By A. Fradkov
Cybernetical physics borrows tools from either theoretical physics and regulate engineering. It offers with the keep watch over of complicated platforms is without doubt one of the most vital facets in facing structures displaying nonlinear habit or comparable positive aspects that defy conventional keep watch over options. This ebook absolutely info this new self-discipline.
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Extra resources for Cybernetical Physics: From Control of Chaos to Quantum Control (Understanding Complex Systems)
For x(0) ∈ Ω. Note that standard control goals in conventional control theory are regulation and tracking. The rest of the aforementioned goals are not typical for conventional control theory because they do not completely specify the desired behavior of the system. These classes of control problems belong to the area of the so-called partial control which has rapidly developed recently [157, 437]. , the design of the control algorithms should meet the small control or weak control requirement.
4) A slightly diﬀerent formulation of control goal is the following H0 (p(t), q(t)) → H∗ , when t → ∞. 5) means convergence of the value of the system energy to the desired value H∗ . 3), meaning convergence of the arguments of the energy function. 3) if S is not compact. 3) for Lagrangian systems with uniformly positive deﬁnite inertia matrix. 3) will be ignored which inﬂuences neither physical nor engineering applications. 6) where x = col(p, q). 5) takes the form Q(x(t)) → 0 when t → ∞. 7) In what follows we assume that the Hamiltonian is linear in control: H(p, q, u) = H0 (p, q) + H1 (p, q)T u, where H0 (p, q) is the internal Hamiltonian and H1 (p, q) is an m-dimensional vector (column) of interaction potentials .
It is based upon methods of controlled system model’s building, methods of system states and parameters estimation (identiﬁcation), and methods of feedback synthesis. The models of controlled system used in cybernetics diﬀer from conventional models of physics and mechanics in that they have explicitly speciﬁed inputs and outputs. Unlike conventional physics results, often formulated as conservation laws, the results of cybernetical physics are formulated in the form of transformation laws, establishing the possibilities and limits of changing properties of a physical system by means of control.