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Observability of complex systems.

ABSTRACT: A quantitative description of a complex system is inherently limited by our ability to estimate the system's internal state from experimentally accessible outputs. Although the simultaneous measurement of all internal variables, like all metabolite concentrations in a cell, offers a complete description of a system's state, in practice experimental access is limited to only a subset of variables, or sensors. A system is called observable if we can reconstruct the system's complete internal state from its outputs. Here, we adopt a graphical approach derived from the dynamical laws that govern a system to determine the sensors that are necessary to reconstruct the full internal state of a complex system. We apply this approach to biochemical reaction systems, finding that the identified sensors are not only necessary but also sufficient for observability. The developed approach can also identify the optimal sensors for target or partial observability, helping us reconstruct selected state variables from appropriately chosen outputs, a prerequisite for optimal biomarker design. Given the fundamental role observability plays in complex systems, these results offer avenues to systematically explore the dynamics of a wide range of natural, technological and socioeconomic systems.

SUBMITTER: Liu YY

PROVIDER: S-EPMC3574950 | biostudies-literature | 2013 Feb

REPOSITORIES: biostudies-literature

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Observability of complex systems.

Liu Yang-Yu YY Slotine Jean-Jacques JJ Barabási Albert-László AL

Proceedings of the National Academy of Sciences of the United States of America 20130128 7

A quantitative description of a complex system is inherently limited by our ability to estimate the system's internal state from experimentally accessible outputs. Although the simultaneous measurement of all internal variables, like all metabolite concentrations in a cell, offers a complete description of a system's state, in practice experimental access is limited to only a subset of variables, or sensors. A system is called observable if we can reconstruct the system's complete internal state ...[more]

PMID: 23359701

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Project description:The actual state of ecological systems is rarely known with certainty, but management actions must often be taken regardless of imperfect measurement (partial observability). Because of the difficulties in accounting for partial observability, it is usually treated in an ad hoc fashion, or simply ignored altogether. Yet incorporating partial observability into decision processes lends a realism that has the potential to improve ecological outcomes significantly. We review frameworks for dealing with partial observability, focusing specifically on dynamic ecological systems with Markovian transitions, i.e., transitions among system states that are influenced by the current system state and management action over time. Fully observable states are represented in an observable Markov decision process (MDP), whereas obscure or hidden states are represented in a partially observable process (POMDP). POMDPs can be seen as a natural extension of observable MDPs. Management under partial observability generalizes the situation for complete observability, by recognizing uncertainty about the system's state and incorporating sequential observations associated with, but not the same as, the states themselves. Decisions that otherwise would depend on the actual state must be based instead on state probability distributions ("belief states"). Partial observability requires adaptation of the entire decision process, including the use of belief states and Bayesian updates, valuation that includes expectations over observations, and optimal strategy that identifies actions for belief states over a continuous belief space. We compare MDPs and POMDPs and highlight POMDP applications to some common ecological problems. We clarify the structure and operations, approaches for finding solutions, and analytic challenges of POMDPs for practicing ecologists. Both observable and partially observable MDPs can use an inductive approach to identify optimal strategies and values, with a considerable increase in mathematical complexity with POMDPs. Better understanding of POMDPs can help decision makers manage imperfectly measured ecological systems more effectively.

Dataset Information

Observability of complex systems.

Publications

Observability of complex systems.

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