60 research outputs found
Non-Asymptotic State and Disturbance Estimation for a Class of Triangular Nonlinear Systems using Modulating Functions
Dynamical models are often corrupted by model uncertainties, external
disturbances, and measurement noise. These factors affect the performance of
model-based observers and as a result, affect the closed-loop performance.
Therefore, it is critical to develop robust model-based estimators that
reconstruct both the states and the model disturbances while mitigating the
effect of measurement noise in order to ensure good system monitoring and
closed-loop performance when designing controllers. In this article, a robust
step by step non-asymptotic observer for triangular nonlinear systems for the
joint estimation of the state and the disturbance is developed. The proposed
approach provides a sequential estimation of the states and the disturbance in
finite time using smooth modulating functions. The robustness of the proposed
observer is both in the sense of model disturbances and measurement noise. In
fact, the structure of triangular systems combined with the modulating
function-based method allows the estimation of the states independently of
model disturbances and the integral operator involved in the modulating
function-based method mitigates the noise. Additionally, the modulating
function method shifts the derivative from the noisy output to the smooth
modulating function which strengthens its robustness properties. The
applicability of the proposed modulating function-based estimator is
illustrated in numerical simulations and compared to a second-order sliding
mode super twisting observer under different measurement noise levels.Comment: 24 page
Finite-time simultaneous estimation of aortic blood flow and differentiation order for fractional-order arterial Windkessel model calibration
A fractional-order vascular model representation for emulating arterial hemody-namics has been recently presented as an alternative to the well-known integer-order arterial Windkessel. The model uses a fractional-order capacitor (FOC) to describe the complex and frequency-dependent arterial compliance. This paper presents a two-stage algorithm based on modulating functions for finite-time simultaneous estimation of the model’s input and the fractional differentiation order. The proposed approach is validated using in-silico human data. Results show the prominent potential of this method for calibrating arterial models and enhancing cardiovascular mechanics research as well as clinical practice
Metric entropy for functions of bounded total generalized variation
We establish a sharp estimate for a minimal number of binary digits (bits)
needed to represent all bounded total generalized variation functions taking
values in a general totally bounded metric space up to an accuracy
of with respect to the -distance. Such an estimate
is explicitly computed in terms of doubling and packing dimensions of
. The obtained result is applied to provide an upper bound on the
metric entropy for a set of entropy admissible weak solutions to scalar
conservation laws in one-dimensional space with weakly genuinely nonlinear
fluxes.Comment: 2
Gibbs posterior concentration rates under sub-exponential type losses
Bayesian posterior distributions are widely used for inference, but their
dependence on a statistical model creates some challenges. In particular, there
may be lots of nuisance parameters that require prior distributions and
posterior computations, plus a potentially serious risk of model
misspecification bias. Gibbs posterior distributions, on the other hand, offer
direct, principled, probabilistic inference on quantities of interest through a
loss function, not a model-based likelihood. Here we provide simple sufficient
conditions for establishing Gibbs posterior concentration rates when the loss
function is of a sub-exponential type. We apply these general results in a
range of practically relevant examples, including mean regression, quantile
regression, and sparse high-dimensional classification. We also apply these
techniques in an important problem in medical statistics, namely, estimation of
a personalized minimum clinically important difference.Comment: 60 pages, 1 figur
Some contributions to model selection and statistical inference in Markovian models
The general theme of this thesis is providing and studying a new understanding of some statistical models and computational methods based on a Markov process/chain. Section 1-4 are devoted to reviewing the literature for the sake of completeness and the better understanding of Section 5-7 that are our original studies. Section 1 is devoted to understanding a Markov process since continuous and discrete types of a Markov process are hinges of the thesis. In particular, we will study some basics/advanced results of Markov chains and Ito diffusions. Ergodic properties of these processes are also documented. In Section 2 we first study the Metropolis-Hastings algorithm since this is basic of other MCMC methods. We then study more advanced methods such as Reversible Jump MCMC, Metropolis-adjusted Langevin algorithm, pseudo marginal MCMC and Hamiltonian Monte Carlo. These MCMC methods will appear in Section 3, 4 and 7. In Section 3 we consider another type of Monte Carlo method called sequential Monte Carlo (SMC). Unlike MCMC methods, SMC methods often give us on-line ways to approximate intractable objects. Therefore, these methods are particularly useful when one needs to play around with models with scalable computational costs. Some mathematical analysis of SMC also can be found. These SMC methods will appear in Section 4, 5, 6 and 7. In Section 4 we first discuss hidden Markov models (HMMs) since all statistical models that we consider in the thesis can be treated as HMMs or their generalisation. Since, in general, HMMs involve intractable objects, we then study approximation ways for them based on SMC methods. Statistical inference for HMMs is also considered. These topics will appear in Section 5, 6 and 7. Section 5 is largely based on a submitted paper titled Asymptotic Analysis of Model Selection Criteria for General Hidden Markov Models with Alexandros Beskos and Sumeetpal Sidhu Singh, https: //arxiv.org/abs/1811.11834v3. In this section, we study the asymptotic behaviour of some information criteria in the context of hidden Markov models, or state space models. In particular, we prove the strong consistency of BIC and evidence for general HMMs. Section 6 is largely based on a submitted paper titled Online Smoothing for Diffusion Processes Observed with Noise with Alexandros Beskos, https://arxiv.org/abs/2003.12247. In this section, we develop sequential Monte Carlo methods to estimate parameters of (jump) diffusion models. Section 7 is largely based on an ongoing paper titled Adaptive Bayesian Model Selection for Diffusion Models with Alexandros Beskos. In this section, we develop adaptive computational ways, based on sequential Monte Carlo samplers and Hamiltonian Monte Carlo on a functional space, for Bayesian model selection
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