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Agent-based control of discrete spatially distributed systems
Abstract
From a control system perspective, spatially distributed systems offer challenges because of their distributed nature, nonlinearity, and high order. in addition, the control structure for these spatially distributed networks combine discrete and distributed components, in the form of complex arrays of sensors and actuators. Manipulation of the network states may require simultaneous control actions in different parts of the system and may need transients through several operating regimes to achieve the desired operation. A hierarchical, agent-based control structure is presented whereby local control objectives may be changed in order to achieve the global control objective. The performance of the hierarchical agent-based control approach is illustrated in a case study where the interaction front between two competing autocatalytic species is moved from one spatial configuration to another. The multi-agent control system is able to effectively explore the parameter space of the network and intelligently manipulate the network flow rates such that the desired spatial distribution of species is achieved.
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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.
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 competition of two species for a common resource is illustrated using the paradigm of autocatalytic replicators inhabiting a continuous stirred tank reactor (CSTR) environment that is continuously fed with the resource. In most cases presented, one species is robust (appears in reactor feed) while the other is not. The introduction of the second (invading) species into the CSTR via an unsustained disturbance has a strong effect on the steady-state and dynamic behavior of the first (host) species. New steady states are added to the bifurcation diagram that show that the invading species can coexist in the system with the host species when its growth and death characteristics are similar to those of the latter. The population levels of the host species are greatly reduced in these cases as a result of the considerable decrease in resource concentration at steady state. Open-loop strategies for the elimination of the invading species are developed and discussed. These strategies involve the manipulation of the reactor residence time to destabilize the states of coexistence.
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.
In this paper we show how hybrid system theory can be used to obtain a state-feedback optimal control law for an electronic throttle. After modelling the electronic throttle as a piece wise affine (PWA) system, we derive an optimal control law for such a hybrid system via dynamic programming. Results indicate that constrained finite time optimal control of small/medium sized PWA systems with fast sampling times can be successfully implemented.
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.< >