WP3: DISTRIBUTED SYSTEMS, DECISION, CONTROL AND COMMUNICATION (UCL, KUL, UGent, ULg, UMons, UNamur)
Introduction and state-of-the art
This workpackage focuses on networked systems, the unifying theme being a group of networked entities (agents) achieving objectives via interaction made possible by (local) interconnections. There is no central unit supervising the system because this may simply be impossible (e.g. for reasons of scale) or, if possible it would not be implementable (e.g. prohibiting cost). The agents themselves are supposed to be basic or elementary in general and identical or similar; they have simple dynamics, or have limited processing power. It is their cooperation through their interconnections that may give rise to nontrivial interesting behavior or performance. This paradigm of interconnected dynamical systems captures a vast array of (engineering) applications besides its modeling potential in different fields in the pure and medical sciences. The broad scope of this research area is e.g. reflected in the study of neural networks (agents being cells), traffic (agents are cars), group dynamics (social networks where agents are individuals), economic systems (agents being clients, or companies), crowd dynamics and control (agents are humans), computer networks (agents being servers), the world wide web, decentralized algorithms (estimating a global optimum from local searches), decentralized (i.e local) control of power systems or interconnected water basins and rivers with distributed control to prevent flooding. These examples represent different fields and have their own specific models leading to different problem formulations and approaches. Looking at this list, one talks about specific dynamics, or algorithms, or systems in general described in dedicated mathematical models, all interconnected through specific networked structures representing communication or interaction links. It is the dynamical interplay between the agents dynamics and the interconnected information flow which has become the subject of such an intensive research -- not in the least by our previous IAP network. Many challenges remain, at the fundamental and conceptual level, at the level of analysis and understanding, and at the optimization and algorithmic level.
Biology and medicine have become a primary area of applications that require the combined expertises of the network in dynamical modeling, statistical estimation, large-scale data assimilation and optimization techniques. Our network is ideally placed to contribute in some of these applications because it combines the required broad methodological expertise with leading expertise in specialized areas such as biochemical process engineering, neural control movement or biomedical signal processing. Computational neuroscience perhaps best illustrates the claim. Even though it is not a focus of the network per se, about every subtopic of the proposal has direct relevance for a specific computational neuroscience problem ranging from single cell dynamics to brain function modeling, simulation, and optimization.
Research objectives and proposed topics
WP3.1 Dynamics, communication, and decision in decentralized networks (theory of multi-agent systems) (UCL, UGent, ULg, UNamur)
Self-organization, task accomplishment and computation in systems of anonymous agents. We intend to study the tasks that can be accomplished by a set of identical agents with no global identifier and no global information about the system. E.g. find the minimal conditions of randomness under which such a system could achieve a certain level of self-organization, i.e., how they could for example obtain a global identifier at minimal cost, obtain enough information about the system and their position within it to route messages, or elect a leader allowing to centralize certain information.
In computation, centralization usually results in faster performance but may not always be desirable in uncertain environments. In particular, variable communication links may make it difficult to route the information between an agent and a central unit. We want to propose new semi-centralized methods for systems with medium variations, and to find a methodology to determine the optimal level of centralization for given problems and systems.
When targeting a global goal, one may tolerate local errors of the agents provided that they remain very limited, or that the multiple errors made by the agents cancel each other on average. We want to focus on the latter case, and to study conditions under which relatively important local errors can be tolerated thanks to global cancellation effects. We will study the mean error made by decentralized systems that compute the average of a set of observations in a locally imperfect way due to asynchronous communications between the agents.
Consensus related problems. We address the following questions. Agents communicate by sending messages about their positions every now and then, according to a fixed strategy, and move in continuous time using this discrete-time information in order to all converge to a same point. What sampling time should be chosen to minimize the number of communications between the agents?
We study how the discrete-time consensus problem is affected when one agent among many behaves in a rogue way, and whether the final consensus point is perturbed significantly.
We also design a novel method to analyze large networks, in order to uncover the densely connected subnetworks. The techniques transform the network into a stochastic system, and perform a study of the autocovariance of various observables of this system, leading to a multiresolution matrix-based method. This allows to find the time scale associated to a consensus problem on the network.
Synchronization in network models of firing oscillators. Phase models of integrate-and-fire oscillators have become popular in neuroscience as models of spiking neurons. Because of the hybrid nature of the dynamics, the analysis of ensemble phenomena (such as synchronization) in those models requires special tools. It has been shown that synchronization and time correlations between biological neurons are important for e.g. grouping characteristics related to a common object (referred to as the "feature binding" mechanism).
WP3.2 Analysis, control, and optimization of infinite dimensional systems (UCL, KUL, UGent, ULg, UNamur)
Infinite-dimensional linear systems with time-varying parameters. A central objective will be to develop numerical methods and control design tools for infinite-dimensional linear systems with time- varying parameters. These methods and tools explicitly take into account uncertainty and can handle the design of gain-scheduled controllers with a prescribed order or structure optimizing stability and H2/H- infinity criteria. The methodology is rooted in recent developments in numerical linear algebra (in particular eigenvalue optimization and algebraic model reduction) and Lyapunov based control design techniques (in particular, formulations in terms of linear and nonlinear matrix inequalities). It will benefit from the solvers for large-scale non-linear and parameterized eigenvalue problems and from the nonlinear programming methods, developed as part of WP1. The control design techniques will be validated on a mechatronic test setup.
Continuum models for multi-agent systems. Multi-agent systems, even those already deployed in industrial applications, typically involve large numbers of agents. In many cases, the continuum limit of those models allows for alternative analysis tools and reveals important structural properties of the finite dimensional models. We will apply this approach to specific multi-agent models motivated by consensus theory and by synchronization studies.
Nonlinear partial differential equations. Motivated by process engineering applications, we will investigate the analysis and design of control laws for specific models of nonlinear partial differential equations. Those include :
- Convection-diffusion-reaction infinite-dimensional nonlinear operators with boundary measurement and control. The goal is to design efficient tools in order to synthesize robust feedback control laws for applications in engineering. A specific topic of interest is the study of the LQ-optimal boundary control problem for the class of Sturm-Liouville systems, with a view to applying the results to particular convection-diffusion-reaction systems with mass action kinetics.
- Reaction systems models. These involve the "classical" tubular reactors but also population balance models encountered in crystallization processes (with a specific application to ice-cream production) and biological systems (where the age distribution is considered a specific independent variable). The analysis of such models should result in improved control design that account for the specific characteristics of the dynamics of such systems that combine partial derivative terms with integral terms.
- Positive systems. Those are dynamical systems whose state trajectories are nonnegative for all nonnegative initial states and input functions. In particular, we will focus on the positive stabilization problem. The main objective is to study this problem for the class of positive infinite- dimensional systems in order to extend the results obtained for finite-dimensional ones to this class and more generally to invariant complex dynamical systems, notably by developing computational methods for generic models of process engineering.
WP3.3 Optimization and control of complex distributed systems (application driven: power systems, mechatronics, flood control, communication networks) (UCL, KUL, UGent, ULg)
Nonlinear control design. Contraction analysis is an alternative to Lyapunov theory that has proven useful in several nonlinear control problems such as observer design or synchronization theory. Motivated by active power electronics and induction motor control problems, the project will aim at using contraction theory to solve important design questions for nonlinear electromechanical models, including a systematic design methodology for anti-windup control. In many mechatronic applications, current control design methodologies can no longer keep pace with the ever increasing performance demands with respect to speed, accuracy, functionalities and environmental impact. The focus is on formulating design methodologies, translating them into a mathematical problem, as well as handling the numerical issues related to solving the problem.
Distributed Control. Unlike the classical control paradigm, where components, i.e. sensors, controllers and actuators, are often co-located and therefore connected via dedicated channels (e.g. serial cables), distributed systems make use of general purpose networks to communicate and exchange information.
We aim at developing distributed model predictive control schemes and supervision strategies for networks of locally regulated, dynamically coupled systems connected via data links and subject to coordination constraints on the evolutions of their relevant variables. Regarding effects of networks issues on the control loop, the main research objectives are the development of control schemes able to deal with packet losses, delays and quantization, as well as the definition of strategies of sensor selection and information routing for the state estimation of processes observed through wireless sensor networks.
We plan to work on coordinated control in considering case studies on the coordinated control of traffic lights, the control of autonomous vehicles in a complex environment (container terminal), and the voltage control for power systems. Computationally simple abstract models of urban traffic are based on the one hand on platoons, and on the other hand on fluid flow analogies. Simulink models that allow particle filtering and model predictive control design have been obtained. Freeway traffic has been modeled using interval based models that allow interesting parallelized state estimation algorithms. For the autonomous vehicles, automata models are used in order to automatically generate supervisory controllers guaranteeing safety. Regarding power systems we plan to continue research on the use of hybrid systems models for emergency voltage control and coordinating voltage control for electrical power systems.
We plan to work on flood control of rivers with nonlinear MPC methods. The dynamics consist of a connection of segments, each one described with a set of two nonlinear partial differential equations, the Saint Venant equations. These two equations describe the relation between the water levels and the discharges in reach in space and time. The segments may be interconnected with different types of gates each with their own equations describing the relation between the surrounding water levels and the controlled discharge. For flood control linear tools are not sufficiently accurate. Heavy rainfall will excite the entire dynamics of a river system, not a certain region close to the working point. One challenge is to get accurate control inputs in a reasonable amount of time based on e.g. distributed MPC. Another challenge is to see what the influence is of the uncertainty on the rainfall predictions on the performance of the controller.
Distributed Power Systems. Power systems are composed of two layers. The top layer is a transmission network where most of the control actions are taken; a second layer consists of distribution networks for which there is little need to develop complex control procedures. In the future, due to the connection of renewable sources of energy at the distribution level and the active management of the load, the distribution layer will exhibit a much more complex dynamics and will have to be carefully managed. Additionally, atop of these two layers, a third layer called the Supergrid, will appear. This Supergrid will be made of HVDC links for transmitting energy over long distances. This switch from two- layer power systems to three-layer systems raises many research questions, including the following ones. How should we study in an integrated way the dynamics of these new systems? How should we control the numerous distributed generators hosted by the distribution system layer, considering that the tasks currently devoted to large power plants connected to the transmission layer will be taken care of progressively by those smaller units connected to lower-voltage distribution networks? How should we coordinate the actions between these three layers? What type of instability mechanisms will these new systems exhibit?
Optimization and control of stochastic systems. Unlike ordinary queuing systems where each server serves a single customer at a time, we investigate queues where a single server serves multiple customers simultaneously. This is the case for so-called batch service queues as well as for paired queues. The server of a batch service queue serves multiple customers of a single queue in group (batch). Applications range from elevators and other transportation devices to group screening (of blood samples for instance). Different decision parameters and modeling aspects are important in these systems, such as the capacity of the server, the minimum number of customers in a served batch, dependence of service times on the number of served customers. For paired queues, the server simultaneously serves customers of a number of parallel queues. Paired queuing systems are most suitable to assess kitting operations. Kitting is a particular strategy for supplying materials to an assembly line: prior to arriving at an assembly unit, the necessary parts are collected into a specific container, referred to as a "materials kit" or "kit". Assuming stochastic production times or order times and/or stochastic demand, kitting can be modeled as a paired queuing system. Due to multidimensionality and pairing, these queuing systems are intrinsically hard to study analytically, numerically as well as by simulation. We use numerical solution techniques for large structured Markov chains as well as perfect sampling techniques. Moreover, as numerical complexity grows with the number of queues, we investigate the limit to the infinite-buffer kitting process. In addition, we attach an economic-order-quantity type cost structure, and explore the corresponding optimization problem.
In addition to these queuing systems, we investigate various branching processes. Branching processes model growth of populations but have found applications in other areas as well (polling systems, queuing systems, random graphs, ...). We are mainly interested in multiclass branching processes with stationary ergodic migration. Despite the generality of the migration process, moment expressions of the population growth can be calculated. Tools to study performance as well as control these branching and migration processes include ergodic theory and joint probability generating functions.
Nonlinear optimization and approximated algorithms. Complex control applications easily lead to hard optimization problems. This computational obstacle motivates the development of dedicated approximated algorithms. Specific objectives include the following ones. When large distributed systems shall be optimally operated, it is desirable that decisions can be made fast on a local level, but that despite these local decisions a common global objective is pursued. The aim of this subtask is to develop an algorithmic framework of distributed Model Predictive Control (MPC) that allows to accommodate these two objectives. The starting point is the idea that a centralized global problem shall be solved by coordinating multiple agents that perform local optimization tasks on possibly different timescales. One promising direction is using the framework of distributed sequential convex programming together with adjoint based optimization and to develop schemes that are based on the permanent exchange of coupling primal and dual variables between neighboring subsystems. Crucial questions regard suitable regularizations that do not impede fast convergence to the centrally optimal solution, the use of approximate solutions and how they might influence the stability and performance of the total system, as well as the efficient implementation of the lower level local convex or nonlinear optimization algorithms, extending the philosophy of online active set strategies and auto-generated real-time iterations.
Relaxation schemes for min-max reinforcement learning. Batch-mode reinforcement learning is a field that derives an optimal control policy for Markov-type systems, based on partial data that was previously collected on the dynamical system. A potential drawback is that it can sometimes badly generalize information from poorly covered areas of the space and lead to dangerous policies. It is possible to overcome the drawback by solving an optimization problem that turns out to be NP-hard. The aim of this research topic is to provide some hints on how to approximately solve the optimization problem in order to obtain cautious policies.
WP 3.4: Modeling, optimization and control of biochemical processes (KUL, UCL, UMons)
Once established the dynamic macroscopic models can bring valuable information for process optimization and control. For bioreactors operating in continuous mode, it is of interest to forecast which initial conditions will lead to nominal operation or to wash out states. The global convergence of the set of equilibrium points and their local stability properties will be investigated in a number of practical applications with a focus on environmental processes, such as anaerobic digestion of solid and liquid effluents from agro-food industry. The effect of an optimal controller on the stability of the equilibrium points will also be considered.
Population models and microbial ecology. In some applications, such as the culture of microalgae or anaerobic digestion of organic waste, population of micro-organisms compete for the same resources or on the contrary, cooperate in some syntrophic relationships. It is of interest to study the effect of the operating conditions on the outcome of this competition (or cooperation) and to determine if some optimal control policy could be deduced from a thorough analysis of the dynamic population models.
MIMO control of separate feedings for microorganism cultures in bioreactors. Nowadays, bioreactors are mostly operated in a relatively simple manner by adjusting the feed flow rate to control the main limiting substrate concentration. However, in this way, the culture medium, which contains a large set of costly compounds in excess, is often under-exploited and wasted. Large benefits could be achieved by dynamically adjusting the composition of the culture medium using several degrees of freedom (i.e. feeding pumps and tanks containing the right “cocktails” of compounds). This challenging problem will be studied both for fed-batch cultures of bacteria, and continuous cultures of animal cells, with pharmaceutical applications in view.
Real-time optimization of bioprocesses, including extremum seeking and optimal output feedback control, is important in many practical applications such as fed-batch cultures of yeast or bacteria for the production of pharmaceuticals, or for hydrogen production in microbial electrolysis cells. One challenge will be to achieve real-world (experimental) investigation of these techniques whereas most of the published reports are restricted to numerical simulations. On a more theoretical side, we will study the type of excitation signal needed and the filtering techniques used to extract the information on the sought optimum. The theory of extremum seeking will also be investigated for specific distributed parameter models.
Aquaculture plants in recirculation loops. Modern processes often combine several technologies in order to ensure a safe and efficient production, together with energy savings (or even co-generation) and environmental constraints. As particular application targets, aquaculture plants in recirculation loops (with different technologies for water treatment including biofilters and membrane reactors) will be thoroughly investigated.
As a continuation of the studies proposed in WP2.6, robust control of Simulated Moving Bed (SMB) chromatographic separation processes will be studied and implemented on a pilot plant available at UMons. Control of SMB processes is particularly delicate as it is a distributed parameter system with hybrid dynamics, i.e. periodic valve switches inducing discrete-time events, and continuous dynamics within each switch interval. Optimization of the switch sequence (involved in various modes of operation of the SMB, such as the VARICOL mode where the number of active columns per zone vary periodically) will also be investigated.
Optimization and control of recombinant protein production by microorganisms. Based on mathematical models describing both biomass growth and induction (leading to protein production) phases, the substrate and inductor feed flow rates should be determined in order to maximize the production of the protein of interest, while minimizing the culture medium consumption. A robust closed- loop control for maintaining these optimal conditions will be developed.
Optimization and control of baker’s yeast cultures in food industry. The criteria to be optimized in the food industry are not the same as the ones in the biopharmaceutical industry. Among the most important criteria for baker’s yeast production are the activity (ability to produce carbon dioxide when the culture is reactivated) and the stability (ability to maintain the activity on long term). Constraining the yeasts to accumulate trehalose during their growth seems to be an efficient mean to act on those criteria. The aim will be to develop a closed-loop controller able to maximize that accumulation.
Development of PAT controllers. Process Analytical Technologies consist of a guidance emitted in 2004 by the Food and Drug Administration. The principle is that a biopharmaceutical process should guarantee the quality of the product by design. A key point is to guarantee the process reproducibility. An objective will be to propose appropriate quantifiers of that reproducibility (combination of hard and software sensors) and to develop closed-loop control based on these quantifiers (PAT controllers) which would guarantee the process reproducibility.
The prevalence of distributed parameter models motivates a theoretical investigation of specific questions. One objective is to analyze and to design nonlinear state estimators for invariant semilinear distributed parameter systems, and to develop numerical methods for the synthesis of such estimators. Another objective is to further explore the links between irreversible thermodynamics and system theory, using tools referring to contact systems and port-Hamiltonian systems. Power-shaping control will also play a major role in this investigation.
WP 3.5: Modeling and control of biomedical systems (KUL, UCL, ULg, UMons, UNamur, UGent)
Neural control of movement. We plan to further investigate the control of eye movements in human subjects. Learning processes related to the maturation of the oculomotor system will be of particular interest (from early childhood to elderly subjects). In addition, the control of eye movements in cerebral palsy patients will be investigated with a particular focus on the link between specific eye movement patterns in children and learning disabilities. Indeed, there are suspicions that these learning disorders could be caused by subtle oculomotor deficits as the eye movements are important in tasks like reading. One of the goals of our project will be to point out subclinical deficits in oculomotor performances of children with low level of severity of cerebral palsy. Finally, this project will address the influence of neurodegenerative diseases on eye movements. In particular, we will focus on the ability of patients to use predictive mechanisms in oculomotor control as a robust marker of the progression of the specific disorders.
We also plan to study motor control and learning in a dynamic environment. Current mathematical approaches to motor control highlight that movements result from a trade-off between the energy spent and the desired performance of the action. In addition, the theory of optimal control predicts that changes in the environment should elicit a change in behavior (motor adaptation) in order to maintain the optimality of the movement, as observed experimentally. Similarly, it predicts that the properties of an object inferred from its perception (fragility of the object, its shape ...) should also influence the corresponding action. Very little is known about this task-dependent adaptation process although task demands vary considerably in real life: reaching for differently-shaped cups; carrying a box of crystal glasses vs. a box of paper of a similar weight, etc. Therefore, we propose to critically extend the understanding of the motor adaptation process to task-dependent adaptation. The investigation of this perception-to-action system will have four main objectives: 1) The extension of the current theoretical framework of optimal control to task-dependent adaptation in order to find specific predictions about changes in behavior elicited by changes in task demands. 2) The validation of these predictions by behavioral experiments in humans. 3) The neural substrate of this task-dependent adaptation process will be investigated by means of non-invasive brain stimulation techniques, which allow real-time interaction with the brain processes under study. Therefore, the project will be interdisciplinary, with mathematical, behavioral, physiological aspects.
Digital signal processing is used in applications focusing on modeling of human physiology. We will pursue research in several directions, including the three-dimensional modeling of human walk, modeling and analysis of human attention in order to detect rare events, and bio-modeling of the respiratory system and blood flow. Biodesign of instruments is then an objective resulting from the study of human walk through the development of orthosis.
Recent methods for brain imaging and direct recording of cortical neuronal activity suggest the possibility of increased temporal and spatial resolution in human studies, and require the development of quantitative methods for analysis that will accurately represent dynamics and structure. The application of complex network tools to neuroscience and neuro-imaging datasets has recently led to major advances in understanding the way in which the brain works at a system level. Our goal is to go beyond a purely static point of view and to develop a robust framework for unraveling how functional networks develop in time and robustly retain properties in spite of environmental fluctuations. Motivated by neural engineering applications, we will also develop novel statistical processing tools specifically tailored to the technology of multichannel neural recordings.