Time-optimal control of a certain second-order nonoscillatory system

Time optimal control of a second order nonlinear plant

Second Order Sliding Mode Control With Finite Time Convergence

In this paper, a new smooth second order sliding mode control is proposed. This algorithm is a modified form of Super Twisting algorithm. The Super Twisting guarantees the asymptotic stability, but the finite time stability of proposed method is proved with introducing a new particular Lyapunov function. The Proposed algorithm which is able to control nonlinear systems with matched structured u...

Linear Perturbations of a Nonoscillatory Second Order Differential Equation Ii

Let y1 and y2 be principal and nonprincipal solutions of the nonoscillatory differential equation (r(t)y′)′ + f(t)y = 0. In an earlier paper we showed that if ∫∞(f − g)y1y2 dt converges (perhaps conditionally), and a related improper integral converges absolutely and sufficently rapidly, then the differential equation (r(t)x′)′ + g(t)x = 0 has solutions x1 and x2 that behave asymptotically like...

Existence of Nonoscillatory Bounded Solutions for a System of Second-order Nonlinear Neutral Delay Differential Equations

A system of second-order nonlinear neutral delay differential equations ( r1(t) ( x1(t) + P1(t)x1(t− τ1) )′)′ = F1 ( t, x2(t− σ1), x2(t− σ2) ) , ( r2(t) ( x2(t) + P2(t)x2(t− τ2) )′)′ = F2 ( t, x1(t− σ1), x1(t− σ2) ) , where τi > 0, σ1, σ2 ≥ 0, ri ∈ C([t0,+∞),R), Pi(t) ∈ C([t0,+∞),R), Fi ∈ C([t0,+∞)× R2,R), i = 1, 2 is studied in this paper, and some sufficient conditions for existence of nonosc...

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 ...