Issues in the design of switched linear systems : a benchmark study

In this paper we present a tutorial overview of some of the issues that arise in the design of switched linear control systems. Particular emphasis is given to issues relating to stability and control system realisation. A benchmark regulation problem is then presented. This problem is most naturally solved by means of a switched control design. The challenge to the community is to design a control system that meets the required performance specifications and permits the application of rigorous analysis techniques. A simple design solution is presented and the limitations of currently available analysis techniques are illustrated with reference to this example

Towards 'smart lasers': self-optimisation of an ultrafast pulse source using a genetic algorithm

Short-pulse fibre lasers are a complex dynamical system possessing a broad space of operating states that can be accessed through control of cavity parameters. Determination of target regimes is a multi-parameter global optimisation problem. Here, we report the implementation of a genetic algorithm to intelligently locate optimum parameters for stable single-pulse mode-locking in a Figure-8 fibre laser, and fully automate the system turn-on procedure. Stable ultrashort pulses are repeatably achieved by employing a compound fitness function that monitors both temporal and spectral output properties of the laser. Our method of encoding photonics expertise into an algorithm and applying machine-learning principles paves the way to self-optimising `smart' optical technologies

Circuit Synthesis of Electrochemical Supercapacitor Models

This paper is concerned with the synthesis of RC electrical circuits from physics-based supercapacitor models describing conservation and diffusion relationships. The proposed synthesis procedure uses model discretisation, linearisation, balanced model order reduction and passive network synthesis to form the circuits. Circuits with different topologies are synthesized from several physical models. This work will give greater understanding to the physical interpretation of electrical circuits and will enable the development of more generalised circuits, since the synthesized impedance functions are generated by considering the physics, not from experimental fitting which may ignore certain dynamics

Transfer Entropy as a Log-likelihood Ratio

Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences, ecology, climatology and econometrics. We show that for a broad class of predictive models, the log-likelihood ratio test statistic for the null hypothesis of zero transfer entropy is a consistent estimator for the transfer entropy itself. For finite Markov chains, furthermore, no explicit model is required. In the general case, an asymptotic chi-squared distribution is established for the transfer entropy estimator. The result generalises the equivalence in the Gaussian case of transfer entropy and Granger causality, a statistical notion of causal influence based on prediction via vector autoregression, and establishes a fundamental connection between directed information transfer and causality in the Wiener-Granger sense

Multivariable proportional-integral-plus (PIP) control of the ALSTOM nonlinear gasifier simulation

Multivariable proportional-integral-plus (PIP) control methods are applied to the nonlinear ALSTOM Benchmark Challenge II. The approach utilises a data-based combined model reduction and linearisation step, which plays an essential role in satisfying the design specifications. The discrete-time transfer function models obtained in this manner are represented in a non-minimum state space form suitable for PIP control system design. Here, full state variable feedback control can be implemented directly from the measured input and output signals of the controlled process, without resorting to the design and implementation of a deterministic state reconstructor or a stochastic Kalman filter. Furthermore, the non-minimal formulation provides more design freedom than the equivalent minimal case, a characteristic that proves particularly useful in tuning the algorithm to meet the Benchmark specifications. The latter requirements are comfortably met for all three operating conditions by using a straightforward to implement, fixed gain, linear PIP algorithm

Order Reduction of the Chemical Master Equation via Balanced Realisation

We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension might be large even for trivial systems. Here, we derive a reduced ODE set that accurately approximates the probabilities of subspaces of interest with a known error bound. Our methodology is based on model reduction by balanced truncation and can be considerably more computationally efficient than the Finite State Projection Algorithm (FSP) when used for obtaining transient responses. We show the applicability of our method by analysing stochastic chemical reactions. First, we obtain a reduced order model for the infinitesimal generator of a Markov chain that models a reversible, monomolecular reaction. In such an example, we obtain an approximation of the output of a model with 301 states by a reduced model with 10 states. Later, we obtain a reduced order model for a catalytic conversion of substrate to a product; and compare its dynamics with a stochastic Michaelis-Menten representation. For this example, we highlight the savings on the computational load obtained by means of the reduced-order model. Finally, we revisit the substrate catalytic conversion by obtaining a lower-order model that approximates the probability of having predefined ranges of product molecules.Comment: 12 pages, 6 figure