Hybrid bounded error observers for uncertain bioreactor models

Biomass concentration in a biotechnological process is one of the states that characterize a bioprocess. Moreover, it is generally the main direct or indirectly desired product. It is well known that the biomass concentration is not normally measured online because this measurement is not possible or this is economically unprofitable. Therefore, for control purposes it is necessary to replace the unavailable biomass concentration measurements with reliable and robust online estimations. To this aim, several states observers can be found in the literature. A review of commonly used techniques can be found in (Bastin & Dochain, 1990; Dochain, 2003) and references therein. Observers can be coarsely divided into two broad classes: first principles or phenomenological estimators and empirical estimators. The phenomenological estimators can be also subdivided into classical observers and asymptotic observers. Classical observers include extended Kalman filter (EKF), extended Luenberger observer, high gain observer, nonlinear observers, and full horizon observer. In this class of estimators, a detailed knowledge of the reaction kinetics and associated transport phenomena are required to represent the balance equations. Modeling the biological kinetics reactions is a difficult and time-consuming task, and therefore the model used by the estimators could differ significantly from reality. This is the main disadvantage of these phenomenological estimators, i.e., their efficiency strongly relies on the model quality. Asymptotic observers are based on the idea that uncertainty in bioprocess models lies in the process kinetics models. The design of these observers is based on a state transformation performed to provide a model which is independent of the kinetics. A potential drawback of the asymptotic observers is that the rate of convergence is completely determined by the operating conditions, i.e., the rate of convergence can be very slow or the observer may not converge. Empirical estimators are based on constructing appropriate nonlinear models of biotechnological processes exclusively from the process input–output data without considering the functional or phenomenological relations between the bioprocess variables. However, the conventional empirical modeling approach is based on the knowledge of the structure (functional form) of the data-fitting model (in advance). This is a difficult task since it involves the heuristic selection of an appropriate nonlinear model structure from numerous alternatives.

A Bounded Error Observer for a Class of Bioreactor Models

Motivated by applications of distributed linear estimation, distributed control, and distributed optimization, we consider the question of designing linear iterative algorithms for computing the average of numbers in a network. Specifically, our interest is in designing such an algorithm with the fastest rate of convergence given the topological constraints of the network. As the main result of this paper, we design an algorithm with the fastest possible rate of convergence using a nonreversible Markov chain on the given network graph. We construct such a Markov chain by transforming the standard Markov chain, which is obtained using the Metropolis-Hastings method. We call this novel transformation <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pseudo-lifting</i> . We apply our method to graphs with geometry, or graphs with doubling dimension. Specifically, the convergence time of our algorithm (equivalently, the mixing time of our Markov chain) is proportional to the diameter of the network graph and hence optimal. As a byproduct, our result provides the fastest mixing Markov chain given the network topological constraints, and should naturally find their applications in the context of distributed optimization, estimation and control.

Underwater acoustic communications especially over shallow water channels suffer from multipath spread that causes inter-symbol interference (ISI). One of the best ways for overcoming ISI is to use adaptive equalizers. In addition to convergence rate and steady-state error, computational complexity influences adaptive equalizers performance. In this paper, we apply least mean fourth-power of two quantizer (LMFPTQ) also we suggest proposed affine projection algorithm (Proposed APA) and proposed normalized least mean fourth (Proposed NLMF) as new algorithms with lower steady-state error and faster convergence rate in comparison with LMF-PTQ, for equalizing underwater acoustic communications. We apply experimental data from Persian Gulf for examining and showing that the proposed method provides a good trade-off between convergence rate and computational complexity over shallow water channels.

A SIMPLE IMPROVEMENT OF INTERVAL ASYMPTOTIC OBSERVERS FOR BIOTECHNOLOGICAL PROCESSES

Consensus conditions and convergence speeds are crucial for distributed consensus algorithms of networked systems. Based on a basic first-order average-consensus protocol with time-varying topologies and additive noises, this paper first investigates its critical consensus condition on network topology by stochastic approximation frameworks. A new joint-connectivity condition called extensible joint-connectivity that contains a parameter $\delta$ (termed the extensible exponent) is proposed. With this and a balanced topology condition, we show that a critical value of $\delta$ for consensus is $1/2$ . Optimization on convergence rate of this protocol is further investigated. It is proved that the fastest convergence rate, which is the theoretic optimal rate among all controls, is of the order $1/t$ for the best topologies, and is of the order $1/t^{1-2\delta }$ for the worst topologies, which are balanced and satisfy the extensible joint-connectivity condition. For practical implementation, certain open-loop control strategies are introduced to achieve consensus with a convergence rate of the same order as the fastest convergence rate. Furthermore, a consensus condition is derived for nonstationary and strongly correlated random topologies. The algorithms and consensus conditions are applied to distributed consensus computation of mobile ad-hoc networks; and their related critical exponents are derived from relative velocities of mobile agents for guaranteeing consensus.

High-gain observers for nonlinear systems with trajectories close to unobservability

Cardiomyopathy refers to gradual weakening of the muscular walls of the cardiac chambers. Due to the hypertrophic condition of the muscular walls, damage and stretching of the muscle may lead to arrhythmias, which is detectable using the ECG. In the past, any deviations from a healthy rhythm provide cardiologists with accurate information regarding the heart condition. However, cardiologists are prone to making inaccurate interpretation from the visual observation, leading to erroneous diagnosis. Hence, this paper proposes a computerized method for accurate analysis and detection of cardiomyopathy disease using MLP network. Data for normal, cardiomyopathy, and other arrhythmias were obtained from the PTB Diagnostic ECG database. The raw signals were preprocessed for high-frequency noise removal using median and moving average filters. Baseline corrections were conducted using two-stage polynomial fitting method. Nine time-based features were extracted from the three bipolar limb leads. A total of 600 beats were used to train, validate and test five different MLP network structures. Four different learning algorithms were implemented to obtain the best classification accuracy and fastest convergence rate. Results show that the Levenberg-Marquardt algorithm shows the highest average classification accuracy of 98.9% for the different structures with the fastest average convergence rate of 12 epochs.

Feedback linearization control is a simple and effective strategy whenever a faithful model of the system and its states are available. Feedback linearization may suffer from the mismatches between the model used in the design and the actual system due to e.g. uncertain parameter values, parasitic dynamics, or because of the impossibility to measure some states of the system. To aleviate such an issue, we suggest a novel robust adaptive control approach using the evolving participatory learning algorithm together with a high-gain observer. The robust evolving granular high-gain observers (RegHGO) controller is suitable to control nonlinear systems that can be input-output linearized by feedback. The approach is robust to modeling mismatches and does not require full state availability because, once the system is in a suitable canonical form, a high gain observer can be constructed to supply the state information required for control. The usefulness and efficacy of the approach is shown using a fan and plate system, and an DC motor driven angular arm-position control. The fan and plate evaluates the controller in a regulation process, and the angular arm position control evaluates reference tracking perfromance. In both cases, time-varying parameter uncertainties disturb the closed-loop control system. Both, qualitative and quantitative performance evaluation of the RegHGO controller are done. Additionally, we compare the performance of the RegHGO controller with well-established methods such as exact feedback linearization with high-gain state observer and extensions. The results show that robust evolving granular control with high-gain observers achieves better performance than its counterparts.

In this article, a novel high gain observer (HGO)-based decentralised indirect adaptive fuzzy controller is developed for a class of uncertain affine large-scale nonlinear systems. By the combination of fuzzy logic systems and an HGO, the state variables are not required to be measurable. The proposed feedback and adaptation mechanisms guarantee that each subsystem is able to adaptively compensate for interconnections and disturbances with unknown bounds. It is ascertained using a singular perturbation method that all the signals of the closed-loop large-scale system stand uniformly ultimately bounded and the tracking errors converge to tunable neighbourhoods of the origin. Simulation results of correlated double inverted pendulums substantiate the effectiveness of the proposed controller.

On the Chebyshev-Cramér Asymptotic Expansions

Noise and interference are the two most common and basic problems in wireless communication systems. The noise in wireless communication channels has the characteristics of randomness and impulsivity, so the performance of adaptive filtering algorithms based on geometric algebra (GA) and second-order statistics is greatly reduced in the wireless communication systems. In order to improve the performance of adaptive filtering algorithms in wireless communication systems, this paper proposes two novel GA-based adaptive filtering algorithms, which are deduced from the robust algorithms based on the minimum error entropy (MEE) criterion and the joint criterion (MSEMEE) of the MEE and the mean square error (MSE) with the help of GA theory. The noise interference in wireless communication is modeled by alpha-stable distribution which is in good agreement with the actual data in this paper. Simulation results show that for the mean square deviation (MSD) learning curve, the GA-based MEE (GA-MEE) algorithm has faster convergence rate and better steady-state accuracy compared to the GA-based maximum correntropy criterion algorithm (GA-MCC) under the same generalized signal-to-noise ratio (GSNR). The GA-MEE algorithm reduces the convergence rate, but improves the steady-state accuracy by 10–15 dB compared to the adaptive filtering algorithms based on GA and second-order statistics. For GA-based MSEMEE (GA-MSEMEE) algorithm, when GA-MSEMEE and the adaptive filtering algorithms based on GA and second-order statistics keep the same convergence rate, its steady-state accuracy is improved by 10–15 dB, and when GA-MSEMEE and GA-MEE maintain approximately steady-state accuracy, its convergence rate is improved by nearly 100 iterations. In addition, when the algorithms are applied to noise cancellation, the average recovery error of the two proposed algorithms is 7 points lower than that of other GA-based adaptive filtering algorithms. The results validate the effectiveness and superiority of the GA-MEE and GA-MSEMEE algorithms in the alpha-stable noise environment, providing new methods to deal with multi-channel interference in wireless networks.

This article was published in the Eurasip Journal on Wireless Communications and Networking [©2016 Published by Springer International Publishing.] and the definite version is available at: http://dx.doi.org/10.1186/s13638-016-0698-x&#13;\n. The article website is at:http://jwcn.eurasipjournals.springeropen.com/articles/10.1186/s13638-016-0698-x

The capacitated arc routing problem (CARP) is a classical NP-Hard combinatorial optimization problem. In this paper, we present a memetic algorithm based on Extension step and Statistical filtering for Large-Scale CARP (ESMAENS) which has improvements in both the global search strategy and the local search strategy. Firstly, ESMAENS adopts the Route Distance Grouping decomposition scheme (RDG) to decompose the large-scale CARP into some independent sub-problems. Then, the initial population would evolve into a new group by using the Evolutionary Algorithm. Furthermore, ESMAENS introduces the extension step search strategy to search the potential solutions around the current solution. As a result, with the increase of the iteration number, it avoids getting to the premature convergence. Meanwhile, the diversity of the population can be increased. Finally, in the local search strategy, the statistical filter is used to filter out some solutions and make the algorithm get the lower bound at a faster convergence rate with a high stability. Compared with RDG-MAENS, experimental results on Beullen’C, D, E, F, egl and EGL-G test set show that ESMAENS has a better convergence rate, and the stability of solutions obtained is improved. Furthermore, ESMAENS achieves a global search for the solutions. Especially for the large-scale EGL-G test set, ESMAENS can converge to a lower bound at a faster convergence rate, and it is suitable for solving large-scale CARP.

This study aims to provide a robust trajectory tracking controller which guarantees the prescribed performance of a robot manipulator, both in transient and steady-state modes, experiencing parametric uncertainties. The main core of the controller is designed based on the adaptive finite-time sliding mode control (SMC) and extreme learning machine (ELM) methods to collectively estimate the parametric model uncertainties and enhance the quality of tracking performance. Accordingly, the global estimation with a fast convergence rate is achieved while the tracking error and the impact of chattering on the control input are mitigated significantly. Following the control design, the stability of the overall control system along with the finite-time convergence rate is proved, and the effectiveness of the proposed method is investigated via extensive simulation studies. The results of simulations confirm that the prescribed transient and steady-state performances are obtained with enough accuracy, fast convergence rate, robustness, and smooth control input which are all required for practical implementation and applications.