Abstract
In the context of continuous-time control systems, we address the problem of guaranteeing that the constraints imposed along the trajectory are in fact satisfied for all times. The problem is relevant and non-trivial in situations in which a continuous-time internal representation of the system is used with a digital device, such as in sampled-data model-based control, in an optimal control solver, or in sampled-data model predictive control. In this letter, we establish a condition that when verified on a finite set of time instants (using limited computational power) can guarantee that the trajectory constraints are satisfied on an uncountable set of times. The case of constrained optimal control problems is further explored here. We develop an algorithm for the numerical solution of constrained nonlinear optimal control problems that combines a guaranteed constraint satisfaction strategy with an adaptive mesh refinement strategy. © 2017 IEEE.

Abstract
This article addresses the problem of controlling a constrained, continuous-time, nonlinear system through Model Predictive Control (MPC). In particular, we focus on methods to efficiently and accurately solve the underlying optimal control problem (OCP). In the numerical solution of a nonlinear OCP, some form of discretization must be used at some stage. There are, however, benefits in postponing the discretization process and maintain a continuous-time model until a later stage. This is because that way we can exploit additional freedom to select the number and the location of the discretization node points. We propose an adaptive time-mesh refinement (AMR) algorithm that iteratively finds an adequate time-mesh satisfying a pre-defined bound on the local error estimate of the obtained trajectories. The algorithm provides a time-dependent stopping criterion, enabling us to impose higher accuracy in the initial parts of the receding horizon, which are more relevant to MPC. Additionally, we analyze the conditions to guarantee closed-loop stability of the MPC framework using the AMR algorithm. The numerical results show that the proposed AMR strategy can obtain solutions as fast as methods using a coarse equidistant-spaced mesh and, on the other hand, as accurate as methods using a fine equidistant-spaced mesh. Therefore, the OCP can be solved, and the MPC law obtained, faster and/or more accurately than with discrete-time MPC schemes using equidistant-spaced meshes.

Abstract
It is a priority to develop intelligent irrigation systems to save water. Using optimal control formulations and techniques, one can make water consumption follow more closely the hydrological needs of the crop, taking into account current weather conditions. Here, the mathematical model presented by the authors in previous publications is improved. This new model incorporates new features like the soil slope, the possibility to include a percentage of water losses due to runoff, and a percentage of water losses if the soil is on the field capacity. A new and efficient replan strategy is applied, taking into account the data measured from moisture sensors to ensure that the hydric needs of the crop are fulfilled. A new approach to deal with multiple irrigation points is also proposed. It allows redistributing the available water if an irrigation point cannot provide the water needed.

Abstract
An airborne wind energy system (AWES) can harvest stronger wind streams at higher altitudes which are not accessible to conventional wind turbines. The operation of AWES requires a controller for the tethered aircraft/kite module (KM), as well as a controller for the ground station module (GSM). The literature regarding the control of AWES mostly focuses on the trajectory tracking of the KM. However, an advanced control of the GSM is also key to the successful operation of an AWES. In this paper we propose a cascaded control strategy for the GSM of an AWES during the traction or power generation phase. The GSM comprises a winch and a three-phase induction machine (IM), which acts as a generator. In the outer control-loop, an integral sliding mode control (SMC) algorithm is designed to keep the winch velocity at the prescribed level. A detailed stability analysis is also presented for the existence of the SMC for the perturbed winch system. The rotor flux-based field oriented control (RFOC) of the IM constitutes the inner control-loop. Due to the sophisticated RFOC, the decoupled and instantaneous control of torque and rotor flux is made possible using decentralized proportional integral (PI) controllers. The unknown states required to design RFOC are estimated using a discrete time Kalman filter (DKF), which is based on the quasi-linear model of the IM. The designed GSM controller is integrated with an already developed KM, and the AWES is simulated using MATLAB and Simulink. The simulation study shows that the GSM control system exhibits appropriate performance even in the presence of the wind gusts, which account for the external disturbance.

Abstract
For an efficient and reliable operation of an Airborne Wind Energy System, it is widely accepted that the kite should follow a pre-defined optimized path. In this article, we address the problem of designing a trajectory controller so that such path is closely followed. The path-following controllers investigated are based on a well-known nonlinear guidance logic termed L1 and on a proposed modification of it, which we termed L0. We have developed and implemented both L0 and L1 controllers for an AWES. The two controllers have an easy implementation with an explicit expression for the control law based on the cross-track error, on the heading angle relative to the path, and on a single parameter L (L-0 or L-1, depending on each controller) that we are able to tune. The L0 controller has an even easier implementation since the explicit control law can be used without the need to switch controllers. Since the switching of controllers might jeopardize stability, the L-0 controller has an important theoretical advantage in being able to guarantee stability on a larger domain of attraction. The simulation study shows that both nonlinear guidance logic controllers exhibit appropriate performance when the L parameter is adequately tuned, with the L0 controller showing a better performance when measured in terms of the average cross-track error.

Abstract