Cybernetical Physics: From Control of Chaos to Quantum by A. Fradkov

By A. Fradkov

Cybernetical physics borrows equipment from either theoretical physics and regulate engineering. It offers with the keep an eye on of complicated platforms is among the most crucial features in facing platforms displaying nonlinear habit or related positive factors that defy conventional keep an eye on ideas. This booklet totally info this new self-discipline.

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Additional resources for Cybernetical Physics: From Control of Chaos to Quantum Control (Understanding Complex Systems)

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However, because of instability of the equilibrium ϕ = π any deflection of initial conditions or any external disturbance leads to violation of the control goal, no matter how small is a disturbance. To find a more efficient way of control, one may try a time-dependent (time-varying) control action. To be precise, if a control parameter is timevarying, it cannot be called a parameter, it should be called a variable. 4 Methodology 27 rule allowing to calculate the value of the control action u(t) in each time instant t is usually called a control algorithm.

50) for all x, u, t. 51) where sign of a vector is understood component-wise: for a vector z = col (z1 , . . , zm ) sign z is defined as sign z = col (sign z1 , . . , sign zm ). In order to make a reasonable choice of the control algorithm parameters the applicability conditions should be verified. The main conditions are: convexity of the function ω(x, u, t) in u and existence of “ideal” control u∗ such that ω(x, u∗ , t) ≤ 0 for all x (attainability condition). More precise formulations and mathematical proofs can be found in [29, 134, 135, 157, 164].

C. Generation (excitation) of oscillations. The third class of control goals corresponds to the problems of excitation or generation of oscillations. Here, it is assumed that the system is initially at rest. ) In this case the goal trajectory of the state vector x∗ (t) is not prespecified. Moreover, the goal trajectory may be unknown, or may even be irrelevant to the achievement of the control goal. Such problems are well known in electrical, radio engineering, acoustics, laser, and vibrational technologies – wherever it is necessary to create an oscillatory mode for the system.

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