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An Agent-Based Framework for Control of Reactor Networks with Autocatalytic Replicators
Abstract
Several recent studies on autocatalytic reactions in single and coupled continuous stirred-tank reactor (CSTR) networks have demonstrated a rich spec-trum of complex behavior. From a control systems perspective, the operating regime of a CSTR network can be manipulated by changing the flow rates between the reactors. Systems of more than one CSTR require multiple controllers and may need transients through several operating regimes to achieve the desired operation. This may require a hierarchical control structure whereby local control objectives can change dynamically in order to achieve the global control objective of the system. An agent-based control system is used to observe and control various aspects of a CSTR network. The primary focus of analyzing complex emergent behavior is demonstrating methods or combinations of methods that influence the behavior and capabilities of the agent-based control system. Simulation studies illustrate scenarios of interest, especially conditions that lead to emergent behavior.
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The paradigm of cubic autocatalytic replicators with decay in coupled isothermal continuous stirred tank reactors is selected as a model to study complex behavior in population dynamics of sexually reproducing species in a heterogenous environment. It is shown that, even a setup with single species in two coupled environments may have regions in parameter space that result in chaotic behavior, hence segregation in the environment causes complexity in the system dynamics. Furthermore, partitioning is found to lead to emergence phenomena exemplified by steady states not obtainable in the equivalent homogeneous system. These phenomena are illustrated through case studies involving single or multiple species. Results show that the coupled environments can host species, that would not survive should the coupling be removed.
Scientific research and practice in multiagent systems focuses on
constructing computational frameworks, principles, and models for how
both small and large societies of intelligent, semiautonomous agents can
interact effectively to achieve their goals. This article provides a
personal view of the key application areas for cooperative multiagent
systems, the major intellectual problems in building such systems, the
underlying principles governing their design, and the major directions
and challenges for future developments in this field
This article has sought to justify precisely why agent-oriented approaches are well suited to developing complex software systems in general and control systems in particular. These general points are then made concrete by showing how they apply in two very different agent-based control systems--Iber- 26 drola's electricity transportation management system and DaimlerChrysler's manufacturing line control system. In making these arguments, proponents of other software engineering paradigms can claim that the key concepts of agent-oriented computing can be reproduced using their technique. This is undoubt- edly true. Agent-oriented systems are, after all, computer programs, and all programs have the same set of computable functions. However, this misses the point. The value of a paradigm is the mindset and the techniques it provides to software engineers. In this respect, agent-oriented concepts and techniques are both well suited to developing complex, distributed systems and an extension of those currently available in other paradigms
The dynamic behavior of the continuous stirred tank reactor is analysed and classified for a variable reactor residence time. Although earlier work, treating the bifurcation to limit cycles and steady states with changing Damköhler number, yields a complete description of the problem, the evolution of multiple steady states and limit cycles is much more bizarre as the reactor residence time varies. In addition, it is the reactor residence time which is most easily varied experimentally so that the present results are more readily compared with experiment. Plots are given to show the influence of system parameters on the reactor behavior.
Multiplicity, stability and dynamics for autocatalytic reactions of the type A⋯ → rR + ⋯ with overall rate expression rA = kCAmCRn in a continuous stirred tank reactor (CSTR) are studied. Exact multiplicity criteria are defined in the parameter space. Stability analysis shows that no periodic oscillation is possible for the system. When multiplicity occurs, some minimum of R present initially in the reactor is required in order for the high steady state to be achieved. Loci of transient extreme for product are also investigated. Multiplicity and uniqueness criteria are further compared with reported experimental data in literature.
The types of dynamic behavior possible for a single first order reaction carried out in a stirred tank reaction are classified according to values of the parameters and plots in parameter space used to define the various possibilites. Analytic criteria are developed which predict the existence and stability character of limit cycles as a function of the system parameters. The types of dynamic behavior predicted are illustrated by numerical computation of the temperature and concentration trajectories. Several kinds of new jump phenomena for this problem are observed and explained in terms of the parameter space plots. The theory and analysis methods can be easily generalized to other types of reaction systems.
In this project, parallel general-purpose software for two classes of mathematical problems has been developed. PVODE is a portable solver for ordinary differential equation systems, based on robustmathematical algorithms, and targeted at large systems on parallel machines. It is the parallel extension of the earlier sequential solver CVODE. A related solver called KINSOL has been developed for systems of nonlinear algebraic equations. KINSOL was first developed as a sequential solver, on a design that permitted extending it to a parallel version with fairly minimal additions. Both PVODE and KINSOL are being used within a parallel version of the tokamak edge plasma model UEDGE. KINSOL is also being applied in the ParFlow groundwater flow model to solve a nonlinear pressure equation.
The recent contention that isothermal systems in a continuously stirred tank reactor can exhibit only extinction (ΔG is positive) as the flow rate is increased (the residence time reduced) and only ignition (ΔG is negative) as the flow rate is decreased is shown not to be correct. The simple, autocatalytic sequence A + 2B → 3B, rate = k1ab2, for which the catalyst B is not indefinitely stable, but undergoes a first-order removal of decay B → inert, rate = k2b, may also have ignition accompanying an increase in the flow rate and extinction accompanying a decrease. This gives rise to S-shaped curves, Z-shaped curves, and also to closed curves in the dependence of the extent of conversion on residence time or flow rate. Under these circumstances, the sign of the free energy change accompanying the observed behavior is determined by the kinetics: the behavior is not determined by the sign of ΔG.
The static and dynamic behavior of the autocatalytic reaction R + 2P → 3P with decay P → D is studied in networks of coupled continuous stirred tank reactors (CSTRs). Numerical bifurcation studies of the system are performed, resulting in rich steady-state bifurcation structures with multiple steady states and isolas. The heterogeneity of the networks is influenced by the number of reactors as well as the network topology. It is shown that the number of steady states of the network increases with heterogeneity, thereby allowing those autocatalytic species to exist in the network that would normally not exist in the homogeneous environment of a single CSTR. Spatial patterns of stable steady states are evident in reactor networks. Dynamic simulation studies are performed to illustrate the transition from one stable state configuration to another or from stable steady states to periodic regimes.
Two types of nonlinear feedback control schemes are introduced and analyzed for their capability of recovering the original state of an isothermal continuous-flow stirred tank reactor with one robust cubic autocatalytic species, perturbed by a temporary disturbance of an invading cubic autocatalytic species in the inflow. The control objectives are to eliminate the invading species from the system and to restore the original state of the host species. The extent of applicability of the control design to different nonrobust invading species is studied, when the controller is tuned for a specific invader. Moreover, a time-delay feature is suggested in one of the control schemes developed to achieve the control objectives in systems with poor detection of invading species.
The purpose of this paper is to consider the well agitated continuous reactor from the standpoint of stability of the steady state. It has been shown in the past that chemical-reaction systems may be unstable in the sense that on slight perturbation they tend to move to a more stable state or that they are stable in their steady states, small perturbations being self-correcting so that the system possesses autoregulation. In this paper methods of developing criteria for the quantitative determination of stability or instability or presented and applied to some simple problems. In order that the effect of large perturbations on the system may be determined, complete solutions of the rigorous equations are obtained on the analogue computer (R.E.A.C.). A complete plot of reaction paths in the concentration-temperature plane may be obtained in this manner. Because of the nonlinearity of the system one cannot predict with certainty what steady state will be approached after a given large perturbation, multiple steady states being assumed possible. From the phase plot of reaction paths the regions in the plane which lead to certain steady states are delineated. Also it is shown that the natural behavior of a reactor is not to approach an unstable state. So far as the reactor is concenrned, the unstable state does not exist. The stability of the system is important to the engineer, as control will be easy or difficult and product quality will be satisfactory or not depending upon the relative stability of the steady state. An unstable state would require more elaborate control than a stable state.
The question of the multiplicity of the steady states of a chemical reactor was one of the concerns in the pioneering work of Bilous and Amundson. Their diagrams showed quite clearly the geometry of the situation, and this kind of analysis sufficed for many years. It remained for Balakotaiah and Luss, using the methods of singularity theory, to give a comprehensive treatment of the question. After a brief survey, we take up the case of consecutive first-order reactions and show that up to seven steady states are possible.
A study of the dynamic behavior of two coupled nonisothermal CSTRs carrying out an irreversible first-order reaction is presented. In particular, we study the case where the behavior of both—not necessarily identical—reactors is oscillatory when uncoupled. Emphasis is placed on the way the dynamics develop with increasing coupling strength from the asymptotic limit of weak coupling where the behavior can be deduced from that of the individual reactors. The detailed two-parameter study provides a coherent framework in which many previous experimental and computational studies can be consistently integrated. A scenario of common dynamic features emerges, which is independent of the order of the reaction, whether the reaction is isothermal or catalytic, the details of the mechanism, or the particular form of the coupling. A strong qualitative relation between this framework and the dynamic behavior of periodically forced chemical reactors is also noted.
The prototype, cubic autocatalytic reaction (A + 2B → 3B) forms the basis for the simplest homogeneous system to display “exotic” behaviour. Even under well-stirred, isothermal, open conditions (CSTR) we may find multistability, hysteresis, extinction, ignition and anomalous relaxation times. Allowing for the finite lifetime of the catalyst (B→inert products) adds another dimension. The dependence of the stationary-states on residence-time now yields isolas or mushrooms. Sustained oscillations (stable limit cycles) are also possible. The onset of oscillation corresponds to a change in the character of the stationary-state (from stable focus to unstable focus) and the conditions for this change can be evaluated analytically. The period of the oscillations and their amplitudes increase as the residence time is lengthened. A total of nine different phase-portraits in the a–b plane has been found.The isothermal system is less complex than the exothermic, first-order reaction in a CSTR, but there are strong analogies between the two.
Static and dynamic properties of multiple cubic autocatalytic reactions in an isothermal continuous stirred tank reactor are investigated. It is shown that in the bifurcation diagram of the system should an n-interaction isola exist, it is to reside in the intersection of all possible (n−1)-interaction isolas of the n species constituting the n-interaction. Next, it is discussed that once the ratio of reproduction to death rates for a species is fixed, then the size of its single species isola is fixed, in logarithmic residence time. Furthermore, it is found that any interaction isola in the bifurcation diagram is unstable, whereas single species isolas will have ranges of stable steady states. Finally, these findings and some dynamic properties of the system are demonstrated in case studies.
Agent-based computing represents an exciting new synthesis both for Artificial Intelligence (AI) and, more generally, Computer Science. It has the potential to significantly improve the theory and the practice of modeling, designing, and implementing computer systems. Yet, to date, there has been little systematic analysis of what makes the agent-based approach such an appealing and powerful computational model. Moreover, even less effort has been devoted to discussing the inherent disadvantages that stem from adopting an agent-oriented view. Here both sets of issues are explored. The standpoint of this analysis is the role of agent-based software in solving complex, real-world problems. In particular, it will be argued that the development of robust and scalable software systems requires autonomous agents that can complete their objectives while situated in a dynamic and uncertain environment, that can engage in rich, high-level social interactions, and that can operate within flexible organisational structures.
Particle swarm optimization is employed here to evaluate the parametric regions where different dynamic phenomena (periodic oscillations, double-period oscillations, chaos) can be expected in dynamic models. The proposed algorithm comprises two fundamental steps: the rough evaluation of regions where the desired solutions can be found and solution refining. The refining step allows the search for unstable solutions that may coexist with the other stable attractors. No preliminary bifurcation analysis is required. Simulations performed for distinct dynamic models show that the proposed algorithm is indeed able to locate different dynamic phenomena in the parameter space and that the algorithm may be of help for those interested in increasing the speed of more traditional dynamic bifurcation analysis.
This article reviews the principles of agent-based computing and discusses its relevance for control. Applications to power generation and manufacturing are also discussed.
The integration of a supervisory knowledge-based system (KBS) with a multivariable control system is examined to provide robust multivariable control of a chemical reaction process. The supervisory KBS is capable of monitoring the process to detect system faults as well as assessing control system performance. If a control system performance deficiency is detected, the KBS formulates and implements the necessary corrective controller tuning. This adaptive capability reduces the conservatism of the robust control system. The underlying mechanisms are discussed and the re-tuning ability of the KBS is illustrated by using rigorous simulations of a chemical reaction process.< >
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