Some recent developments in necessary conditions of optimality for impulsive control problems

Necessary conditions of optimality for impulsive control systems whose dynamics are defined by differential inclusions and whose state trajectory is subject to state constraints endpoint constraints are discussed. After discussing the motivation of this general control paradigm in the context of space systems, a natural concept of robust solution is introduced and some of his properties presented. Besides an independent interest for the construction of schemes approximating impulsive con- trol processes by conventional ones, it is shown in a brief outline of the proof how these properties play an important role in the derivation of the considered optimal- ity conditions. Finally, the relation between these conditions and the ones recently developed in the context of the considered solution concept

An indirect numerical method for a time-optimal state-constrained control problem in a steady two-dimensional fluid flow

This article concerns the problem of computing solutions to state-constrained optimal control problems whose trajectory is affected by a flow field. This general mathematical framework is particularly pertinent to the requirements underlying the control of Autonomous Underwater Vehicles in realistic scenarii. The key contribution consists in devising a computational indirect method which becomes effective in the numerical computation of extremals to optimal control problems with state constraints by using the maximum principle in Gamkrelidze's form in which the measure Lagrange multiplier is ensured to be continuous. The specific problem of time-optimal control of an Autonomous Underwater Vehicle in a bounded space set, subject to the effect of a flow field and with bounded actuation, is used to illustrate the proposed approach. The corresponding numerical results are presented and discussed

Attainable-Set Model Predictive Control for AUV Formation Control

In this article, we focus on the motion control of an AUV formation in order to track a given path along which data will be gathered. A computationally efficient architecture enables the conciliation of onboard resources optimization with state feedback control - to deal with the typical a priori high uncertainty - while managing the formation with a low computational and power budgets. To meet these very strict requirements, a novel Model Predictive Control (MPC) scheme is used. The key idea is to pre-compute data which is known to be time invariant for a number of likely scenarios and store it on-board in appropriate look-up tables. Then, as the mission proceeds, sampled motion sensor data, and communicated data is processed in each one of the AUVs and fed to the onboard proposed MPC scheme implemented with the dynamics of the formation that, by combining with information extracted from the pertinent on-board look-up tables, determine the best control action with inexpensive computational operations

Optimality conditions for asymptotically stable control processes

In this article, we present and discuss the infinite horizon optimal controlproblem subject to stability constraints. First, we consider optimality conditionsof the Hamilton-Jacobi-Bellman type, and present a method to define a feedbackcontrol strategy. Then, we address necessary conditions of optimality in the form ofa maximum principle. These are derived from an auxiliary optimal control problemwith mixed constraints

Dynamic optimization in the coordination and control of autonomous underwater vehicles

The coordination and control problems arising in team composition and tasking of autonomous underwater vehicles are discussed in the framework of dynamic optimization. Team composition and tasking are specified in terms of sets and relations among the elements of these sets. Results from dynamic optimization and non-smooth analysis are used to show that these coordination and control problems can be phrased in terms of concepts such as invariance, solvability, monotonicity, and switchings among value functions