Asynchronous H

This paper is devoted to the problem of asynchronous H∞ estimation for a class of two-dimensional (2D) nonhomogeneous Markovian jump systems with nonlocal sensor nonlinearity, where the nonlocal measurement nonlinearity is governed by a stochastic variable satisfying the Bernoulli distribution. The asynchronous estimation means that the switching of candidate filters may have a lag to the switching of system modes, and the varying character of transition probabilities is considered to reside in a convex polytope. The jumping process of the error system is modeled as a two-component Markov chain with extended varying transition probabilities. A stochastic parameter-dependent approach is provided for the design of H∞ filter such that, for randomly occurring nonlocal sensor nonlinearity, the corresponding error system is mean-square asymptotically stable and has a prescribed H∞ performance index. Finally, a numerical example is used to illustrate the effectiveness of the developed estimation method

Output peak control of nonhomogeneous markov jump system with unit-energy disturbance

This paper considers output peak controller design for discrete nonhomogeneous Markov jump systems under unit-energy disturbance. The mode-dependent output peak feedback controller is designed to ensure that the resulting closed-loop system is stochastically stable and the peak of the output is within a specified range. Furthermore, the optimal energy-to-peak gain indices of the mode-dependent and the mode-independent state feedback controllers are evaluated and compared. A numerical example is presented to illustrate the applicability of the results obtained

Asynchronous switching control for fuzzy Markov jump systems with periodically varying delay and its application to electronic circuits

This article focuses on addressing the issue of asynchronous H∞ control for Takagi-Sugeno (T-S) fuzzy Markov jump systems with generally incomplete transition probabilities (TPs). The delay is assumed to vary periodically, resulting in one monotonically increasing interval and one monotonically decreasing interval during each period. Meanwhile, a new Lyapunov-Krasovskii functional (LKF) is devised, which depends on membership functions (MFs) and two looped functions formulated for the monotonic intervals. Since the modes and TPs of the original system are assumed to be unavailable, an asynchronous switching fuzzy controller on the basis of hidden Markov model is proposed to stabilize the fuzzy Markov jump systems (FMJSs) with generally incomplete TPs. Consequently, a stability criterion with improved practicality and reduced conservatism is derived, ensuring the stochastic stability and H∞ performance of the closed-loop system. Finally, this technique is employed to the tunnel diode circuit system, and a comparison example is given, which verifies the practicality and superiority of the method

Positive invertibility of matrices and exponential stability linear stochastic systems with delay

publishedVersio

Fault detection filter and fault accommodation controller design for uncertain systems

Model-based Fault Detection (FD) and Fault Accommodation (FA) approaches have been applied in a variety of cases. We propose several techniques to include uncertainties in the design process. First, we focus on the design of the Fault Detection Filter (FDF) and Fault Accommodation Controller (FAC) for Markovian Jump Linear Systems (MJLS). The MJLS framework allows us to include the network behavior (packet loss) during the design of the FDF and FAC.Second, we propose an FDF and FAC design for the MJLS, under the assumption that the Markov chain mode is not directly accessible. Since we are using the MJLS framework to model the network behavior, the assumption that the network state is not instantly accessible is useful because from a practical standpoint this is a truthful assumption. Third, from the results presented for the MJLS framework, we provided follow-up results using Lur'e Markov Jump System. This is compelling since on some occasions the non-linear behavior cannot be ignored. Therefore, applying the Lur'e MJS framework allows us to consider the same assumptions from MJLS, but now adds the non-linearities. Fourth, we propose the design Gain-Scheduled FDF and FAC for Linear Parameter Varying (LPV) systems, under the assumption that the schedule parameter is not directly acquired. We assume that the schedule parameter is subject to additive noise. This imprecision is included during the design, using change of variables and multi-simplex techniques. Finally, throughout the thesis, we provide some numerical examples to illustrate the viability of the proposed approaches

A pure-jump market-making model for high-frequency trading

We propose a new market-making model which incorporates a number of realistic features relevant for high-frequency trading. In particular, we model the dependency structure of prices and order arrivals with novel self- and cross-exciting point processes. Furthermore, instead of assuming the bid and ask prices can be adjusted continuously by the market maker, we formulate the market maker\u27s decisions as an optimal switching problem. Moreover, the risk of overtrading has been taken into consideration by allowing each order to have different size, and the market maker can make use of market orders, which are treated as impulse control, to get rid of excessive inventory. Because of the stochastic intensities of the cross-exciting point processes, the optimality condition cannot be formulated using classical Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI), so we extend the framework of constrained forward backward stochastic differential equation (CFBSDE) to solve our optimal control problem

Probabilistic modeling for single-photon lidar

Lidar is an increasingly prevalent technology for depth sensing, with applications including scientific measurement and autonomous navigation systems. While conventional systems require hundreds or thousands of photon detections per pixel to form accurate depth and reflectivity images, recent results for single-photon lidar (SPL) systems using single-photon avalanche diode (SPAD) detectors have shown accurate images formed from as little as one photon detection per pixel, even when half of those detections are due to uninformative ambient light. The keys to such photon-efficient image formation are two-fold: (i) a precise model of the probability distribution of photon detection times, and (ii) prior beliefs about the structure of natural scenes. Reducing the number of photons needed for accurate image formation enables faster, farther, and safer acquisition. Still, such photon-efficient systems are often limited to laboratory conditions more favorable than the real-world settings in which they would be deployed. This thesis focuses on expanding the photon detection time models to address challenging imaging scenarios and the effects of non-ideal acquisition equipment. The processing derived from these enhanced models, sometimes modified jointly with the acquisition hardware, surpasses the performance of state-of-the-art photon counting systems. We first address the problem of high levels of ambient light, which causes traditional depth and reflectivity estimators to fail. We achieve robustness to strong ambient light through a rigorously derived window-based censoring method that separates signal and background light detections. Spatial correlations both within and between depth and reflectivity images are encoded in superpixel constructions, which fill in holes caused by the censoring. Accurate depth and reflectivity images can then be formed with an average of 2 signal photons and 50 background photons per pixel, outperforming methods previously demonstrated at a signal-to-background ratio of 1. We next approach the problem of coarse temporal resolution for photon detection time measurements, which limits the precision of depth estimates. To achieve sub-bin depth precision, we propose a subtractively-dithered lidar implementation, which uses changing synchronization delays to shift the time-quantization bin edges. We examine the generic noise model resulting from dithering Gaussian-distributed signals and introduce a generalized Gaussian approximation to the noise distribution and simple order statistics-based depth estimators that take advantage of this model. Additional analysis of the generalized Gaussian approximation yields rules of thumb for determining when and how to apply dither to quantized measurements. We implement a dithered SPL system and propose a modification for non-Gaussian pulse shapes that outperforms the Gaussian assumption in practical experiments. The resulting dithered-lidar architecture could be used to design SPAD array detectors that can form precise depth estimates despite relaxed temporal quantization constraints. Finally, SPAD dead time effects have been considered a major limitation for fast data acquisition in SPL, since a commonly adopted approach for dead time mitigation is to operate in the low-flux regime where dead time effects can be ignored. We show that the empirical distribution of detection times converges to the stationary distribution of a Markov chain and demonstrate improvements in depth estimation and histogram correction using our Markov chain model. An example simulation shows that correctly compensating for dead times in a high-flux measurement can yield a 20-times speed up of data acquisition. The resulting accuracy at high photon flux could enable real-time applications such as autonomous navigation

Aggregation methods in dynamical systems and applications in population and community dynamics

Approximate aggregation techniques allow one to transform a complex system involving many coupled variables into a simpler reduced model with a lesser number of global variables in such a way that the dynamics of the former can be approximated by that of the latter. In ecology, as a paradigmatic example, we are faced with modelling complex systems involving many variables corresponding to various interacting organization levels. This review is devoted to approximate aggregation methods that are based on the existence of different time scales, which is the case in many real systems as ecological ones where the different organization levels (individual, population, community and ecosystem) possess a different characteristic time scale. Two main goals of variables aggregation are dealt with in this work. The first one is to reduce the dimension of the mathematical model to be handled analytically and the second one is to understand how different organization levels interact and which properties of a given level emerge at other levels. The review is organized in three sections devoted to aggregation methods associated to different mathematical formalisms: ordinary differential equations, infinite-dimensional evolution equations and difference equations