A gradient algorithm for solution of the optimal control problem for hybrid switching systems

In this article, an algorithm is presented for solving the optimal control problem for the general form of a hybrid switching system. The cost function comprises terminal, running and switching costs. The controlled system is an autonomous hybrid switching system with jumps either at some switching times or some time varying switching manifolds. The proposed algorithm is an extension of the first-order gradient method for the conventional optimal control problem. The algorithm requires a low computational effort. The system's dynamical equations together with a set of algebraic equations are solved at each iteration in order to find the descent direction. The convergence of algorithm is proved and examples are provided to demonstrate the efficiency of the algorithm for different types of hybrid switching system optimal control problems.     

C1侧块骨折Magerl技术内固定的数字化模拟及应用

目的 探讨计算机软件应用于C1侧块骨折三维重建、复位以及数字化模拟Magerl技术内固定的方法及临床意义,以指导临床应用.方法 将1具颈椎标本制作成C1侧块骨折类型,进行高速CT薄层扫描,在Mimics中对C1侧块骨折模型进行重建、复位,以Solidworks进行螺钉的设计,并在骨折复位三维模型上进行虚拟Magerl技术内固定.结果 对骨折进行了三维重建、复位,根据三维模型测量数据,完成虚拟螺钉内固定,并成功指导临床手术21例.结论 应用Mimics及Solidworks可在个人电脑上设计出C1侧块骨折数字化螺钉固定,对临床手术有很好的参考意义.     

A new analytical method for solving a class of nonlinear optimal control problems

In this paper, we introduce a new analytic technique for a class of nonlinear optimal control problems and present a theorem of convergence of the method. In this scheme, first, the original optimal control problem is transformed into a nonlinear two‐point boundary value problem via the Pontryagin's maximum principle, and then, we apply a new method for solving two‐point boundary value problem. The proposed modification is made by introducing He's polynomials in the correction functional. The suggested algorithm is quite efficient and is practically well suited for using in these problems. The proposed iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions. Copyright © 2013 John Wiley & Sons, Ltd.     

A novel approach for the numerical investigation of optimal control problems containing multiple delays

This paper deals with the numerical solution of optimal control problems with multiple delays in both state and control variables. A direct approach based on a hybrid of block‐pulse functions and Lagrange interpolating polynomials is used to convert the original problem into a mathematical programming one. The resulting optimization problem is then solved numerically by the Lagrange multipliers method. The operational matrix of delay for the presented framework is derived. This matrix plays an imperative role to transfer information between 2 consecutive switching points. Furthermore, 2 upper bounds on the error with respect to the L²‐norm and infinity norm are established. Several optimal control problems containing multiple delays are carried out to illustrate the various aspects of the proposed approach. The simulation results are compared with either analytical or numerical solutions available in the literature.     

A discretization method for the numerical solution of Dieudonné–Rashevsky type problems with application to edge detection within noisy image data

The present paper is concerned with the numerical solution of multidimensional control problems of Dieudonné–Rashevsky type by discretization methods and large‐scale optimization techniques. We prove first a convergence theorem wherein the difference of the minimal value and the objective values along a minimizing sequence is estimated by the mesh size of the underlying triangulations. Then we apply the proposed method to the problem of edge detection within raw image data. Instead of using an Ambrosio–Tortorelli type energy functional, we reformulate the problem as a multidimensional control problem. The edge detector can be built immediately from the control variables. The quality of our numerical results competes well with those obtained by applying variational techniques. Copyright © 2011 John Wiley & Sons, Ltd.     

A novel continuous genetic algorithm for the solution of optimal control problems

In this paper, the Continuous Genetic Algorithm (CGA), previously developed by the principal author, is applied for the solution of optimal control problems. The optimal control problem is formulated as an optimization problem by the direct minimization of the performance index subject to constraints, and is then solved using CGA. In general, CGA uses smooth operators and avoids sharp jumps in the parameter values. This novel approach possesses two main advantages when compared to other existing direct and indirect methods that either suffer from low accuracy or lack of robustness. First, our method can be applied to optimal control problems without any limitation on the nature of the problem, the number of control signals, and the number of mesh points. Second, high accuracy can be achieved where the performance index is globally minimized while satisfying the constraints. The applicability and efficiency of the proposed novel algorithm for the solution of different optimal control problems is investigated. Copyright © 2010 John Wiley & Sons, Ltd.     

A numerical method for computing optimal controls in feedback and digital forms and its application to the blowing‐venting control system of manned submarines

On the basis of the classical variational reformulation of optimal control problems, we introduce a numerical scheme for solving those problems where the goal is the computation of optimal controls in feedback and digital forms defined on a discrete time mesh. The algorithm reduces the computation of such controls to solving a suitable nonlinear mathematical programming problem where the unknowns are the controls and slope of the state variable of the original problem. The motivation for this study comes from the real‐world engineering problem which consists of maneuvering a manned submarine by using the blowing‐venting control system of the ballast tanks of the vehicle. After checking the proposed algorithm in an academic example, we apply it to the maneuvering problem of submarines whose mathematical model includes a state law which is composed of a system of twenty‐four nonlinear ordinary differential equations. Numerical results illustrate the performance of the numerical scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

A new method of using gas exchange measurements for the noninvasive determination of cardiac output: clinical experiences in adults following cardiac surgery

New mathematical algorithms have been applied to a computer controlled closed breathing circuit system for non-invasive measurement of cardiac output (COniv). This system has been described in an animal study. Forty patients were studied 5 and 18 hours after cardiac surgery using the thermodilution technique as the reference (COtd). The variables entered into the algorithms for COniv were oxygen uptake, carbon dioxide elimination, end-tidal carbon dioxide partial pressure, tidal volume and arterial oxygen saturation. Mixed venous carbon dioxide partial pressure was obtained from an automatically implemented short rebreathing manoeuvre. Pulmonary perfusion was calculated by a modified Fick equation for carbon dioxide and the shunt flow added to obtain COniv. During mechanical ventilation, there was a good agreement between COtd and COniv (r=0.8). The bias was -0.14 1/min and the precision was 0.77 1/min. The reproducibility of COniv was 0.03 1/min and for COtd -0.03 1/min with a standard deviation of the difference being 0.35 1/min for COniv and 0.31 1/min for COtd. In awake, but sedated extubated patients, the method proved unsatisfactory on account of uneven tidal volumes and difficulties with leakage around the mouth piece. We conclude that this new technique provides reliable and reproducible measures of cardiac output in sedated, ventilated patients.