Luís Tiago Paiva

Software for slip-tendency analysis in 3D: A plug-in for Coulomb

Slip-tendency analysis is a valuable tool in fault reactivation evaluation and seismic hazard assessment as it provides a means of quantifying the slip potential on mapped or suspected faults in a known or inferred stress field. We developed an interactive graphic tool to perform slip-tendency analysis. The application is written in MATLAB in the form of plug-ins for COULOMB, a graphic-rich deformation and stress change open-source software. In addition to identifying the faults most prone to reactivation, we compute and plot synthetic focal mechanisms from the direction and sense of likely slip. This allows compatibility between focal mechanisms and geological structures to be verified. Both individual faults and fault networks can be considered in three dimensions. The potential for slip depends on the prevailing stress field, the fault surface orientation and the coefficient of friction. These parameters are given interactively in a Windows environment. The application thus offers an easy-to-use graphical interface with the possibility of fast parameter modification and 3D visualization of the results.

Mesh refinement strategy for optimal control problems

Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform nodes collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. After computing a solution in a coarse mesh, the local error is evaluated, which gives information about the subintervals of time domain where refinement is needed. This procedure is repeated until the local error reaches a user-specified threshold. The technique is applied to solve the car-like vehicle problem aiming minimum consumption. The approach developed in this paper leads to results with greater accuracy and yet with lower overall computational time as compared to using a time meshes having equidistant spacing.

Optimal electric power generation with underwater kite systems

In this article we investigate the problem of generating electricity through an underwater kite power system (UKPS). For this problem, we develop the dynamical model for the UKPS and we formulate an optimal control problem to devise the trajectories and controls of the kite that maximize the total energy produced in a given time interval. This is a highly nonlinear problem for which the optimization is challenging. We also develop a numerical solution scheme for the optimal control problem based on direct methods and on adaptive time-mesh refinement. We report results that show that the problem can be quickly solved with a high level of accuracy when using our adaptive mesh refinement strategy. The results provide a set of output power values for different design choices and confirm that electrical energy that can be produced with such device.

Optimal control of underwater kite power systems

We address the problem of generating electricity through Underwater Kite Power Systems. For this problem, we develop an optimal control problem formulation using a continuous-time model of the kite to devise the trajectories and controls for the kite that maximize the total energy produced in a given time interval. This is an highly nonlinear problem for which the optimization is challenging. We also develop a numerical solution scheme for the optimal control problem based on direct methods and on adaptive time-mesh refinement. We report results that show that the problem can be quickly solved with a high level of accuracy when using our adaptive mesh refinement strategy. The results confirm the values of electrical power that can be produced with such device.

An optimal control approach to reference level tracking in general anesthesia

In this paper the neuromuscular blockade level and the bispectral index level tracking problems by means of automatic control are considered in the context of general anesthesia. These tracking problems are formulated as optimal control problems that are numerically solved using direct methods. The results shown in this paper are preliminary but illustrate a good performance of this strategy when applied to biomedical problems.

Sampled–Data Model Predictive Control Using Adaptive Time–Mesh Refinement Algorithms

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.

Optimization–based control of constrained nonlinear systems with continuous–time models: Adaptive time–grid refinement algorithms

We address optimal control problems for nonlinear systems with pathwise state-constraints. These are challenging non-linear 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, alth...

Reference Tracking of Depth of Anesthesia Using Optimal Control.

Optimal control theory has gained increasing importance in biomedical applications, e.g., in the automatic administration of anesthetics during general anesthesia. In this context, one of the features that needs to be monitored is the depth of anesthesia. This is usually achieved by the joint administration of hypnotics and analgesics. The depth of anesthesia is quantified by the bispectral index that varies between 97.7% and 0%. This index should usually be kept at a reference level between 40% and 60% during surgeries with general anesthesia. In this contribution, we consider an open-loop control strategy to achieve this goal. In order to determine a suitable controller, we formulate a nonlinear optimal control problem and we solve it using direct methods. These methods have become increasingly useful when computing the numerical solution of an optimal control problem. Moreover, they are known to provide a very robust and general approach.