## Invited Session Tue.2.H 2035

#### Tuesday, 13:15 - 14:45 h, Room: H 2035

**Cluster 24: Variational analysis** [...]

### Control and optimization of impulsive systems I

**Chair: Aram V. Arutyunov and Fernando Lobo Pereira**

**Tuesday, 13:15 - 13:40 h, Room: H 2035, Talk 1**

**Dmitry Karamzin**

Existence theorems and Pontryagin's Maximum Principle for impulsive control problems

**Coauthors: Aram V. Arutyunov, Fernando L. Pereira**

**Abstract:**

This report addresses existence theorems and Pontryagin's Maximum Principle for constrained impulsive control problems with a new concept of impulsive control. This concept enables extra controls (conventional bounded controls) which act on the discontinues of the impulsive system. Such type of impulsive controls can be encountered in different engineering applications in which, for example, it might be necessary to take into account rapid variations in mass distribution of a mechanical system during the short time when the impulse is being applied. There are, of course, many other applications. We provide a detailed example showing how these controls could be useful.

**Tuesday, 13:45 - 14:10 h, Room: H 2035, Talk 2**

**Geraldo Nunes Silva**

Optimal impulsive control problems under uncertainty

**Coauthor: Valeriano A. Oliveira**

**Abstract:**

This work provides an approach to treat optimal impulsive control problems with uncertain parameters and provide necessary conditions in the form of a maximum principle. The uncertain parameter is a vector in the objetive function and is chosen from a set *A* which is taken to be a compact metric space.

The necessary conditions obtained here is a generalization of the minimax maximum principle derived earlier for non impulsive optimal control problems [Vinter04].

**Tuesday, 14:15 - 14:40 h, Room: H 2035, Talk 3**

**Valeriano Antunes de Oliveira**

An Invexity Type Condition on Impulsive Optimal Control Systems

**Coauthor: Geraldo Silva Silva**

**Abstract:**

It is well-known in optimal control theory that the maximum principle furnishes necessary optimality conditions for an admissible process to be an optimal one. It is also well-known that if a process satisfies the maximum principle in a problem with convex data, the maximum principle turns to be likewise a sufficient condition. We here define an invexity type condition for impulsive optimal control problems. We then show that this is a sufficient optimality condition. Our definition was motivated by the one given by [Martin85], where a generalized invexity notion, called KT-invexity is introduced for mathematical programming problems. Martin took into account the KT conditions when he designed the KT-invexity. In this work we do the same, but with the Maximum Principle for optimal control problems in the impulsive setting.

V.A. de Oliveira thanks the financial support from FAPESP - Grant 2011/01977-2