The paper describes a continuous second-variation algorithm to solve optimal control problems where the control is defined on a closed set. A second order expansion of a Lagrangian provides linear updates of the control to construct a locally feedback optimal control of the problem. Since the process involves a backward and a forward stage, which require storing trajectories, a method has been ...

Discontinuous dynamical systems arise in a large number of applications. In optimal control problems, open-loop bang-bang controllers switch discontinuously between extremum values of the bounded inputs to generate minimum-time trajectories from one state to another. Thermostats implement closed-loop bang-bang controllers to regulate room temperature. In nonsmooth mechanics, the evolution of ri...

This paper is concerned with the problem of finding a time-optimal velocity profile along the predefined path for static formations of mobile robots in order to traverse the path in shortest time and to satisfy, for each mobile robot in the formation, velocity, acceleration, tip over and wheel slip prevention constraints. Time-optimal velocity planning is achieved using so called bang-bang cont...

The Big Bang-Big Crunch (BB–BC) method is a relatively new meta-heuristic algorithm which inspired by one of the theories of the evolution of universe. In the BB–BC optimization algorithm, firstly random points are produced in the Big Bang phase then these points are shrunk to a single representative point via a center of mass or minimal cost approach in the Big Crunch phase. In this paper, the...

We consider Euler discretizations to a class of linear-quadratic optimal control problems. Assuming that the discrete controls are of bang-bang type and define switching functions with a uniform structure independent of the discretization we show, that the discrete controls converge to a bang-bang control, which is a solution of the original problem.

Second order sufficient optimality conditions for bang-bang control problems in a very general form have been obtained in [15, 21, 13, 12, 1]. These conditions require the positive definiteness (coercivity) of an associated quadratic form on the finite-dimensional critical cone. In the present paper, we investigate similar conditions for optimal control problems with a control variable having t...

A large collection of financial contracts offering guaranteed minimum benefits are often posed as control prob4 lems, in which at any point in the solution domain, a control is able to take any one of an uncountable number of 5 values from the admissible set. Often, such contracts specify that the holder exerts control at a finite number of 6 deterministic times. The existence of an optimal ban...

This paper presents experimental results for time-optimal control of robotic manipulators along specified paths. The implementation of time-optimal control represents several unique problems: (1) the control is generally discontinuous (bang-bang), (2) actuator dynamics are usually ignored in order to reduce the system order, and (3) the optimal control leaves no control authority to compensate ...

A constrained version of the Big Bang-Big Crunch algorithm for the efficient solution of the optimal reservoir operation problems is proposed in this paper. Big Bang-Big Crunch (BB-BC) algorithm is a new meta-heuristic population-based algorithm that relies on one of the theories of the evolution of universe namely, the Big Bang and Big Crunch theory. An improved formulation of the algorithm na...