Bang-bang control problems subject to a state inequality constraint are considered. It is shown that the control problem induces an optimization problem, where the optimization vector assembles the switching and junction times for bangbang and boundary arcs. Second order sufficient conditions (SSC) for the stateconstrained control problem are given which require that SSC for the induced optimiz...

Here, we assume that Ω is a bounded domain in R, 1 ≤ n ≤ 3, with a Lipschitz boundary Γ, Q = Ω × (0, T ), Σ = Γ × (0, T ), and y0 ∈ L∞(Ω). BV (0, T ) denotes the space of bounded variation functions defined in (0, T ), with 0 < T < ∞ given. The controllers in (P) are supposed to be separable functions with respect to fixed spatial shape functions gj and free temporal amplitudes uj . The specifi...

The problem of optimal feed-rate planning along a curved tool path for 3-axis CNC machines with a jerk limit for each axis is addressed. We prove that the optimal feed-rate planning must use “Bang-Bang” control, that is, at least one of the axes reaches its jerk bound throughout the motion. As a consequence, the optimal parametric velocity can be expressed as a piecewise analytic function of th...

We present a stability criterion for switched nonlinear systems which involves Lie brackets of the individual vector fields but does not require that these vector fields commute. A special case of the main result says that a switched system generated by a pair of globally asymptotically stable nonlinear vector fields whose third-order Lie brackets vanish is globally uniformly asymptotically sta...

Considering a positive portfolio diffusion X with negative drift, we investigate optimal stopping problems of the form inf θ E f  Xθ sup s∈[0,τ ] Xs   , where f is a non-increasing function, τ is the next random time where the portfolio X crosses zero and θ is any stopping time smaller than τ . Hereby, our motivation is the obtention of an optimal selling strategy minimizing the relativ...