Adaptive nonlinear observers of microbial growth processes

Adaptive nonlinear observers are studied for a class of biochemical processes expressed by a nonlinearly parametrized Monod's growth model. Simultaneous on-line estimations of system states and parameters are performed for the plants with unknown parameters. Asymptotic nonlinear observers and parameter updating laws are constructed using Lyapunov stability technology. A persistence of excitation (PE) condition is investigated for the parameter convergence of the adaptive observers. Numerical simulations are provided to show the effectiveness of the proposed scheme.     

On the Lyapunov stability of discrete-time processes modeled by difference inclusions

The subject of this note is the stability in the sense of Lyapunov of difference inclusions. Connection with the convergence of algorithms is also discussed.     

Simulation of convection and diffusion processes by standard finite difference schemes and by influence schemes

It is helpful to consider the error in a finite difference solution as arising from two sources: the profile error component arises because the assumed profile used in deriving the scheme does not match the exact solution; the operator error component is due to the failure of the finite-difference operator to accurately simulate the convection-diffusion process. Profile error is relatively easy to quantify but to understand the performance of any differencing scheme to be used in a problem where convection is important, or dominant, requires a test for operator error. The first contribution of this paper is to propose such a test. Upstream difference, central difference, and influence schemes are subjected to the operator error test.While the influence schemes perform well, it is shown that they may still lead to substantial errors when velocities and diffusion coefficients change sharply over the solution domain. The second contribution of the paper is to show how errors from these sources can be greatly reduced.     

Adaptive schemes for distributed web caching

In distributed web caching architectures, institutional proxies take advantage of their neighbors’ contents in order to reduce the number of requests forwarded to the server. Intuitively, the maximum benefit from this cooperation is expected when the proxies that exhibit similar requests are grouped together. The current practice is to follow a static and manual configuration of neighbors. Such an approach has a number of drawbacks: (i) static allocation may not determine the best neighbors, especially if global knowledge of the participating proxies is not available, (ii) a manual allocation places significant administrative burden, (iii) static schemes are insensitive to changes in access patterns, and (iv) they cannot deal with the introduction of new, potentially useful, proxies. In this paper, we propose a set of algorithms that allow proxies to independently explore the network for better neighbors and continuously update their configuration in an adaptive fashion. The simulation experiments illustrate that dynamic neighbor reconfiguration leads to significantly higher hit ratios compared to the static approach. Although some researchers in the past have recognized the need for adaptive caching, to the best of our knowledge this is the first study to propose concrete algorithms and evaluate their efficacy.     

Adaptive partitioning schemes for bipartite ranking

Recursive partitioning methods are among the most popular techniques in machine learning. The purpose of this paper is to investigate how to adapt this methodology to the bipartite ranking problem. Following in the footsteps of the TreeRank approach developed in Clémençon and Vayatis (Proceedings of the 2008 Conference on Algorithmic Learning Theory, 2008 and IEEE Trans. Inf. Theory 55(9):4316–4336, 2009), we present tree-structured algorithms designed for learning to rank instances based on classification data. The main contributions of the present work are the following: the practical implementation of the TreeRank algorithm, well-founded solutions to the crucial issues related to the splitting rule and the choice of the “right” size for the ranking tree. From the angle embraced in this paper, splitting is viewed as a cost-sensitive classification task with data-dependent cost. Hence, up to straightforward modifications, any classification algorithm may serve as a splitting rule. Also, we propose to implement a cost-complexity pruning method after the growing stage in order to produce a “right-sized” ranking sub-tree with large AUC. In particular, performance bounds are established for pruning schemes inspired by recent work on nonparametric model selection. Eventually, we propose indicators for variable importance and variable dependence, plus various simulation studies illustrating the potential of our method.     

Adaptive nonlinear output-feedback schemes with Marino-Tomeicontroller

Three new adaptive nonlinear output-feedback schemes are presented. The first scheme employs the tuning functions design. The other two employ a novel estimation-based design consisting of a strengthened controller-observer pair and observer-based and swapping-based identifiers. They remove restrictive growth and matching conditions present in the previous output-feedback nonlinear estimation-based designs and allow a systematic improvement of transient performance     

Adaptive binary sorting schemes and associated interconnectionnetworks

Many routing problems in parallel processing, such as concentration and permutation problems, can be cast as sorting problems. In this paper, we consider the problem of sorting on a new model, called an adaptive sorting network. We show that any sequence of n bits can be sorted on this model in O(lg² n) bit-level delay using O(n) constant fanin gates. This improves the cost complexity of K.E. Batcher's binary sorters (1968) by a factor of O(lg² n) while matching their sorting time. The only other network that can sort binary sequences in O(n) cost is the network version of columnsort algorithm, but this requires excessive pipelining. In addition, using binary sorters, we construct permutation networks with O(n lg n) bit-level cost and O(lg³ n) bit-level delay. These results provide the asymptotically least-cost practical concentrators and permutation networks to date. We note, of course, that the well-known AKS sorting network has O(lg n) sorting time and O(n lg n) cost, but the constants hidden in these complexities are so large that our complexities outperform those of the AKS sorting network until n becomes extremely large     

Stability of annealing schemes and related processes

An approach for establishing stability of annealing schemes and related processes is described. This extends the approach developed in Borkar and Meyn (SIAM J. Control Optim. 38 (2000) 447) for stochastic approximation algorithms. The proof uses a possibly degenerate stochastic differential equation obtained as a scaling limit of the interpolated algorithm.     

Centralized and decentralized control schemes for Gauss-Poisson processes

Gauss-Poisson processes are defined as jump processes with jump times according to a Poisson process and Gaussian jump size. Filtering and prediction recursive schemes are obtained and used in the derivation of optimal control schemes. Dynamic programming sufficient conditions are given for both centralized and delayed information sharing decentralized schemes. For the linear quadratic model, we derive explicit solutions for the optimal control.     

Linguistic quantifiers modeled by Sugeno integrals

Since quantifiers have the ability of summarizing the properties of a class of objects without enumerating them, linguistic quantification is a very important topic in the field of high level knowledge representation and reasoning. This paper introduces a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures, and the truth value of a quantified proposition is evaluated by using Sugeno's integral. This framework allows us to have some elegant logical properties of linguistic quantifiers. We compare carefully our new model of quantification and other approaches to linguistic quantifiers. A set of criteria for linguistic quantification was proposed in the previous literature. The relationship between these criteria and the results obtained in the present paper is clarified. Some simple applications of the Sugeno's integral semantics of quantifiers are presented.     

Divergent growth processes

Here we consider the general Markov birth process X(t), If the birth rate is sufficiently large, such a process may diverge in the sense that P(X(t) = ∞) > 0. Interest then focuses on the size of the population conditional on its remaining finite, We find the asymptotic distribution of the population in these circumstances, enabling us to determine whether the conditional moments are finite or not. These results resolve some conjectures of Roehner (1986).     

Adaptive control of hammerstein systems with unknown input nonlinearity and partially modeled linear dynamics

We numerically investigate that an adaptive control law achieves internal model principle control in the presence of plant input nonlinearities. We focus on retrospective cost adaptive control (RCAC) applied to Hammerstein systems with unknown input nonlinearity and limited modeling of the linear dynamics. The goal is to determine whether the control law achieves the correct gain and phase shift for internal stability along with asymptotic command following and disturbance rejection.     

Testing timed systems modeled by Stream X-machines

Stream X-machines have been used to specify real systems where complex data structures. They are a variety of extended finite state machine where a shared memory is used to represent communications between the components of systems. In this paper we introduce an extension of the Stream X-machines formalism in order to specify systems that present temporal requirements. We add time in two different ways. First, we consider that (output) actions take time to be performed. Second, our formalism allows to specify timeouts. Timeouts represent the time a system can wait for the environment to react without changing its internal state. Since timeous affect the set of available actions of the system, a relation focusing on the functional behavior of systems, that is, the actions that they can perform, must explicitly take into account the possible timeouts. In this paper we also propose a formal testing methodology allowing to systematically test a system with respect to a specification. Finally, we introduce a test derivation algorithm. Given a specification, the derived test suite is sound and complete, that is, a system under test successfully passes the test suite if and only if this system conforms to the specification.     

Implicit–explicit numerical schemes for jump–diffusion processes

Abstract We study the numerical approximation of solutions for parabolic integro-differential equations (PIDE). Similar models arise in option pricing, to generalize the Black–Scholes equation, when the processes which generate the underlying stock returns may contain both a continuous part and jumps. Due to the non-local nature of the integral term, unconditionally stable implicit difference schemes are not practically feasible. Here we propose using implicit-explicit (IMEX) Runge-Kutta methods for the time integration to solve the integral term explicitly, giving higher-order accuracy schemes under weak stability time-step restrictions. Numerical tests are presented to show the computational efficiency of the approximation. Mathematics Subject Classification (1991): Primary: 65M12; Secondary: 35K55, 49L25     

Adaptive estimation of doubly stochastic poisson processes

The optimal adaptive estimator structures for a class of doubly stochastic Poisson processes (DSPP) are presented. The structure is used along with a moment assumption to obtain implementable estimators. The class of DSPP considered is that of a linear Markov diffusion process modulating a linear intensity rate. The uncertainty for which the adaptation process is developed includes both structures uncertainty in the Markov diffusion process and parameter uncertainty in the Markov diffusion process and the intensity rate process. Results are given on the problem of adaptation of which of a finite number of Markov realizations is modulating the intensity process. The nonlinear adaptive estimator structures are obtained by use of a particular theorem that yields an optimal structure for the adaptive estimator. The structure is used to obtain a quasi-optimal adaptive estimator for the problem by use of a zero third central moment assumption. The estimator structure consists of a nonlinear, nonadaptive part, and a nonlinear, adaptive part which contains the parameter structure adaptations. The necessary covariance equations for performance evaluation are obtained. The theory is applied to the problem of wavefront estimation in adaptive optics for use in high-energy lasers and in imaging through atomospheric turbulence. Other examples are given.     

Electric batteries and fuel cells modeled by Bondgraphs

In an electric battery, electric charge flows against the electric field, driven by the concentration gradient or chemical tension. Outside it flows with the electric field through the load resistor to which it supplies energy. The whole is well represented by a Bondgraph (BG) and we develop the associated equations, especially for the element SPAC (see Section 2), which affords the coupling of chemical and electric flows. So it is a case of coupled reactions, driven by the concentration gradients between the two battery compartments. The electric charge is taken in ions against its potential gradient, driven by the chemical tension or potential.The BG has an electrical and a chemical part, connected by two elements SPAC. There is also a flow source in the chemical part, which is driven when an external current flows. The reaction proceeds between two multiport C which represent chemical effort sources and entrains the electric charge. The whole is programmed and simulated by the 20SIM program and shows the switching on and off of electric current and the gradual equalization of concentrations with depletion of the voltage: the battery is discharged.Essential is the selective membrane, that divides two compartments with different concentrations, and lets one species of ions run through. Fuel cells are similar but have two constituents, hydrogen and oxygen, and one product, water. Other substances can be used.     

Smoothing for random fields modeled by partial differentialequations

The authors present an efficient, numerically reliable smoothing algorithm for random fields modeled by linear, constant coefficient, partial differential equations. The estimate is computed from discrete measurements by using the discrete Fourier transform to convert the two-dimensional (2D) problem to a collection of uncoupled one-dimensional (1D) problems which are then solved using stable iterations     

Adaptive on-line steady-state optimization of slow dynamic processes

A software package OLIOPT was developed for the on-line optimization of the steady-state behaviour of slow dynamic processes in a relatively short time period. In the starting phase, the independently variable inputs are changed according to a special test signal. A nonlinear dynamic process model is identified on-line. Based on the static part of the model and the known inputs, the gradients of the performance index are calculated. An optimization algorithm changes the inputs towards their optimal values. On-line identification of the nonlinear model continues and the prediction of the optimum improves. In the last phase, the inputs take their optimal values and the process follows, feedforward controlled, to its optimal steady-state. The method is suited for industrial processes with one or more variable inputs, where a small gain in efficiency turns out to give a relatively large financial return. Results are shown for the on-line optimization of a thermal pilot process.     

Optimization of microorganisms growth processes

Microorganisms growth processes are encountered in many biotechnological applications. For an increased economic benefit, optimizing their productivity is of great interest. Often the growth is inhibited by the presence in excess of other components. Inhibition determines the occurrence of multiple equilibrium points, which makes the optimal steady state reachable only from a small region of the system state space. Thus dynamic control is needed to drive the system from an initial state (characterized by a low concentration of microorganisms) to the optimal steady state. The strategy presented in this paper relies on the solutions of two optimization problems: the problem of optimal operation for maximum productivity in steady state (steady state optimization) and the problem of the start-up to the optimal steady state (transient optimization). Steady state optimization means determining the optimal equilibrium point (the amount of microorganisms harvested is maximum). The transient optimization is solved using the maximum principle of Pontryagin.The proposed control law, which drives the bioreactor from an initial state to the optimal steady state while maximizing the productivity, consists of switching the manipulated variable (dilution rate) from the minimum to the maximum value and then to the optimal value at well defined instants. This control law substantially increases the stability region of the optimal equilibrium point. Aside its efficiency, the strategy is also characterized by simplicity, being thus appropriate for implementation in real-life systems. Another important advantage is its generality: this technique may be applied to any microorganisms growth process which involves only one biochemical reaction. This means that the sequence of the control levels does not depend on the structure and parameters of the reaction kinetics, the values of the yield coefficients or the number of components in the bioreactor.