By Gennady Leonov
ISBN-10: 9814282316
ISBN-13: 9789814282314
The papers during this edited quantity goal to supply a greater figuring out of the dynamics and keep an eye on of a big type of hybrid dynamical platforms which are defined by means of assorted versions in numerous country house domain names. They not just disguise vital facets and instruments for hybrid platforms research and keep watch over, but additionally a couple of experimental realizations. distinct recognition is given to synchronization - a common phenomenon in nonlinear technological know-how that received great importance on the grounds that its discovery through Huygens within the seventeenth century. attainable functions of the consequences brought within the booklet comprise regulate of cellular robots, regulate of CD/DVD gamers, versatile production strains, and intricate networks of interacting brokers. The publication is predicated at the fabric awarded at a equally entitled minisymposium on the sixth eu Nonlinear Dynamics convention held in St Petersburg in 2008. it truly is targeted in that it includes result of numerous overseas and interdisciplinary collaborations within the box, and displays cutting-edge technological improvement within the sector of hybrid mechanical platforms on the vanguard of the twenty first century.
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Additional info for Dynamics and Control of Hybrid Mechanical Systems (World Scientific Series on Nonlinear Science, Series B)
Example text
1), for the determination of xh2 (t) and yh2 (t) we obtain dxh2 (t) = −yh2 (t) + ufh2 (t), dt dyh2 (t) = xh2 (t) + ugh2 (t). 3. 17) Lyapunov Quantities and Limit Cycles of Two-dimensional Dynamical Systems 15 we have t xhk (t) = ughk (0) cos(t) cos(τ ) (ughk (τ )) + ufhk (τ ) dτ + + cos(t) 0 t sin(τ ) (ughk (τ )) + ufhk (τ ) dτ − ughk (t), + sin(t) 0 t yhk (t) = ughk (0) sin(t) cos(τ ) (ughk (τ )) + ufhk (τ ) dτ − + sin(t) 0 t sin(τ ) (ughk (τ )) + ufhk (τ ) dτ. 18) can be verified by direct differentiation.
Algebraic Riccati equations with nonsmoothing observation arising in hyperbolic and Euler-Bernoulli boundary control problems. Annali di Matematica Pura Applicata, 153, pp. 307–382. Yakubovich, V. , Leonov, G. A. and Gelig, A. Kh. (2004). Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities. World Scientific, Singapore. Han, W. and Sofonea, M. (2000). Evolutionary variational inequalities arising in viscoelastic contact problems. SIAM J. Numer. , 38 (2), pp. 556–579.
7) ξ(0) = ξ0 ∈ E(y0 ) , z(t) = Dy(t) + E ξ(t) . 8) it is supposed that C ∈ L(Y−1 , W ), D ∈ L(Y1 , Z) and E ∈ L(Ξ, Z) are linear operators, Ξ, W and Z are real Hilbert spaces, Y1 ⊂ Y0 ⊂ Y−1 is a real Gelfand triple and A ∈ L(Y0 , Y−1 ), B ∈ L(Ξ, Y−1 ), ϕ : R+ × W → 2Ξ is a set-valued map, ψ : Y1 → R+ and f : R+ → Y−1 are given nonlinear maps. 7) shows that this value in general also depends on certain “initial state” ξ0 of ϕ taken from a set E(y0 ) ⊂ Ξ . This situation is typical for hysteresis nonlinearities [Reitmann, 2005].
Dynamics and Control of Hybrid Mechanical Systems (World Scientific Series on Nonlinear Science, Series B) by Gennady Leonov
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