Showing papers by "Richard H. Middleton published in 2014"

Necessary and Sufficient LMI Conditions for Stability and Performance Analysis of 2-D Mixed Continuous-Discrete-Time Systems

Abstract: This paper proposes necessary and sufficient conditions for stability and performance analysis of 2-D mixed continuous-discrete-time systems that can be checked with convex optimization, in particular linear matrix inequalities (LMIs). Specifically, the first contribution of the paper is a condition for exponential stability based on the introduction of a complex Lyapunov function depending polynomially on a parameter and on the use of the Gram matrix method. It is shown that this condition is sufficient for any chosen degree of the complex Lyapunov function, and necessary for an a priori known degree. The second contribution is a non-Lyapunov condition for exponential stability based on eigenvalue products. This condition is necessary and sufficient, and has the advantage of requiring a significantly smaller computational burden for achieving necessity. Lastly, the third contribution is to show how upper bounds on the H∞ norm of 2-D mixed continuous-discrete-time systems can be obtained through a semidefinite program based on complex Lyapunov functions. A necessary and sufficient condition is provided for establishing the tightness of the found upper bounds.

Switching Strategies to Mitigate HIV Mutation

Abstract: HIV mutates rapidly and may develop resistance to specific drug therapies. There is no general agreement on how to optimally schedule the available treatments for mitigating the effects of mutations. With a switched positive linear system, we examined different control strategies applied to a higher order nonlinear mutation model. Simulation results suggest that model predictive control could outperform the common clinical treatment recommendations. This brief is a step forward to develop further tools for helping the practitioners to find the optimal treatment schedule.

Optimal real-time distributed V2G and G2V management of electric vehicles

Abstract: This paper exploits the analogy between the electrical grid and modern communication networks to implement Electric Vehicle (EV) battery charging scheduling algorithms inspired by popular communication network techniques. In preliminary works, a similar approach was used to manage the Grid-to-Vehicle (G2V) active power flows. In this paper, we extend this framework to both implement the Vehicle-to-Grid (V2G) concept and to provide reactive power compensation capabilities that do not affect charging times. The ability of the proposed algorithms to optimally share the available/desired power in a fair way, with minimum communication requirements, in a very uncertain, dynamically changing framework, is illustrated through several examples for different scenarios of interest.

An independent system for real-time dynamic multileaf collimation trajectory verification using EPID.

Abstract: A new tool has been developed to verify the trajectory of dynamic multileaf collimators (MLCs) used in advanced radiotherapy techniques using only the information provided by the electronic portal imaging devices (EPID) measured image frames. The prescribed leaf positions are resampled to a higher resolution in a pre-processing stage to improve the verification precision. Measured MLC positions are extracted from the EPID frames using a template matching method. A cosine similarity metric is then applied to synchronise measured and planned leaf positions for comparison. Three additional comparison functions were incorporated to ensure robust synchronisation. The MLC leaf trajectory error detection was simulated for both intensity modulated radiation therapy (IMRT) (prostate) and volumetric modulated arc therapy (VMAT) (head-and-neck) deliveries with anthropomorphic phantoms in the beam. The overall accuracy for MLC positions automatically extracted from EPID image frames was approximately 0.5 mm. The MLC leaf trajectory verification system can detect leaf position errors during IMRT and VMAT with a tolerance of 3.5 mm within 1 s.

Equilibria and stability of a class of positive feedback loops

Abstract: Positive feedback loops are common regulatory elements in metabolic and protein signalling pathways The length of such feedback loops determines stability and sensitivity to network perturbations Here we provide a mathematical analysis of arbitrary length positive feedback loops with protein production and degradation These loops serve as an abstraction of typical regulation patterns in protein signalling pathways We first perform a steady state analysis and, independently of the chain length, identify exactly two steady states that represent either biological activity or inactivity We thereby provide two formulas for the steady state protein concentrations as a function of feedback length, strength of feedback, as well as protein production and degradation rates Using a control theory approach, analysing the frequency response of the linearisation of the system and exploiting the Small Gain Theorem, we provide conditions for local stability for both steady states Our results demonstrate that, under some parameter relationships, once a biological meaningful on steady state arises, it is stable, while the off steady state, where all proteins are inactive, becomes unstable We apply our results to a three-tier feedback of caspase activation in apoptosis and demonstrate how an intermediary protein in such a loop may be used as a signal amplifier within the cascade Our results provide a rigorous mathematical analysis of positive feedback chains of arbitrary length, thereby relating pathway structure and stability

Spatial Quantification of Cytosolic Ca $^{2+}$ Accumulation in Nonexcitable Cells:An Analytical Study

Abstract: Calcium ions act as messengers in a broad range of processes such as learning, apoptosis, and muscular movement. The transient profile and the temporal accumulation of calcium signals have been suggested as the two main characteristics in which calcium cues encode messages to be forwarded to downstream pathways. We address the analytical quantification of calcium temporal-accumulation in a long, thin section of a nonexcitable cell by solving a boundary value problem. In these expressions we note that the cytosolic Ca $^{2+}$ accumulation is independent of every intracellular calcium flux and depends on the Ca $^{2+}$ exchange across the membrane, cytosolic calcium diffusion, geometry of the cell, extracellular calcium perturbation, and initial concentrations. In particular, we analyse the time-integrated response of cytosolic calcium due to i) a localised initial concentration of cytosolic calcium and ii) transient extracellular perturbation of calcium. In these scenarios, we conclude that i) the range of calcium progression is confined to the vicinity of the initial concentration, thereby creating calcium microdomains; and ii) we observe a low-pass filtering effect in the response driven by extracellular Ca $^{2+}$ perturbations. Additionally, we note that our methodology can be used to analyse a broader range of stimuli and scenarios.

On the robust stability of 2D mixed continuous-discrete-time systems with uncertainty

Abstract: This paper addresses the problem of establishing robust exponential stability of 2D mixed continuous-discrete-time systems affected by uncertainty. Specifically, it is supposed that the matrices of the system are polynomial functions of an uncertain vector constrained over a semialgebraic set. First, it is shown that robust exponential stability is equivalent to the existence of a complex Lyapunov functions depending polynomially on the uncertain vector and an additional parameter of degree not greater than a known quantity. Second, a condition for establishing robust exponential stability is proposed via convex optimization by exploiting sums-of-squares (SOS) matrix polynomials. This condition is sufficient for any chosen degree of the complex Lyapunov function candidate, and is also necessary for degrees sufficiently large.

Optimal anti-aliasing filter based on multi criteria sampled-data ℋ ∞ control

Abstract: A systematic evaluation procedure is presented and applied to generate optimal anti-aliasing filters. It is based on multi criteria ℋ ∞ optimization, where sampled-data measures are introduced to capture the intersample behavior. The optimization scheme is based on linear matrix inequalities (LMIs) formulated in the delta operator, and the result is a low order controller of PID type. Both low frequency performance, mid frequency stability margins and high frequency control activity are taken into account. A detailed investigation shows that a new simple rule for design of anti-aliasing filters gives nearly optimal closed loop performance for a number of representative plant models.

Lymph compartment models and HIV intra patient infection dynamics.

Abstract: A compartment model is proposed to describe the HIV infection in humans. The compartments describe the blood, several lymph nodes and connecting lymph vessels. The dynamics in each compartment are ...

Multiple access Gaussian channels with feedback

Abstract: We consider the problem of multiple access communication with feedback, and show that the well known schemes of Ozarow and Kramer may be represented as feedback systems with a marginally unstable decoder. Other approaches represent these schemes as feedback systems with a strictly unstable encoder. Both approaches achieve the same rate of convergence, however the latter has a Bode sensitivity function which can be very large, indicating the potential for poor robustness and disturbance response.

To boost or not to boost: Immune activation in HIV infection

Abstract: Various clinical experiments have suggested the significant role of CD4+ T cells activation in viral spread and immune control of HIV infection. In this paper, we use a new mathematical model to explore the intricate interactions among immune activation, CTL response, T cell depletion, and immune escape. It is shown that enhanced immune activation and proliferation of CD4+ T cells, opposite to its beneficial effects in other infections, may facilitate infection and lead to the depletion of CD4+ T cells if effective immune control is not established. By contrast, once effective CTL response to HIV is mounted, the boost of CD4+ T cell response may be beneficial for controlling infection and alleviating immune impairment. Another finding is that immune escape may occur when the infection rate is low, and enhanced activation may prevent the escape if effective immune control can be established. Simulations are provided to illustrate the theoretical analysis.

Cyclic interconnection in 1-D vehicle formation control

Abstract: In this paper, we study a formation control scheme for a 1D string of vehicles. Each member tracks the movement of its immediate predecessor but also the first vehicle tracks the position of the last member of the string. We discuss conditions for the stability of the full interconnected system and show that if a constant inter-vehicle spacing policy is used, the interconnection becomes unstable after the string size surpasses a critical value. Moreover, we show that if constant time headway is used in the spacing policy, stability can be recovered for any string size. String stability is also achieved as a consequence.