Publications

2013
M. - I. Strutu, Stoican, F., Prodan, I., Popescu, D., and Olaru, S., “A characterization of the relative positioning of mobile agents for full sensorial coverage in an augmented space with obstacles”, in Proceedings of the 21st Mediterranean Conference on Control and Automation, Platania-Chania, Crete, Grecee, 2013, p. 936-941.Abstract
This paper addresses the coverage problem for a collection of agents and fixed obstacles (e.g., the “gallery” and the “patrolling” problems). A collection of sufficient conditions over the positions of the agents are provided such that whenever these are verified there is no “blind” region in the feasible space. These conditions are expressed by making use of hyperplane arrangements which lead to a mixed-integer formulation. Practical applications regarding the coverage problem inside an augmented space with obstacles validate these concepts and provide an efficient implementation (in terms of computing power).
F. Stoican, Prodan, I., and Olaru, S., “Hyperplane Arrangements in Mixed-Integer Programming Techniques. Collision avoidance application with Zonotopic Sets”, in Proceedings of the 2013 European Control Conference, Zurich, Switzerland, 2013, p. 3155-3160.Abstract
The current paper addresses the problem of minimizing the computational complexity of optimization problems with non-convex and possibly non-connected feasible region of polyhedral type. Using hyperplane arrangements and Mixed-Integer Programming we provide an efficient description of the feasible region in the solution space. Moreover, we exploit the geometric properties of the hyperplane arrangements and adapt this description in order to provide an efficient solution of the mixed-integer optimization problem. Furthermore, a zonotopic representation of the sets appearing in the problem is considered. The advantages of this representation are highlighted and exploited through proof of concepts illustrations as well as simulation results.
Mixed-Integer Programming Techniques in Distributed MPC Problems
I. Prodan, Stoican, F., Olaru, S., Stoica, C. N., and Niculescu, S. I., “Mixed-Integer Programming Techniques in Distributed MPC Problems”, in Distributed Model Predictive Control Made Easy, J. M. Maestre and Negenborn, R. R. New York: Springer, 2013, p. 273-288. Online infoAbstract
This chapter proposes a distributed approach for the resolution of a multiagent problem under collision and obstacle avoidance conditions. Using hyperplane arrangements and mixed integer programming, we provide an efficient description of the feasible region verifying the avoidance constraints. We exploit geometric properties of hyperplane arrangements and adapt this description to the distributed scheme in order to provide an efficient Model Predictive Control (MPC) solution. Furthermore,we prove constraint validation for a hierarchical ordering of the agents.
2012
I. Prodan, Stoican, F., Olaru, S., and Niculescu, S. I., “Enhancements on the hyperplanes arrangements in mixed integer techniques”, Journal of Optimization Theory and Applications, vol. 154, no. 2, p. 549-572, 2012.Abstract
This paper is concerned with improvements in constraints handling for mixed-integer optimization problems. The novel element is the reduction of the number of binary variables used for expressing the complement of a convex (polytopic) region. As a generalization, the problem of representing the complement of a possibly not connected union of such convex sets is detailed. In order to illustrate the benefits of the proposed improvements, a typical control application, the control of multiagent systems using receding horizon optimization techniques, is considered.
2011
F. Stoican, Prodan, I., and Olaru, S., “On the hyperplanes arrangements in mixed-integer techniques”, in Proceedings of the 30th American Control Conference, San Francisco, California, USA, 2011, p. 1898–1903.Abstract
This paper is concerned with the improved constraints handling in mixed-integer optimization problems. The novel element is the reduction of the number of binary variables used for expressing the complement of a convex (polytopic) region. As a generalization, the problem of representing the complement of a possibly non-connected union of such convex sets is detailed. In order to illustrate the benefits of the proposed improvements, a practical implementation, the problem of obstacle avoidance using receding horizon optimization techniques is considered.
F. Stoican, Prodan, I., and Olaru, S., “Enhancements on the hyperplane arrangements in mixed integer techniques”, in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, Florida, USA, 2011, p. 3986–3991.Abstract
The current paper addresses the problem of optimizing a cost function over a non-convex and possibly non-connected feasible region. A classical approach for solving this type of optimization problem is based on Mixed integer technique. The exponential complexity as a function of the number of binary variables used in the problem formulation highlights the importance of reducing them. Previous work which minimize the number of binary variables is revisited and enhanced. Practical limitations of the procedure are discussed and a typical control application, the control of Multi-Agent Systems is exemplified.