlet of the combustion chamber. Temporal oscillations of equivalence ratio along the axial direction are dissipated over a long distance, and therefore the effects of time-varying fuel/air ratio on the flame response are not considered. Simultaneous measurements of inlet velocity and heat release rate oscillations were made using a hot wire anemometer and photomultiplier tubes with narrowband OH*/CH* interference filters. Time-averaged CH* chemiluminescence intensities were measured using an intensified CCD camera. Results show that flame stabilization mechanisms vary depending on stratification ratio for a constant global equivalence ratio. For a uniformly premixed condition, an enveloped M-shaped flame is observed. For stratified conditions, however, a dihedral V-flame and a detached flame are developed for outer stream and inner stream fuel enrichment cases, respectively. Flame transfer function (FTF) measurement results indicate that a V-shaped flame tends to damp incident flow oscillations, while a detached flame acts as a strong amplifier relative to the uniformly premixed condition. The phase difference of FTF increases in the presence of stratification. More importantly, the dynamic characteristics obtained from the forced stratified flame measurements are well correlated with unsteady flame behavior under limit-cycle pressure oscillations. The results presented in this paper provide insight into the impact of nonuniform reactant stoichiometry on combustion instabilities, which has not been well explored to date. Copyright © 2011 by ASME.

Transient flows in enclosures: A generalised approach for modelling the effects of geometry, heat gains and wind

Transient flows in a confined ventilated space induced by a buoyancy source of time-varying strength and an external wind are examined. The space considered has varying cross-sectional area with height. A generalised theoretical model is proposed to investigate the flow dynamics following the activation of an external wind and an internal source of buoyancy. To investigate the effect of geometry, we vary the angle of the wall inclination of a particular geometry in which a point source of constant buoyancy is activated in the absence of wind. Counter-intuitively the ventilation is worse and lower airflow rates are established for geometries of increasing cross-sectional areas with height. We investigate the effect of the source buoyancy strength by comparing two cases: (1) when the buoyancy input is constant and (2) when the buoyancy input gradually increases over time so that after a finite time the total buoyancy inputs for (1) and (2) are identical. The rate at which the source heat gains are introduced has a significant role on the flow behaviour as we find that, in case (2), a warmer layer and a more pronounced overshoot are obtained than in case (1). The effect of assisting and opposing wind on the transient ventilation of an enclosure of constant cross-sectional area with height and constant heat gains is examined. A Froude number Fr is used to define the relative strengths of the buoyancy-induced and wind-induced velocities and five different transient states and their associated critical Fr are identified. © 2010 Elsevier Ltd.

Optimal constraint tightening policies for robust variable horizon model predictive control

This paper develops a technique for improving the region of attraction of a robust variable horizon model predictive controller. It considers a constrained discrete-time linear system acted upon by a bounded, but unknown time-varying state disturbance. Using constraint tightening for robustness, it is shown how the tightening policy, parameterised as direct feedback on the disturbance, can be optimised to increase the volume of an inner approximation to the controller's true region of attraction. Numerical examples demonstrate the benefits of the policy in increasing region of attraction volume and decreasing the maximum prediction horizon length. © 2012 IEEE.

Synchronization with partial state feedback on SO(n)

In this paper we consider the problem of constructing a distributed feedback law to achieve synchronization for a group of k agents whose states evolve on SO(n) and which exchange only partial state information along communication links. The partial state information is given by the action of the state on reference vectors in ℝn. We propose a gradient based control law which achieves exponential local convergence to a synchronization configuration under a rank condition on a generalized Laplacian matrix. Furthermore, we discuss the case of time-varying reference vectors and provide a convergence result for this case. The latter helps reach synchronization, requiring less communication links and weaker conditions on the instantaneous reference vectors. Our methods are illustrated on an attitude synchronization problem where agents exchange only their relative positions observed in the respective body frames. ©2009 IEEE.

Synchronization in networks of identical linear systems

The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected. The result can be interpreted as a generalization of classical consensus algorithms. Stronger conditions are shown to be sufficient-but to some extent, also necessary-to ensure synchronization with the diffusive static output coupling often considered in the literature. © 2009 Elsevier Ltd. All rights reserved.

Consensus optimization on manifolds

The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative state according to a communication graph. The consensus problem is formulated in terms of the extrema of a cost function. This leads to efficient gradient algorithms to synchronize (i.e., maximizing the consensus) or balance (i.e., minimizing the consensus) the agents; a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time-varying. The cost function is linked to a specific centroid definition on manifolds, introduced here as the induced arithmetic mean, that is easily computable in closed form and may be of independent interest for a number of manifolds. The special orthogonal group SO (n) and the Grassmann manifold Grass (p, n) are treated as original examples. A link is also drawn with the many existing results on the circle. © 2009 Society for Industrial and Applied Mathematics.

Synchronization in networks of identical linear systems

The paper investigates the synchronization of a network of identical linear time-invariant state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected. Stronger conditions are shown to be sufficient - but to some extent, also necessary - to ensure synchronization with the diffusive static output coupling often considered in the literature. © 2008 IEEE.

Stabilization of planar collective motion with limited communication

This paper proposes a design methodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particles around the same circle. Particles exchange relative information according to a communication graph that can be undirected or directed and time-invariant or time-varying. The emphasis of this paper is to show how previous results assuming all-to-all communication can be extended to a general communication framework. © 2008 IEEE.

Stabilization of collective motion in three dimensions: A consensus approach

This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the stabilization problem is reduced to a consensus problem. We first derive the stabilizing control laws in the presence of all-to-all communication. Providing each agent with a consensus estimator, we then extend the results to a general setting that allows for unidirectional and time-varying communication topologies. © 2007 IEEE.

Synchronization and balancing on the N-torus

In this paper, we study the behavior of a network of N agents, each evolving on the circle. We propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the (possibly time-varying and unidirectional) communication graphs. The global convergence analysis on the N-torus is a distinctive feature of the present work with respect to previous results that have focused on convergence in the Euclidean space. © 2006 Elsevier B.V. All rights reserved.

Collective optimization over average quantities

This paper addresses the design of algorithms for the collective optimization of a cost function defined over average quantities in the presence of limited communication. We argue that several meaningful collective optimization problems can be formulated in this way. As an application of the proposed approach, we propose a novel algorithm that achieves synchronization or balancing in phase models of coupled oscillators under mild connectedness assumptions on the (possibly time-varying and unidirectional) communication graphs. © 2006 IEEE.

Differential geometry and design coupling in MDO

The notion of coupling within a design, particularly within the context of Multidisciplinary Design Optimization (MDO), is much used but ill-defined. There are many different ways of measuring design coupling, but these measures vary in both their conceptions of what design coupling is and how such coupling may be calculated. Within the differential geometry framework which we have previously developed for MDO systems, we put forth our own design coupling metric for consideration. Our metric is not commensurate with similar types of coupling metrics, but we show that it both provides a helpful geo- metric interpretation of coupling (and uncoupledness in particular) and exhibits greater generality and potential for analysis than those similar metrics. Furthermore, we discuss how the metric might be profitably extended to time-varying problems and show how the metric's measure of coupling can be applied to multi-objective optimization problems (in unconstrained optimization and in MDO). © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.