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Controllability and observability are dual aspects of the same problem. Roughly, the concept of controllability denotes the ability to move a system around in its entire configuration space using only certain admissible manipulations. The exact definition varies slightly within the framework or the type of models applied.
Observability is a measure of how well internal states of a system can be inferred from knowledge of its external outputs. In control theory, the observability and controllability of a linear system are mathematical duals. The concept of observability was introduced by the Hungarian-American engineer Rudolf E. Kálmán for linear dynamic systems.
Controllability and observability are main issues in the analysis of a system before deciding the best control strategy to be applied, or whether it is even possible to control or stabilize the system. Controllability is related to the possibility of forcing the system into a particular state by using an appropriate control signal.
[1] [2] To improve observability, software engineers use a wide range of logging and tracing techniques to gather telemetry information, and tools to analyze and use it. Observability is foundational to site reliability engineering, as it is the first step in triaging a service outage. One of the goals of observability is to minimize the amount ...
The observability and controllability of a system are mathematical duals (i.e., as controllability provides that an input is available that brings any initial state to any desired final state, observability provides that knowing an output trajectory provides enough information to predict the initial state of the system).
Controllability in the context of highly complex systems (whether discrete or not, like integrated circuits) is the measure of (abilty) an input stimulus to change the state of internal state (regardless of whether it can be observed - that's observability).--71.245.164.83 00:40, 12 September 2010 (UTC)
In the behavioral setting, a dynamical system is a triple = (,,) where is the "time set" – the time instances over which the system evolves, is the "signal space" – the set in which the variables whose time evolution is modeled take on their values, and
The resulting digraph is called the cacti (see Fig.d). According to the structural controllability theorem, [5] since there is a cacti structure spanning the controlled network (see Fig.e), the system is controllable. The cacti structure (Fig.d) underlying the controlled network (Fig.e) is the "skeleton" for maintaining controllability.