A Multiobjective Optimization Based Fuzzy Control for Nonlinear Spatially Distributed Processes With Application to a Catalytic Rod

Modeling and analysis of complex systems are important aspects of understanding systemic behavior. In the lack of detailed knowledge about a system, we often choose modeling equations out of convenience and search the (high-dimensional) parameter space randomly to learn about model properties. Qualitative modeling sidesteps the issue of choosing specific modeling equations and frees the inference from specific properties of the equations. We consider classes of ordinary differential equation (ODE) models arising from interactions of species/entities, such as (bio)chemical reaction networks or ecosystems. A class is defined by imposing mild assumptions on the interaction rates. In this framework, we investigate whether there can be multiple positive steady states in some ODE models in a given class. We have developed and implemented a method to decide whether any ODE model in a given class cannot have multiple steady states. The method runs efficiently on models of moderate size. We tested the method on a large set of models for gene silencing by sRNA interference and on two publicly available databases of biological models, KEGG and Biomodels. We recommend that this method is used as (i) a pre-screening step for selecting an appropriate model and (ii) for investigating the robustness of non-existence of multiple steady state for a given ODE model with respect to variation in interaction rates. Scripts and examples in Maple are available in the Supplementary Information. wiuf@math.ku.dk Supplementary data are available at Bioinformatics online.

Experimental results have shown that anti-cancer therapies, such as radiotherapy and chemotherapy, can modulate the cell cycle and generate cell cycle phase-dependent responses. As a result, obtaining a detailed understanding of the cell cycle is one possible path towards improving the efficacy of many of these therapies. Here, we consider a basic structured partial differential equation (PDE) model for cell progression through the cell cycle, and derive expressions for key quantities, such as the population growth rate and cell phase proportions. These quantities are shown to be periodic and, as such, we compare the PDE model to a corresponding ordinary differential equation (ODE) model in which the parameters are linked by ensuring that the long-term ODE behaviour agrees with the average PDE behaviour. By design, we find that the ODE model does an excellent job of representing the mean dynamics of the PDE model within just a few cell cycles. However, by probing the parameter space we find cases in which this mean behaviour is not a good measure of the PDE population growth. Our analytical comparison of two caricature models (one PDE and one ODE system) provides insight into cases in which the simple ODE model is an appropriate approximation to the PDE model.

US high school (HS) students are lagging behind their foreign peers in math performance. It is thus necessary to design teaching modules that motivate US HS students to learn more math and to improve their math skills. Our study set out to test two different software programs designed for the development of such skills. MATLAB Simulink provides a friendly interface with which HS students can build ordinary differential equation (ODE) models. An alternative programming language, the R language is free and extensively used in the field of statistical learning and engineering. In this study, a group of HS students first got trained in both Simulink and R and then solved an ODE model of a microbial fuel cell (MFC), which can convert the organic compounds found in waste water into electricity, using both Simulink and R. Three anonymous surveys were conducted for: 1) students’ feedback on the module-based teaching approaches with R and Simulink training, 2) students’ self-evaluation in the improvement of their skills in solving ODE models following their training in R and Simulink, and 3) students’ comparison of R and Simulink in their learning and modeling experience. The instructor also evaluated students’ modeling skills with R and Simulink based on their performance in developing the MFC ODE model. Both students’ self-evaluation and the instructor’s direct evaluation indicate that students’ skills in solving ODE models with both R and Simulink were significantly improved after this R-Simulink modeling project. The surveys show that students generally enjoyed the module-based teaching format and that they would recommended this project to their peers. It was shown in the surveys that students preferred Simulink over R in solving ODE models and that they preferred learning Simulink first and then following up by learning R. Students’ comments for opening questions indicate that the major hurdle in this project was their limited background knowledge in biology and electrochemistry for microbial fuel cells.

For system identification, the ordinary differential equations (ODEs) model is popular for its accuracy and effectiveness. Consequently, the ODEs model is extended to the stochastic differential equations (SDEs) model to tackle the stochastic case intuitively. But the existence of stochastic integral is a rigid barrier. We simply transform the SDEs to their corresponding stochastic difference equations (SDCEs) to eliminate stochastic integrals and propose an easy but effective solution to stochastic system identification. In this solution, the maximum likelihood estimation can be applied and the evolutionary algorithms are used to determine structures and parameters of the unknown system.

Ordinary differential equation (ODE) models are quite popular for modelling complex dynamic processes in many scientific fields, and the parameters in these models are usually unknown, and we need to estimate them using statistical methods. When some observations are contaminated, regular estimation methods, such as nonlinear least-square estimation, will bring large bias. In this paper, robust estimations of both constant and time-varying parameters in ODE models using M-estimators are proposed, and their asymptotic properties are obtained under some mild conditions. We focus on Huber M-estimator, and also provide a method to adjust the Huber parameter automatically to the observations. The proposed method is compared to existing methods in numerical simulations and CD8+ T cell data analysis. It is demonstrated that our method gain substantial efficiency as well as robust properties.

Vector-borne diseases provide unique challenges to public health because the epidemiology is so closely tied to external environmental factors such as climate, landscape, and population migration, as well as the complicated biology of vector-transmitted pathogens. In particular, this close link between the epidemiology, the environment, and pathogen biology means that the traditional view that many vector-borne diseases are relatively stable in numerous regions does not provide a complete picture of their complexity. In fact, several regions exist with low levels of endemicity most of the time, punctuated by severe, often explosive, epidemics. These regions are considered unstable transmission settings. Ordinary differential equation (ODE) models have thus far dominated the study of vector-borne disease and have provided considerable insight into our understanding of transmission and effective control in stable transmission settings. To address the short-­comings of autonomous ODE models, we present a class of models, differential-delay equation (DDE) models, that have the potential to better describe unstable endemic settings for vector-borne disease. These models develop naturally out of the biology of diseases transmitted by vectors because of the extrinsic and intrinsic incubation periods and vector maturation process necessary for successful transmission of vector-transmitted pathogens. In this chapter, we introduce five examples of vector-borne diseases that span the globe, and discuss the clinical implications of unstable transmission of these diseases. Next, we present the original ODE version of the Ross-Macdonald model for vector-borne diseases, modify this model by introducing different types of naturally occurring delays, then illustrate how these models can exhibit more complex behavior such as oscillations via Hopf bifurcation and chaos via period-doubling, that the ODE model cannot produce. Finally, we explore the possibility for delay-models to contribute to our understanding of unstable transmission settings, which in turn will inform the development of effective control strategies for these epidemic-prone regions.

We find concrete evidence for a recently discovered form of intermittency, referred to as in–out intermittency, in both partial differential equation (PDE) and ordinary differential equation (ODE) models of mean field dynamos. This type of intermittency [introduced in P. Ashwin, E. Covas, and R. Tavakol, Nonlinearity 9, 563 (1999)] occurs in systems with invariant submanifolds and, as opposed to on–off intermittency which can also occur in skew product systems, it requires an absence of skew product structure. By this we mean that the dynamics on the attractor intermittent to the invariant manifold cannot be expressed simply as the dynamics on the invariant subspace forcing the transverse dynamics; the transverse dynamics will alter that tangential to the invariant subspace when one is far enough away from the invariant manifold. Since general systems with invariant submanifolds are not likely to have skew product structure, this type of behavior may be of physical relevance in a variety of dynamical settings. The models employed here to demonstrate in–out intermittency are axisymmetric mean-field dynamo models which are often used to study the observed large-scale magnetic variability in the Sun and solar-type stars. The occurrence of this type of intermittency in such models may be of interest in understanding some aspects of such variabilities.

This paper presents new stability conditions satisfying decay rate for both continuous and discrete fuzzy control systems. Linear matrix inequality (LMI) based designs for decay rate are also considered using the concept of parallel distributed compensation (PDC). To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The PDC is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. The stability analysis discussed here is reduced to a problem of finding a common Lyapunov function for a set of LMIs. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function and stable feedback gains satisfying decay rate. A simple example demonstrates the utility of the LMI-based designs proposed in this paper.

This paper presents a Takagi-Sugeno (TS) fuzzy state-feedback controller based on a linear matrix inequality (LMI) approach for the permanent magnet synchronous generator of wind energy conversion system (PMSG-WECS). A dc/dc converter is considered to regulate the maximum power output of the system. To show its effectiveness, the dynamic model is replaced by the TS fuzzy model, which the proposed controller can be applied to the PMSG-WECS, while the controller gains can be obtained by solving set of a LMI approach. The proposed controller guarantees the stability of the system. Therefore, the performance of the proposed TS fuzzy state-feedback controller is assessed through the computer simulation.

For many real complicated industrial processes, the accurate system model is often unavailable. In this paper, we consider the partially unknown spatially distributed processes (SDPs) which are described by general highly dissipative nonlinear partial differential equations (PDEs) and develop a data-based adaptive suboptimal neuro-control method by introducing the thought of reinforcement learning (RL). First, based on the empirical eigenfunctions computed with Karhunen–Loève decomposition, singular perturbation theory is used to derive a reduced-order model of an ordinary differential equation that represents the dominant dynamics of the SDP. Second, the Hamilton–Jacobi–Bellman (HJB) approach is used for the suboptimal control design, and the thought of policy iteration (PI) is introduced for online learning of the solution of the HJB equation, and its convergence is established. Third, a neural network (NN) is employed to approximate the cost function in the PI procedure, and a NN weight tuning algorithm based on the gradient descent method is proposed. We prove that the developed online adaptive suboptimal neuro-controller can ensure that the original closed-loop PDE system is semiglobally uniformly ultimately bounded. Finally, the developed data-based control method is applied to a nonlinear diffusion-reaction process, and the achieved results demonstrate its effectiveness.

This paper addresses the issue of tracking the output of an activated sludge process using fuzzy integral control. First, the dynamics of the nonlinear process are modeled with a dynamic state space fuzzy model integrating the effect of external disturbances, and then an additional integral state of the output tracking error is introduced to obtain an augmented Takagi-Sugeno (TS) fuzzy model. The TS fuzzy model is able to describe the dynamics of complex nonlinear systems with an excellent degree of accuracy. It is formulated by fuzzy if-then rules which can give local linear representation of the overall nonlinear system. Second, the design of the fuzzy integral control is performed, in which the state feedback gains are obtained by solving linear matrix inequalities (LMI). The objective is to ensure trajectory tracking of an activated sludge process (ASP) by controlling two key variables: the substrate concentration and the level of dissolved oxygen. To assess the performance of the proposed control strategy, a comparative analysis is carried out with a gain scheduling PI (GS-PI) controller. Simulation results are provided to illustrate the effectiveness of the proposed approach. Where, the fuzzy integral control reduces the high energy consumption in water treatment plants.

The primary aim of a vehicle's suspension system is to isolate the vehicle's main body from road irregularities, thus improving passenger comfort and ensuring optimal handling stability. This research discusses a stabilizing fuzzy control design for active vehicle suspension systems. The nonlinear model of the active suspension is then represented using a Takagi-Sugeno (TS) fuzzy model. The control approach uses a TS fuzzy controller utilizing an observer to estimate the state while reducing road disturbances. The closed-loop stability requirements of the vehicle utilizing the fuzzy controller and observer are expressed as a Linear Matrix Inequalities (LMI) problem, which can be effectively resolved through convex optimization methods. In this paper, we study the stability of the nonlinear automotive active suspension system with two degrees of freedom represented by a TS fuzzy model, where we will present the stabilization conditions by state feedback via the PDC (Parallel Distributed Compensation) control law and in the last section we introduced the TS fuzzy observer for the case of non-measurable premise variables.

This paper presents new stability conditions and LMI (linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. First, Takagi and Sugeno's fuzzy models and some stability results are recalled. To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The concept of parallel distributed compensation is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. New stability conditions are obtained by relaxing the stability conditions derived in previous papers. The stability analysis of the feedback system is reduced to a problem of finding a common Lyapunov function for a set of linear matrix inequalities. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function. A procedure to design the fuzzy controller is constructed using the parallel distributed compensation and the relaxed stability conditions. Some stability issues are remarked. A simple example demonstrates the effects of the derived stability conditions.

We study the presence of social communities in mobility traces from vehicular fleets. By analyzing publicly available sets of fleet vehicle mobility traces obtained from two real-world deployments — consisting of more than 2000 taxis in Shanghai and Beijing respectively, we confirm the existence of small numbers of distinct social communities in vehicular networks, which is in direct contrast to the general belief that vehicular networks are best modeled as a relatively homogeneous system. We examine the spatio-temporal characteristics of social communities, gaining the insight that they are driven primarily by social proximity induced by geographic locality. We then develop a parsimonious multi-community ordinary differential equation (ODE) model, which uses the heterogeneous structure introduced by social communities to model information dissemination. We show through simulations that this approach dramatically outperforms the conventional homogeneous ODE model in capturing the dynamics of the dissemination process. We further demonstrate that the use of the ODE model to optimize seeding of an initial set of vehicles results in improved utility for information dissemination compared to seed-optimization using a homogeneous model.

This paper proposed a method of improved genetic algorithm (IGA)-based secure communications in multiple time delay chaotic (MTDC) systems with optimal H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> performance and advanced encryption standard (AES). First, we apply an initial round key via AES encryption function to acquire the encrypted message. The encrypted message is used to carry out double encryption by chaotic synchronization. A robust fuzzy control design is then presented to address the effects of modeling errors between the MTDC systems and Takagi-Sugeno (T-S) fuzzy models. Next, in terms of Lyapunov's direct method, a delay dependent exponential stability criterion is derived to guarantee that the trajectories of the slave system can approach those of the master system. Subsequently, the stability conditions of this criterion are transformed into linear matrix inequalities (LMIs). In addition, the genetic algorithm (GA) has drawn great attention from researchers due to the capability of GA in random search for achieving near-optimal solutions. The lower and upper bounds of the search space based on the LMI approach can be set so that the GA will seek better feedback gains of fuzzy controllers in order to speed up the synchronization. However, the GA has the shortcomings of premature convergence and local search. Therefore, an improved genetic algorithm (IGA) is proposed in this study to effectively overcome the weakness of the traditional GA. On the basis of the IGA, a fuzzy controller is synthesized to not only realize the exponential synchronization, but also achieve optimal H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> performance by minimizing the disturbance attenuation level. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach.