Ionela Prodan

Enhancements on the Hyperplanes Arrangements in Mixed-Integer Programming Techniques

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.

On the hyperplanes arrangements in mixed-integer techniques

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.

Predictive control for trajectory tracking and decentralized navigation of multi-agent formations

This paper addresses a predictive control strategy for a particular class of multi-agent formations with a time-varying topology. The goal is to guarantee tracking capabilities with respect to a reference trajectory which is pre-specified for an agent designed as the leader. Then, the remaining agents, designed as followers, track the position and orientation of the leader. In real-time, a predictive control strategy enhanced with the potential field methodology is used in order to derive a feedback control action based only on local information within the group of agents. The main concern is that the interconnections between the agents are time-varying, affecting the neighborhood around each agent. The proposed method exhibits effective performance validated through some illustrative examples.

Predictive Control for Tight Group Formation of Multi-Agent Systems*

Abstract This paper addresses the real-time control problem of a group of agents in the presence of non-convex collision avoidance constraints. The goal is to guarantee the convergence towards a tight formation. Convex (polyhedral) regions will be used to define safety regions around each agent. Then, using the dynamics and constraints, an optimization-based control design can be adopted upon an appropriate receding horizon principle. A single optimal control problem is solved based on a prediction of the future evolution of the system and the resulting control law is implemented in a centralized way. At the supervision level, it is shown that the decision about which agents should take on what role in the desired tight formation is equivalent with a classical pairing (or task assignment) problem. An important contribution is the re-evaluation of the pairing at each iteration. Copyright

Flat trajectory generation for way-points relaxations and obstacle avoidance

This paper addresses some alternatives to classical trajectory generation for an autonomous vehicle which needs to pass through a priori given way-points. Using differential flatness for trajectory generation and B-splines for the flat output parametrization, the current study concentrates on constraint relaxations and on obstacle avoidance conditions. The results are validated through simulations over standard UAV dynamics.

Enhancements on the hyperplane arrangements in mixed integer techniques

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.

An optimization-based control approach for reliable microgrid energy management under uncertainties

This paper proposes an optimization-based control approach for microgrid energy management. For exemplification of the approach consider a microgrid system connected to an external grid via a transformer and containing a local consumer, a renewable generator (wind turbine) and a storage facility (battery). The objective of minimizing the costs is achieved through a predictive control framework for scheduling the battery usage in the microgrid system. The proposed control framework takes into account cost values, power consumption, generation profiles as well as functional constraints under uncertainties in the wind speed profile. Simulation results using real numerical data are presented for a reliability test system.

On the tight formation for multi-agent dynamical systems

This paper addresses the real-time control of multiple agents in the presence of disturbances and non-convex collision avoidance constraints. The goal is to guarantee the convergence towards a tight formation. A single optimal control problem is solved based on a prediction of the future evolution of the system and the resulting controller is implemented in a centralized way. At the supervision level, it is shown that the decision about which agents should take on what role in the desired tight formation is equivalent with a classical pairing (or task assignment) problem. Furthermore, the pairing is re-evaluated at each iteration. The proposed method exhibits effective performance validated through some illustrative examples.

Predictive Control for Path-Following. From Trajectory Generation to the Parametrization of the Discrete Tracking Sequences

This chapter discusses a series of developments on predictive control for path following via a priori generated trajectory for autonomous aerial vehicles. The strategy partitions itself into offline and runtime procedures with the assumed goal of moving the computationally expensive part into the offline phase and of leaving only tracking decisions to the runtime. First, it will be recalled that differential flatness represents a well-suited tool for generating feasible reference trajectory. Next, an optimization-based control problem which minimizes the tracking error for the nonholonomic system is formulated and further enhanced via path following mechanisms. Finally, possible changes of the selection of sampling times along the path and their impact on the predictive control formulation will be discussed in detail.

A characterization of the relative positioning of mobile agents for full sensorial coverage in an augmented space with obstacles

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).