Abstract
We consider the problem of robust model predictive control for linear sampled data dynamical systems subject to state and control constraints and additive and bounded disturbances. We propose a rigid tube model predictive control algorithm utilizing recent and topologically compatible notions for the sampled data forward reach sets as well as robust positively invariant sets. The proposed method inherits almost all desirable features associated with rigid tube model predictive control of discrete-time systems, and, in addition, it ensures robust constraint satisfaction and safety in a continuous-time sense.

Abstract
In a previous study, the authors developed the planning of the water used in the irrigation systems of a given farmland in order to ensure that the field cultivation is in a good state of preservation. In this paper, we introduce a model to minimize the water flowing into a reservoir that supplies different fields with different types of crops. This model is described as an optimal control problem where the water flow from a tap and the water used in the fields are the controls. The trajectories are described as the humidity in the soil and the amount of water in the reservoir. © Springer International Publishing Switzerland 2017.

Abstract
We address sampled–data nonlinear Model Predictive Control (MPC) schemes, in particular we address methods to efficiently and accurately solve the underlying continuous-time optimal control problems (OCP). In nonlinear OCPs, the number of discretization points is a major factor affecting the computational time. Also, the location of these points is a major factor affecting the accuracy of the solutions. We propose the use of an algorithm that iteratively finds the adequate time–mesh to satisfy some pre–defined error estimate on the obtained trajectories. The proposed adaptive time–mesh refinement algorithm provides local mesh resolution considering a time–dependent stopping criterion, enabling an higher accuracy in the initial parts of the receding horizon, which are more relevant to MPC. The results show the advantage of the proposed adaptive mesh strategy, which leads to results obtained approximately as fast as the ones given by a coarse equidistant–spaced mesh and as accurate as the ones given by a fine equidistant–spaced mesh. © Springer International Publishing Switzerland 2017.

Abstract
This chapter proposes a sampled-data model predictive control (MPC) architecture to solve the decentralized cooperative path-following (CPF) problem of multiple unmanned aerial vehicles (UAVs). In the cooperative path-following proposed scenario, which builds on previous work on CPF, multiple vehicles are required to follow pre-specified paths at nominal speed profiles (that may be path dependent) while keeping a desired, possibly time-varying, geometric formation pattern. In the proposed framework, we exploit the potential of optimization-based control strategies with significant advantages on explicitly addressing input and state constraints and on the ability to allow the minimization ofmeaningful cost functions. An example consisting of three fixed wing UAVs that are required to follow a given desired maneuver illustrates the proposed framework.We highlight and discuss some features of the UAVs trajectories. © Springer International Publishing Switzerland 2015.

Abstract
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, itwill be recalled that differential flatness represents a well-suited tool for generating feasible reference trajectory. © Springer International Publishing Switzerland 2015.

Abstract
This chapter concerns a discrete-time sampling state feedback control optimizing framework for dynamic impulsive systems. This class of control systems differs from the conventional ones in that the control space is enlarged to contain measures and, thus, the associated trajectories are merely of bounded variation. In other words, it may well exhibit jumps. We adopt the most recent impulsive control solution concept that pertains to important classes of engineering systems and, in this context, present impulsive control theory results on invariance, stability, and sampled data trajectories having in mind the optimization-based framework that relies on an MPC-like scheme. The stability of the proposed MPC scheme is addressed. © Springer International Publishing Switzerland 2015.