The finite-horizon optimal control problem with input constraints consists in controlling the state of a dynamical system over a finite time interval (possibly unknown) minimizing a cost functional, while satisfying hard constraints on the input. For linear systems the solution of the problem often relies upon the use of bang-bang control signals. For nonlinear systems the “shape” of the optima...

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...

This paper addresses the problem of designing jerk limited timeoptimal control profiles for rest-to-rest maneuvers of flexible structures. The variation of the structure of the jerk profile as a function of the permissible jerk is studied. An optimal control problem is formulated which includes constraints to cancel the poles corresponding to the rigid body and flexible modes of the system and ...

We consider the optimal control of feedback linearizable dynamic systems subject to mixed state and control constraints. The optimal controller is allowed to be discontinuous including bang-bang control. Although the nonlinear system is assumed to be feedback linearizable, in general, the optimal control does not linearize the dynamics. The continuous optimal control problem is discretized usin...

The task of decoupling, i.e., removing unwanted internal couplings of a quantum system and its couplings to an environment, plays an important role in quantum control theory. There are many efficient decoupling schemes based on combinatorial concepts such as orthogonal arrays, difference schemes, and Hadamard matrices. So far these combinatorial decoupling schemes have relied on the ability to ...

In this paper, his only venture into control theory, Levinson solves the following basic problem of fundamental importance in the theory of linear control systems. Use IR m to denote real m-dimensional Euclidean space, thought of as a space of column vectors. Let P be a compact convex polyhedron in IR m , and let the set of vertices of P be denoted by V : Let a; b] be a given compact subinterva...

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...

The authors apply their recent work on the Lyapunov theorem in locally convex Hausdorff spaces to the bang-bang principle for control systems in infinite dimensions. They show that the bang-bang principle holds for every integrably bounded, measurable, weakly compact convex-valued multifunction if and only if the underlying measure space is saturated. They also demonstrate the equivalence of th...