Optimal oscillatory time for a class of second order nonlinear dissipative ODE

finite time adaptive optimal integral sliding mode control for a class of uncertain second order nonlinear systems with input nonlinearity

in this paper, a new robust controller based on geometric homogeneity and adaptive integral sliding mode is proposed for a class of second order systems. the upper bound of the system disturbances is not required. fully unknown parameters have been considered in the described model and its finite–time convergence to zero equilibrium point is proved. moreover, the controller is developed in the ...

Sharp decay estimates of the solutions to a class of nonlinear second order ODE

We establish the rate of decay to 0 and we study the oscillation properties of solutions to the scalar second order ODE : u′′ + c|u′|αu′ + |u|u = 0 where c, α, β are positive constants. Various extensions (forced equation, system) are considered.

Optimal energy decay rate for a class of weakly dissipative second-order systems with memory

In this paper we study the asymptotic behavior of a class of linear dissipative integral differential equations utt(t)+Au(t)− ∫ ∞ 0 g(s) A u(t−s)ds = 0.We show that the solution decays and the decay rate is optimal. © 2010 Elsevier Ltd. All rights reserved.

Time optimal control of a second order nonlinear plant

Fuzzy time-optimal controller (FTOC) for second order nonlinear systems.

The motivation behind this paper is to seek alternative techniques to achieve a near optimal controller for non-linear systems without solving the analytical problem. In classical optimal control systems, the system states and optimization co-state parameters generate a two-point boundary value problem (TPBVP) using Pontryagin's minimum principle (PMP). The paper contributes a new fuzzy time-op...