In this paper, a new numerical method is presented for solving the optimal control problems of Bang-Bang type with free or fixed terminal time. The method is based on Bezier polynomials which are presented in any interval as $[t_0,t_f]$. The problems are reduced to a constrained problems which can be solved by using Lagrangian method. The constraints of these problems are terminal state and con...

Time-optimal controls for 2-link robots are often of bang-bang type. Many algorithms to solve timeoptimal robot control problems a-priori assume the optimal control to be bang-bang. Industrial robot,s very often have 5 or 6 links and then the associated time-optimal controls are usually singular. This paper presents a new algorithm that enables computation of both bang-bang and singular time-op...

The problem of controlling a perturbed open loop system so as to keep its performance errors within bounds is considered. The objective is to maximize the time during which performance errors remain below a prescribed ceiling, while the controlled system’s parameters are within a specified neighborhood of their nominal values. It is shown that there is an optimal open-loop controller that achie...

The time-optimal control of a distributed parameter system is derived in closed form. The class of systems studied in this work is distributed parameter systems whose dynamics are governed by the wave equation. A frequency domain approach is utilized to arrive at the time-optimal solution that is bang-off-bang. To corroborate the optimally of the control profile derived for the distributed para...

We study bang–bang control problems that depend on a parameter p. For a fixed nominal parameter p0, it is assumed that the bang-bang control has finitely many switching points and satisfies second order sufficient conditions (SSC). SSC are formulated and checked in terms of an associated finitedimensional optimization problem w.r.t. the switching points and the free final time. We show that the...

The minimum-time problem frequently arises in the design of control for actuators, and is usually solved assuming to know the correct model of the system. In industrially important cases, however, important parts of the dynamics, like friction forces or disturbances by exosystems, are hardly known or even unknown. Against this background, this paper presents an iterative approach to achieve the...