Polynomial tuning of multiparametric combinatorial samplers

Boltzmann samplers and the recursive method are prominent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial structures, such as maps, tilings, RNA sequences or various tree-like structures. In their multiparametric variants, these samplers allow to control the profile of expected values corresponding to multiple combinatorial parameters. One can control, for instance, the number of leaves, profile of node degrees in trees or the number of certain subpatterns in strings. However, such a flexible control requires an additional non-trivial tuning procedure. In this paper, we propose an efficient polynomial-time, with respect to the number of tuned parameters, tuning algorithm based on convex optimisation techniques. Finally, we illustrate the efficiency of our approach using several applications of rational, algebraic and P\'olya structures including polyomino tilings with prescribed tile frequencies, planar trees with a given specific node degree distribution, and weighted partitions.Comment: Extended abstract, accepted to ANALCO2018. 20 pages, 6 figures, colours. Implementation and examples are available at [1] https://github.com/maciej-bendkowski/boltzmann-brain [2] https://github.com/maciej-bendkowski/multiparametric-combinatorial-sampler

Robust PI Controller Design Satisfying Gain and Phase Margin Constraints

This paper presents a control design algorithm for determining PI-type controllers satisfying specifications on gain margin, phase margin, and an upper bound on the (complementary) sensitivity for a finite set of plants. Important properties of the algorithm are: (i) it can be applied to plants of any order including plants with delay, unstable plants, and plants given by measured data, (ii) it is efficient and fast, and as such can be used in near real-time to determine controller parameters (for on-line modification of the plant model including its uncertainty and/or the specifications), (iii) it can be used to identify the optimal controller for a practical definition of optimality, and (iv) it enables graphical portrayal of design tradeoffs in a single plot (highlighting tradeoffs among the gain margin, complementary sensitivity bound, low frequency sensitivity and high frequency sensor noise amplification)

Predictive pole-placement control with linear models

The predictive pole-placement control method introduced in this paper embeds the classical pole-placement state feedback design into a quadratic optimisation-based model-predictive formulation. This provides an alternative to model-predictive controllers which are based on linear–quadratic control. The theoretical properties of the controller in a linear continuous-time setting are presented and a number of illustrative examples are given. These results provide the foundation for novel linear and nonlinear constrained predictive control methods based on continuous-time models

Dynamically Driven Renormalization Group

We present a detailed discussion of a novel dynamical renormalization group scheme: the Dynamically Driven Renormalization Group (DDRG). This is a general renormalization method developed for dynamical systems with non-equilibrium critical steady-state. The method is based on a real space renormalization scheme driven by a dynamical steady-state condition which acts as a feedback on the transformation equations. This approach has been applied to open non-linear systems such as self-organized critical phenomena, and it allows the analytical evaluation of scaling dimensions and critical exponents. Equilibrium models at the critical point can also be considered. The explicit application to some models and the corresponding results are discussed.Comment: Revised version, 50 LaTex pages, 6 postscript figure

Classical and quantum shortcuts to adiabaticity for scale-invariant driving

A shortcut to adiabaticity is a driving protocol that reproduces in a short time the same final state that would result from an adiabatic, infinitely slow process. A powerful technique to engineer such shortcuts relies on the use of auxiliary counterdiabatic fields. Determining the explicit form of the required fields has generally proven to be complicated. We present explicit counterdiabatic driving protocols for scale-invariant dynamical processes, which describe for instance expansion and transport. To this end, we use the formalism of generating functions, and unify previous approaches independently developed in classical and quantum studies. The resulting framework is applied to the design of shortcuts to adiabaticity for a large class of classical and quantum, single-particle, non-linear, and many-body systems.Comment: 17 pages, 5 figure