scispace - formally typeset
Search or ask a question

Showing papers by "Richard H. Middleton published in 2012"


Journal ArticleDOI
TL;DR: This technical note proposes the use of homogeneous polynomial Lyapunov functions in the non-restrictive case where all the subsystems are Hurwitz, showing that a sufficient condition can be provided in terms of an LMI feasibility test by exploiting a key representation of polynomials.
Abstract: Ensuring stability of switched linear systems with a guaranteed dwell time is an important problem in control systems. Several methods have been proposed in the literature to address this problem, but unfortunately they provide sufficient conditions only. This technical note proposes the use of homogeneous polynomial Lyapunov functions in the non-restrictive case where all the subsystems are Hurwitz, showing that a sufficient condition can be provided in terms of an LMI feasibility test by exploiting a key representation of polynomials. Several properties are proved for this condition, in particular that it is also necessary for a sufficiently large degree of these functions. As a result, the proposed condition provides a sequence of upper bounds of the minimum dwell time that approximate it arbitrarily well. Some examples illustrate the proposed approach.

156 citations


Journal ArticleDOI
TL;DR: A number of distributed algorithms for achieving relative average fairness whilst maximising utilisation are described, borrowing from communication networks and distributed convex optimisation.
Abstract: Motivated by the problems of charging a number of electric vehicles via limited capacity infrastructure, this article considers the problem of individual load adjustment under a total capacity constraint. For reasons of scalability and simplified communications, distributed solutions to this problem are sought. Borrowing from communication networks (AIMD algorithms) and distributed convex optimisation, we describe a number of distributed algorithms for achieving relative average fairness whilst maximising utilisation. We present analysis and simulation results to show the performance of these algorithms. In the scenarios examined, the algorithm's performance is typically within 5% of that achievable in the ideal centralised case, but with greatly enhanced scalability and reduced communication requirements.

115 citations


Proceedings ArticleDOI
04 Mar 2012
TL;DR: In this article, the authors investigated the policy to share the available power to charge EVs in a distributed way, motivated by the expected increase of the penetration level of electric vehicles (EVs), and the wider usage of renewable energies.
Abstract: Motivated by the expected increase of the penetration level of Electric Vehicles (EVs), and the wider usage of renewable energies, this paper investigates policy to share the available power to charge EVs. This paper follows the preliminary work [1] of the authors, where AIMD (Additive Increase Multiplicative Decrease) [2] based techniques were first proposed to charge EVs in a distributed way. The same mathematical framework is adopted in this paper, but the algorithms are tailored to deal with new scenarios of interest, as illustrated in detail in Section III.

37 citations


Journal ArticleDOI
TL;DR: The conclusion is that the scaling procedure is (somewhat surprisingly) much more essential for shorter sampling periods than avoiding the cancellation problem.
Abstract: The numerical sensitivity of linear matrix inequalities (LMIs) arising from discrete-time control with short sampling periods is analyzed using shift and delta operators. The delta operator avoids cancellation problems for short sampling periods, and it includes a system scaling proportional to the inverse of the sampling period. The numerical sensitivity of both these mechanisms is investigated analytically, and verified by numerical examples. The conclusion is that the scaling procedure is (somewhat surprisingly) much more essential for shorter sampling periods than avoiding the cancellation problem.

29 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed a two-state feedback motif for the integrative modelling of Parkinson's disease, which is based on the switch-like transition of a bistable feedback process from "healthy" homeostatic levels of reactive oxygen species and the protein α-synuclein, to an alternative "disease" state in which concentrations of both molecules are stable at damagingly high-levels associated with PD.
Abstract: Previous article on the integrative modelling of Parkinson's disease (PD) described a mathematical model with properties suggesting that PD pathogenesis is associated with a feedback-induced biochemical bistability. In this article, the authors show that the dynamics of the mathematical model can be extracted and distilled into an equivalent two-state feedback motif whose stability properties are controlled by multi-factorial combinations of risk factors and genetic mutations associated with PD. Based on this finding, the authors propose a principle for PD pathogenesis in the form of the switch-like transition of a bistable feedback process from ‘healthy’ homeostatic levels of reactive oxygen species and the protein α-synuclein, to an alternative ‘disease’ state in which concentrations of both molecules are stable at the damagingly high-levels associated with PD. The bistability is analysed using the rate curves and steady-state response characteristics of the feedback motif. In particular, the authors show how a bifurcation in the feedback motif marks the pathogenic moment at which the ‘healthy’ state is lost and the ‘disease’ state is initiated. Further analysis shows how known risks (such as: age, toxins and genetic predisposition) modify the stability characteristics of the feedback motif in a way that is compatible with known features of PD, and which explain properties such as: multi-factorial causality, variability in susceptibility and severity, multi-timescale progression and the special cases of familial Parkinson's and Parkinsonian symptoms induced purely by toxic stress.

26 citations


01 Dec 2012
TL;DR: The dynamics of the mathematical model can be extracted and distilled into an equivalent two-state feedback motif whose stability properties are controlled by multi-factorial combinations of risk factors and genetic mutations associated with PD.
Abstract: Previous article on the integrative modelling of Parkinson's disease (PD) described a mathematical model with properties suggesting that PD pathogenesis is associated with a feedback-induced biochemical bistability. In this article, the authors show that the dynamics of the mathematical model can be extracted and distilled into an equivalent two-state feedback motif whose stability properties are controlled by multi-factorial combinations of risk factors and genetic mutations associated with PD. Based on this finding, the authors propose a principle for PD pathogenesis in the form of the switch-like transition of a bistable feedback process from 'healthy' homeostatic levels of reactive oxygen species and the protein α-synuclein, to an alternative 'disease' state in which concentrations of both molecules are stable at the damagingly high-levels associated with PD. The bistability is analysed using the rate curves and steady-state response characteristics of the feedback motif. In particular, the authors show how a bifurcation in the feedback motif marks the pathogenic moment at which the 'healthy' state is lost and the 'disease' state is initiated. Further analysis shows how known risks (such as: age, toxins and genetic predisposition) modify the stability characteristics of the feedback motif in a way that is compatible with known features of PD, and which explain properties such as: multi-factorial causality, variability in susceptibility and severity, multi-timescale progression and the special cases of familial Parkinson's and Parkinsonian symptoms induced purely by toxic stress.

8 citations


Proceedings ArticleDOI
13 Dec 2012
TL;DR: Previous work on suboptimal control of a simplified model of HIV infection with mutations is extended to include a `dwell time' constraint on the switching actions, that is, impose a strict minimum time between altering therapy.
Abstract: Regulation of mutant viri is important in many disease including HIV infection. Under current multi-drug Anti-Retroviral Therapies for HIV treatment, resistant mutations and failure to regulate viral load is typically observed after approximately 6 years. When this occurs, the current therapy must be abandoned and a new therapy initiated. An alternate approach is to treat this as a switching control problem, wherein therapy may be alternated well before virological failure is observed. In this paper we extend previous work on suboptimal control of a simplified model of HIV infection with mutations. The particular extension here is to include a ‘dwell time’ constraint on the switching actions, that is, impose a strict minimum time between altering therapy.

8 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examine two industrial case studies to illustrate the power of nonlinear MPC in practice and point to future research challenges and opportunities, as well as future research opportunities.

8 citations


Book ChapterDOI
18 Jun 2012
TL;DR: In this paper a technique is presented that implicitly disambiguates these detected field line objects in order to use them for localization purposes.
Abstract: The Standard Platform League (SPL) provides an environment that is essentially static; with the exception of other robots and the audience, the area in which a robot is expected to localise itself is quite favourable. However, a large number of the predefined landmarks in the given world model can be perceived as ambiguous in many scenarios, with the prime example being field line markings. In this paper a technique is presented that implicitly disambiguates these detected field line objects in order to use them for localization purposes.

6 citations


Journal ArticleDOI
TL;DR: Two biologically justified approximations are developed which study the role of feedback loops in spatiotemporal signal progression and results can be applied to studies in cell proliferation, cell differentiation and cell death in other spatially extended cells.

5 citations


Proceedings Article
01 Nov 2012
TL;DR: In this paper, the authors considered a platoon as a two-dimensional (2D) continuous-discrete system with an unavoidable singularity on the stability boundary and care is needed in their analysis.
Abstract: String stability issues in vehicle platoons have been studied in various ways. In the homogeneous unidirectional case, the platoon can be considered as a two dimensional (2D) continuous-discrete systems with an unavoidable singularity on the stability boundary and care is needed in their analysis. Frequency domain analysis of such 2D systems allows analysis of BIBO stability and other features.

Proceedings ArticleDOI
01 Dec 2012
TL;DR: The numerical sensitivity of Linear Matrix Inequalities arising in the H∞ norm computation in discrete time is analyzed and it is shown that rescaling of the shift operator formulation gives substantial improvements in numerical conditioning, whilst recentering is of more limited benefit.
Abstract: The numerical sensitivity of Linear Matrix Inequalities (LMIs) arising in the H ∞ norm computation in discrete time is analyzed. Rapid sampling scenarios are examined comparing both shift and delta operator formulations of the equations. The shift operator formulation is shown in general to be arbitrarily poorly conditioned as the sampling rate increases. The delta operator formulation includes both recentering (to avoid cancellation problems) and rescaling, and avoids these difficulties. However, it is also shown that rescaling of the shift operator formulation gives substantial improvements in numerical conditioning, whilst recentering is of more limited benefit.

Book ChapterDOI
01 Jan 2012
TL;DR: This chapter explores the association of repetitive firing pattern of these neurons and cytosolic calcium using a mathematical model and proposes a role of low voltage activated L-type calcium channel in creating an energy stress within vulnerable neurons.
Abstract: Cytosolic calcium ion levels are critical in sustaining neuronal activity. They have an intricate relationship with the neuronal energy systems, and Parkinson’s disease (PD) probably involves a dysfunctional energy system in the pacemaking neurons of the Substantia nigra. This chapter explores the association of repetitive firing pattern of these neurons and cytosolic calcium using a mathematical model. In particular, a theory is examined that proposes a role of low voltage activated L-type calcium channel in creating an energy stress within vulnerable neurons.

Proceedings ArticleDOI
01 Dec 2012
TL;DR: The time-integrals of a class of nonlinear reaction-diffusion systems commonly found in networks of biochemical reactions allow us to understand how signal transmission depends on initial and boundary conditions, spatial geometry and the turnover rates of some species.
Abstract: In this work we analytically derive the time-integral of a class of nonlinear reaction-diffusion systems commonly found in networks of biochemical reactions. This formula is inferred using the Laplacian Spectral Decomposition method, which approximates the solution of the Partial Differential Equations by a finite series capturing the most relevant dynamics. The time-integrals allow us to understand how signal transmission depends on initial and boundary conditions, spatial geometry and the turnover rates of some species.

Proceedings ArticleDOI
01 Dec 2012
TL;DR: It is shown that the existence of a negative semidefinite solution Q of the Lyapunov equation ATP+AP = Q with a positive definite block diagonal matrix P = PT together with simple additional conditions is sufficient to guarantee asymptotic stability.
Abstract: It is shown that the existence of a negative semidefinite solution Q of the Lyapunov equation ATP+AP = Q with a positive definite block diagonal matrix P = PT together with simple additional conditions is sufficient to guarantee asymptotic stability. The stability conditions presented can be used to study a wider range of dynamical systems, including systems with singularities at the stability boundary, which cannot be exponentially stable.


Journal ArticleDOI
TL;DR: It is shown that the Kamke–Muller conditions for bimodal piecewise-smooth systems are equivalent to simple conditions on the vector fields defining the system, and monotonicity is equivalent to continuity.

Proceedings ArticleDOI
27 Jun 2012
TL;DR: A class of reaction-diffusion PDEs is considered, where a suitable state transformation allows conversion to a heat equation together with a lower order PDE set and by giving an explicit solution to the heat equation the authors are able to obtain a complete solutions to the original PDE.
Abstract: In this paper, we consider a class of reaction-diffusion PDEs. For this class, a suitable state transformation allows conversion to a heat equation together with a lower order PDE set. By giving an explicit solution to the heat equation we are able to obtain a complete solution to the original PDE. By focusing on the computational load, we give a comparison of the pure numerical, analytical/numerical, analytical/approximated, and approximated methods of solving the PDE. In some examples, we note an almost order of magnitude improvement in computational load.

01 Jan 2012
TL;DR: In this paper, the association of repetitive firing pattern of these neurons and cytosolic calcium using a mathematical model was explored, and a theory was examined that proposes a role of low voltage activated L-type calcium channel in creating an energy stress within vulnerable neurons.
Abstract: Cytosolic calcium ion levels are critical in sustaining neuronal activity. They have an intricate relationship with the neuronal energy systems, and Parkinson’s disease (PD) probably involves a dysfunctional energy system in the pacemaking neurons of the Substantia nigra. This chapter explores the association of repetitive firing pattern of these neurons and cytosolic calcium using a mathematical model. In particular, a theory is examined that proposes a role of low voltage activated L-type calcium channel in creating an energy stress within vulnerable neurons.