Representations and algorithms for finite-state bisimulations of linear discrete-time control systems

While a large amount of research over the past two decades has focused on discrete abstractions of infinite-state dynamical systems, many structural and algorithmic details of these abstractions remain unknown. To clarify the computational resources needed to perform discrete abstractions, this paper examines the algorithmic properties of an existing method for deriving finite-state systems that are bisimilar to linear discrete-time control systems. We explicitly find the structure of the finite-state system, show that it can be enormous compared to the original linear system, and give conditions to guarantee that the finite-state system is reasonably sized and efficiently computable. Though constructing the finite-state system is generally impractical, we see that special cases could be amenable to satisfiability based verification techniques. ©2009 IEEE.

Trading the stability of finite zeros for global stabilization of nonlinear cascade systems

This note analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a Stable nonlinear system. It is shown that the instability of the zeros of the linear System can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term. Below this limit, global stabilization is achieved by smooth static-state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions.

Trading the stability of finite zeros for global stabilization of nonlinear cascade systems

This paper analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a stable nonlinear system. It is shown that the instability of the zeros of the linear system can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term. Below this limit, global stabilization is achieved by smooth static state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions.

Language model combination and adaptation using weighted finite state transducers

In speech recognition systems language model (LMs) are often constructed by training and combining multiple n-gram models. They can be either used to represent different genres or tasks found in diverse text sources, or capture stochastic properties of different linguistic symbol sequences, for example, syllables and words. Unsupervised LM adaptation may also be used to further improve robustness to varying styles or tasks. When using these techniques, extensive software changes are often required. In this paper an alternative and more general approach based on weighted finite state transducers (WFSTs) is investigated for LM combination and adaptation. As it is entirely based on well-defined WFST operations, minimum change to decoding tools is needed. A wide range of LM combination configurations can be flexibly supported. An efficient on-the-fly WFST decoding algorithm is also proposed. Significant error rate gains of 7.3% relative were obtained on a state-of-the-art broadcast audio recognition task using a history dependently adapted multi-level LM modelling both syllable and word sequences. ©2010 IEEE.

Fixed-lag blind equalization and sequence estimation in digital communications systems using sequential importance sampling

We present methods for fixed-lag smoothing using Sequential Importance sampling (SIS) on a discrete non-linear, non-Gaussian state space system with unknown parameters. Our particular application is in the field of digital communication systems. Each input data point is taken from a finite set of symbols. We represent transmission media as a fixed filter with a finite impulse response (FIR), hence a discrete state-space system is formed. Conventional Markov chain Monte Carlo (MCMC) techniques such as the Gibbs sampler are unsuitable for this task because they can only perform processing on a batch of data. Data arrives sequentially, so it would seem sensible to process it in this way. In addition, many communication systems are interactive, so there is a maximum level of latency that can be tolerated before a symbol is decoded. We will demonstrate this method by simulation and compare its performance to existing techniques.

Rigorous finite-time guarantees for optimization on continuous domains by simulated annealing

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated annealing which allows one to guarantee finite-time performance in the optimization of functions of continuous variables. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-date theory of convergence of Markov chain Monte Carlo methods on continuous domains. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.

ℓasso MPC: Smart regulation of over-actuated systems

In this paper, a novel MPC strategy is proposed, and referred to as asso MPC. The new paradigm features an 1-regularised least squares loss function, in which the control error variance competes with the sum of input channels magnitude (or slew rate) over the whole horizon length. This cost choice is motivated by the successful development of LASSO theory in signal processing and machine learning. In the latter fields, sum-of-norms regularisation have shown a strong capability to provide robust and sparse solutions for system identification and feature selection. In this paper, a discrete-time dual-mode asso MPC is formulated, and its stability is proven by application of standard MPC arguments. The controller is then tested for the problem of ship course keeping and roll reduction with rudder and fins, in a directional stochastic sea. Simulations show the asso MPC to inherit positive features from its corresponding regressor: extreme reduction of decision variables' magnitude, namely, actuators' magnitude (or variations), with a finite energy error, being particularly promising for over-actuated systems. © 2012 AACC American Automatic Control Council).