Feed forward (control)

In systems theory, an open system is a feed forward system that does not have any feedback loop to control its output. In contrast, a closed system uses on a feedback loop to control the operation of the system. In an open system, the output of the system is not fed back into the input to the system for control or operation.

In physiology, feed-forward control is exemplified by the normal anticipatory regulation of heartbeat in advance of actual physical exertion by the central autonomic network. Feed-forward control can be likened to learned anticipatory responses to known cues (predictive coding). Feedback regulation of the heartbeat provides further adaptiveness to the running eventualities of physical exertion. Feedforward systems are also found in biological control of other variables by many regions of animals brains.

Even in the case of biological feedforward systems, such as in the human brain, knowledge or a mental model of the plant (body) can be considered to be mathematical as the model is characterized by limits, rhythms, mechanics and patterns.[9][17]

A pure feed-forward system is different from a homeostatic control system, which has the function of keeping the body's internal environment 'steady' or in a 'prolonged steady state of readiness.' A homeostatic control system relies mainly on feedback (especially negative), in addition to the feedforward elements of the system.

Feed-forward loops (FFLs), a three-node graph of the form A affects B and C and B affects C, are frequently observed in transcription networks in several organisms including E. coli and S. cerevisiae, suggesting that they perform functions that are important for the functioning of these organisms. In E. coli and S. cerevisiae transcription networks have been extensively studied, FFLs occur approximately three times more frequently than expected based on random (Erdös-Rényi) networks.[20][21]

Edges in transcription networks are directed and signed, as they represent activation (+) or repression (-). The sign of a path in a transcription network can be obtained by multiplying the signs of the edges in the path, so a path with an odd number of negative signs is negative. There are eight possible three-node FFLs as each of the three arrows can be either repression or activation, which can be classified into coherent or incoherent FFLs. Coherent FFLs have the same sign for both the paths from A to C, and incoherent FFLs have different signs for the two paths.[22]

The temporal dynamics of FFLs show that coherent FFLs can be sign-sensitive delays that filter input into the circuit. We consider the differential equations for a Type-I coherent FFL, where all the arrows are positive:

${\displaystyle {\frac {\delta B}{\delta t}}=\beta _{B}(A)-\gamma _{B}B}$

${\displaystyle {\frac {\delta C}{\delta t}}=\beta _{C}(A,B)-\gamma _{C}C}$

Where ${\displaystyle \beta _{y}}$ and ${\displaystyle \beta _{z}}$ are increasing functions in ${\displaystyle A}$ and ${\displaystyle B}$ representing production, and ${\displaystyle \gamma _{Y}}$ and ${\displaystyle \gamma _{z}}$ are rate constants representing degradation or dilution of ${\displaystyle B}$ and ${\displaystyle C}$ respectively. ${\displaystyle \beta _{C}(A,B)}$ can represent an AND gate where ${\displaystyle \beta _{C}(A,B)=0}$ if either ${\displaystyle A=0}$ or ${\displaystyle B=0}$, for instance if ${\displaystyle \beta _{C}(A,B)=\beta _{C}\theta _{A}(A>k_{AC})\theta _{A}(B>k_{ABC})}$ where ${\displaystyle \theta _{A}}$ and ${\displaystyle \theta _{B}}$ are step functions. In this case the FFL creates a time-delay between a sustained on-signal, i.e. increase in ${\displaystyle A}$ and the output increase in ${\displaystyle C}$. This is because production of ${\displaystyle A}$ must first induce production of ${\displaystyle B}$, which is then needed to induce production of ${\displaystyle C}$. However, there is no time-delay in for an off-signal because a reduction of ${\displaystyle A}$ immediately results in a decrease in the production term ${\displaystyle \beta _{C}(A,B)}$. This system therefore filters out fluctuations in the on-signal and detects persistent signals. This is particularly relevant in settings with stochastically fluctuating signals. In bacteria these circuits create time delays ranging from a few minutes to a few hours.[22][23]

Similarly, an inclusive-OR gate in which ${\displaystyle C}$ is activated by either ${\displaystyle A}$ or ${\displaystyle B}$ is a sign-sensitive delay with no delay after the ON step but with a delay after the OFF step. This is because an ON pulse immediately activates B and C, but an OFF step does not immediately result in deactivation of C because B can still be active. This can protect the system from fluctuations that result in the transient loss of the ON signal and can also provide a form of memory. Kalir, Mangan, and Alon, 2005 show that the regulatory system for flagella in E. coli is regulated with a Type 1 coherent feedforward loop.[24]

For instance, the regulation of the shift from one carbon source to another in diauxic growth in E. coli can be controlled via a type-1 coherent FFL. In diauxic growth cells growth using two carbon sources by first rapidly consuming the preferred carbon source, and then slowing growth in a lag phase before consuming the second less preferred carbon source. In E. coli, glucose is preferred over both arabinose and lactose. The absence of glucose is represented via a small molecule cAMP. Diauxic growth in glucose and lactose is regulated by a simple regulatory system involving cAMP and the lac operon. However, growth in arabinose is regulated by a feedforward loop with an AND gate which confers an approximately 20 minute time delay between the ON-step in which cAMP concentration increases when glucose is consumed and when arabinose transporters are expressed. There is no time delay with the OFF signal which occurs when glucose is present. This prevents the cell from shifting to growth on arabinose based on short term fluctuations in glucose availability.[25]

Additionally, feedforward loops can facilitate cellular memory. Doncic and Skotheim (2003) show this in the regulation in the mating of yeast, where extracellular mating pheromone which indices mating behavior including preventing cells from entering the cell cycle.[26] The mating pheromone activates the MAPK pathway which then activates the cell-cycle inhibitor Far1 and activates the Ste12 transcription factor that increases the synthesis of inactive Far1. In this system the concentration of active Far1 depends on the time integral of a function of the external mating pheromone concentration. This dependence on past levels of mating pheromone is a form of cellular memory. This system simultaneously allows for the stability and reversibility.

Incoherent feedforward loops, in which the two paths from the input to the output node have different signs result in short pulses in response to an ON signal. In this system input A simultaneous directly increases and indirectly decreases synthesis of output node C. If the indirect path to C (via B) is slower than the direct path a pulse of output is produced in the time period before levels of B are high enough to inhibit synthesis of C. Response to epidermal growth factor (EGF) in dividing mammalian cells is an example of a Type-1 incoherent FFL.[27]

The frequent observation of feed-forward loops in several biological contexts across scales suggests that they have structural properties that are highly adaptive in several contexts. Several theoretical and experimental studies including those discussed here show that FFLs create a mechanism for biological systems to process and store information, which is important for predictive behavior and survival in complex dynamically changing environments.

In computing, feed-forward normally refers to a perceptron network in which the outputs from all neurons go to following but not preceding layers, so there are no feedback loops. The connections are set up during a training phase, which in effect is when the system is a feedback system.

In the early 1970s, intercity coaxial transmission systems, including L-carrier, used feed-forward amplifiers to diminish linear distortion. This more complex method allowed wider bandwidth than earlier feedback systems. Optical fiber, however, made such systems obsolete before many were built.

Feedforward control is a discipline within the field of automatic controls used in automation.

The method is rather a new technique that changes the phase of an open-loop transfer function of a non-minimum phase system into minimum phase.[28]