Abstract
We propose a mathematical model to study the water usage for the irrigation of given farmland to guarantee that the field crop is kept in a good state of preservation. This problem is formulated as an optimal control problem. The lack of analytic solution leads us to turn to numerical methods to solve the problem numerically. We then apply necessary conditions of optimality to validate the numerical solution. To deal with the high degree of unpredictability of water inflow due to weather, we further propose a replan strategy and we implement it.

Abstract
The present paper addresses the path following problem of nonholonomic systems by considering a predictive control-based framework. The particularity of the present study resides in the use of differential flatness formalism for a reference trajectory generation. Furthermore, having the reference trajectory available in a parameterized form, an optimization-based problem which minimizes the tracking error for the nonholonomic system can be formulated and further enhanced via path following. The proposed method exhibits effective performance validated through simulations for the control of autonomous aerial vehicles.

Abstract
In this work, we address the daily irrigation problem of minimizing water consumption. This problem has the particularity that the dynamics is described via field capacity modes which can model the fact that the soil has different dynamics when it is saturated or not. An analysis is carried out to ensure that the normal Maximum Principle for nonsoomoth problems can be applied to this problem, and, it is observed that the numerical solution fulfills the necessary conditions of optimality.

Abstract
This paper introduces a novel control design method for stabilization of input constrained non-holonomic wheeled systems. Important classes of mobile robots can be controlled by the proposed method, namely differential drive robots and car like systems where certain constraints are imposed on the system inputs and states. The proposed control is based on the recently developed Constrained Directions Method (CDM). CDM guarantees stabilization and preservation of the constraints on the inputs and provides control over the transient performance of robot. Moreover, it has been shown that CDM has a built-in preventive measure against wheel slip due to the inverse proportionality of robot forward velocity to the curvature of the path. Simulation results are used to show the validity of the proposed stabilizing control and to compare the performance of CDM with several well-known methods from the literature. © 2017 American Automatic Control Council (AACC).

Abstract
We address optimal control problems for nonlinear systems with pathwise state-constraints. These are challenging nonlinear problems for which the number of discretization points is a major factor determining the computational time. Also, the location of these points has a major impact in the accuracy of the solutions. We propose an algorithm that iteratively finds an adequate time-grid to satisfy some predefined error estimate on the obtained trajectories, which is guided by information on the adjoint multipliers. The obtained results show a highly favorable comparison against the traditional equidistant spaced time grid methods, including the ones using discrete time models. This way, continuous time plant models can be directly used. The discretization procedure can be automated and there is no need to select a priori the adequate time step. Even if the optimization procedure is forced to stop in an early stage, as might be the case in real time problems, we can still obtain a meaningful solution, although it might be a less accurate one. The extension of the procedure to a Model Predictive Control (MPC) context is proposed here. By defining a time dependent accuracy threshold, we can generate solutions that are more accurate in the initial parts of the receding horizon, which are the most relevant for MPC.

Abstract
This article addresses the problem of optimizing electrical power generation using kite power systems (KPSs). KPSs are airborne wind energy systems that aim to harvest the power of strong and steady high-altitude winds. With the aim of maximizing the total energy produced in a given time interval, we numerically solve an optimal control problem and thereby obtain trajectories and controls for kites. Efficiently solving these optimal control problems is crucial when the results are used in real-time control schemes, such as model predictive control. For this highly nonlinear problem, we derive continuous-time models-in 2D and 3D-and implement an adaptive time-mesh refinement algorithm. By solving the optimal control problem with such an adaptive refinement strategy, we generate a block-structured adapted mesh which gives results as accurate as those computed using fine mesh, yet with much less computing effort and high savings in memory and computing time.