An internal model principle is necessary and sufficient for linear output synchronization

Output synchronization of a network of heterogeneous linear state–space models under time-varying and directed interconnection structures is investigated. It is shown that, assuming stabilizability and detectability of the individual systems and imposing very mild connectedness assumptions on the interconnection structure, an internal model requirement is necessary and sufficient for synchronizability of the network to polynomially bounded trajectories. The resulting dynamic feedback couplings can be interpreted as a generalization of existing methods for identical linear systems.     

Observability of switching structured linear systems with unknown input. A graph-theoretic approach

This paper deals with the observability of the discrete mode, the internal state and the input of switching structured linear systems with unknown input. The proposed method, based on a graph-theoretic approach, assumes only the knowledge of the system’s structure. We express, in graphical terms, necessary and sufficient conditions for the generic observability of the discrete mode, the continuous internal state and the input of a switching structured linear system. These conditions can be implemented by classical graph theory algorithms based on finding particular paths and cycles in a digraph.     

Redesign of adaptive observers for improved parameter identification in nonlinear systems

We propose a method for redesigning adaptive observers for nonlinear systems. The redesign uses an adaptive law that is based on delayed observers. This increases the computational burden, but gives significantly better parameter identification and robustness properties. In particular, given that a special persistency of excitation condition is satisfied, we prove uniform global asymptotic stability and semi-global exponential stability of the origin of the state and parameter estimation error, and give explicit lower bounds on the convergence rate of both the state and parameter estimation error dynamics. For initial conditions with a known upper bound, we prove tunable exponential convergence rate. To illustrate the use of the proposed method, we apply it to estimate the unmeasured flow rate and the uncertain friction parameters in a model of a managed pressure drilling system. The simulation results clearly show the improved performance of the redesigned adaptive observer compared to a traditional design.     

Analysis of autocatalytic networks in biology

Autocatalytic networks, in particular the glycolytic pathway, constitute an important part of the cell metabolism. Changes in the concentration of metabolites and catalyzing enzymes during the lifetime of the cell can lead to perturbations from its nominal operating condition. We investigate the effects of such perturbations on stability properties, e.g., the extent of regions of attraction, of a particular family of autocatalytic network models. Numerical experiments demonstrate that systems that are robust with respect to perturbations in the parameter space have an easily “verifiable” (in terms of proof complexity) region of attraction properties. Motivated by the computational complexity of optimization-based formulations, we take a compositional approach and exploit a natural decomposition of the system, induced by the underlying biological structure, into a feedback interconnection of two input–output subsystems: a small subsystem with complicating nonlinearities and a large subsystem with simple dynamics. This decomposition simplifies the analysis of large pathways by assembling region of attraction certificates based on the input–output properties of the subsystems. It enables numerical as well as analytical construction of block-diagonal Lyapunov functions for a large family of autocatalytic pathways.     

A global piecewise smooth Newton method for fast large-scale model predictive control

In this paper, the strictly convex quadratic program (QP) arising in model predictive control (MPC) for constrained linear systems is reformulated as a system of piecewise affine equations. A regularized piecewise smooth Newton method with exact line search on a convex, differentiable, piecewise-quadratic merit function is proposed for the solution of the reformulated problem. The algorithm has considerable merits when applied to MPC over standard active set or interior point algorithms. Its performance is tested and compared against state-of-the-art QP solvers on a series of benchmark problems. The proposed algorithm is orders of magnitudes faster, especially for large-scale problems and long horizons. For example, for the challenging crude distillation unit model of Pannocchia, Rawlings, and Wright (2007) with 252 states, 32 inputs, and 90 outputs, the average running time of the proposed approach is 1.57 ms.     

On singular perturbations due to fast actuators in hybrid control systems

A stability result is given for hybrid control systems singularly perturbed by fast but continuous actuators. If a hybrid control system has a compact set globally asymptotically stable when the actuator dynamics are omitted, or equivalently, are infinitely fast, then the same compact set is semiglobally practically asymptotically stable in the finite speed of the actuator dynamics. This result, which generalizes classical results for differential equations, justifies using a simplified plant model that ignores fast but continuous actuator dynamics, even when using a hybrid feedback control algorithm.     

A Quantum Monte Carlo method at fixed energy

In this paper we explore ways to study the zero temperature limit of quantum statistical mechanics using Quantum Monte Carlo simulations. We develop a Quantum Monte Carlo method in which one fixes the ground state energy as a parameter. The Hamiltonians we consider are of the form H=H₀+λV with ground state energy E. For fixed H₀ and V, one can view E as a function of λ whereas we view λ as a function of E. We fix E and define a path integral Quantum Monte Carlo method in which a path makes no reference to the times (discrete or continuous) at which transitions occur between states. For fixed E we can determine λ(E) and other ground state properties of H.     

Toward large-scale Hybrid Monte Carlo simulations of the Hubbard model on graphics processing units

One of the most efficient non-perturbative methods for the calculation of thermal properties of quantum systems is the Hybrid Monte Carlo algorithm, as evidenced by its use in large-scale lattice quantum chromodynamics calculations. The performance of this algorithm is determined by the speed at which the fermion operator is applied to a given vector, as it is the central operation in the preconditioned conjugate gradient iteration. We study a simple implementation of these operations for the fermion matrix of the Hubbard model in d+1 spacetime dimensions, and report a performance comparison between a 2.66 GHz Intel Xeon E5430 CPU and an NVIDIA Tesla C1060 GPU using double-precision arithmetic. We find speedup factors ranging between 30 and 350 for d=1, and in excess of 40 for d=3. We argue that such speedups are of considerable impact for large-scale simulational studies of quantum many-body systems.     

Abstract processes of place/transition systems

A well-known problem in Petri net theory is to formalise an appropriate causality-based concept of process or run for place/transition systems. The so-called individual token interpretation, where tokens are distinguished according to their causal history, giving rise to the processes of Goltz and Reisig, is often considered too detailed. The problem of defining a fully satisfying more abstract concept of process for general place/transition systems has so-far not been solved. In this paper, we recall the proposal of defining an abstract notion of process, here called BD-process, in terms of equivalence classes of Goltz-Reisig processes, using an equivalence proposed by Best and Devillers. It yields a fully satisfying solution for at least all one-safe nets. However, for certain nets which intuitively have different conflicting behaviours, it yields only one maximal abstract process. Here we identify a class of place/transition systems, called structural conflict nets, where conflict and concurrency due to token multiplicity are clearly separated. We show that, in the case of structural conflict nets, the equivalence proposed by Best and Devillers yields a unique maximal abstract process only for conflict-free nets. Thereby BD-processes constitute a simple and fully satisfying solution in the class of structural conflict nets.