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Biomimetic and Biologically Inspired Control 401

System control is not simply limited to regulation or adjustment as that in the feedback control,
it also includes management. In the 1960s, system optimization was extensively discussed in
modern control theory. This brought forth the optimal control theory typified by Pontryagin’s
maximum principle (Boltyanski et al., 1960) and Bellman’s dynamic programming (Bellman and
Kalaba, 1960). Optimal control is related to the optimization of a dynamic system while the theory
to optimize a static system is referred to as optimalizing control. Both concepts correspond to
planning and management or supervision. They are different from regulation. An example of
optimal control problem is a terminal control problem, such as to design trajectories of a rocket
to send a satellite accurately onto a preprogrammed orbit. This can be regarded as the problem of
obtaining a desired command input for a follow-up control in the feedback control problem.
Therefore, it is recognized that this control strategy is on the planning level, which is generally
one level higher than the strategy of feedback control. Mathematically, Pontryagin’s maximum
principle and Bellman’s dynamic programming can be regarded as an extension of the classical
calculus of variations to control problems, that is, the Hamilton’s canonical equations and the
Hamilton–Jacobi formula. On the other hand, optimalizing control optimizes a performance
function by considering only the static input–output relationship in steady state as opposed to
optimizing dynamic processes in optimal control. In early 1951, Draper and Li first considered
the optimalizing control problem in order to keep the internal combustion engine running at an
optimum operating condition regardless of variations in load (Draper and Li, 1951). Recent
electronic fuel injection (EFI) system, in which a microprocessor adjusts the air–fuel ratio, has
replaced the carburetor in some automobiles. Although it was not exactly what Draper and Li
intended to do, optimalizing control has been implemented in various fields. In this way, optimaliz-
ing control determines the optimum set point (i.e., target value) of the constant value control, it can
also be regarded as an upper level above feedback control.
Though half a century has passed since Wiener’s Cybernetics, machines are not even close to
resembling animals and their abilities. When we dreamed of flying like a bird, the airplane was
born, far outdoing the birds in speed and size. However, the airplane cannot realize the bird’s agility
to move from branch to branch. The same thing can be found for the present robots and computers.
Nowadays, industrial robots can only perform predefined operations in a well-structured task space
but do not have full capability to deal with unexpected situations in natural complex environment.
An autonomous robot, which is able to identify its own environment and determine its own
voluntary actions, is yet something of the future. Similarly, though the computer has increased
enormous computational capabilities, it is nevertheless a serial sequential machine that can perform
only preprogrammed actions. Therefore, although machines have been made to imitate and to
amplify special functions of human and animals, they are far from achieving the level of the
autonomy, flexibility, environmental adaptability, and functional variety of biological systems.
Recently, as marked by the rapid spread of computers, internet, and mobile communication, the
developments of the information science and technologies make it possible for us to process higher
capacity of information much faster and more intelligently in the worldwide scale. It provides us
with enormous challenging realms. Meanwhile, the systems around us are becoming larger and
more complex. It becomes more and more important for the artificial systems to have high
flexibility, diversity, reliability, and affinity. System control theory, which forms the core founda-
tion for understanding, designing, and operating of systems, is still limited and insufficient to
handle complex large-scale systems and to process spatial temporal information in real time as
biological systems. Under this background, biomimetic and biologically inspired control research
is becoming a very important subject. This subject is widely expected to breakthrough the next
information and system control theories.
Animals acquire and develop their extremely sophisticated movement through active interaction
with the environment using parallel decentralized processing of spatial temporal information in real
time. They also use logical recognition together with dynamic physical motion. The analysis
and clarification of these functions mathematically at the system level, and imitation of them in