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• The fuel-optimal control problem is formulated as a constrained nonlinear system optimal control problem. • A novel piecewise state linear feedback controller is introduced. • A quadratic regularization approach is developed for solving the optimal control problem. • Convergence results indicate that the proposed algorithm is convergent. • Numerical results show that the proposed method is effective. This paper considers a fuel-optimal control problem for soft lunar landing. Firstly, the fuel-optimal control problem is formulated as an optimal control problem of constrained nonlinear systems with a novel piecewise state linear feedback controller, which can be transformed into an optimal control problem of switched systems. However, it is difficult to solve this fuel-optimal control problem analytically by using conventional optimization techniques due to its nonlinear nature and the existence of the continuous-time inequality constraint. Next, to obtain the numerical solution of the fuel-optimal control problem, a numerical computation method is developed by using a quadratic regularization approach with a cubic sufficient-descent condition. Convergence results indicate that the proposed algorithm is convergent. Finally, a numerical experiment shows that the proposed algorithm is more effective than the existing method. [ABSTRACT FROM AUTHOR]

In the paper, we consider the bioprocess system optimal control problem. Generally speaking, it is very difficult to solve this problem analytically. To obtain the numerical solution, the problem is transformed into a parameter optimization problem with some variable bounds, which can be efficiently solved using any conventional optimization algorithms, e.g. the improved Broyden-Fletcher-Goldfarb-Shanno algorithm. However, in spite of the improved Broyden-Fletcher-Goldfarb-Shanno algorithm is very efficient for local search, the solution obtained is usually a local extremum for non-convex optimal control problems. In order to escape from the local extremum, we develop a novel stochastic search method. By performing a large amount of numerical experiments, we find that the novel stochastic search method is excellent in exploration, while bad in exploitation. In order to improve the exploitation, we propose a hybrid numerical optimization algorithm to solve the problem based on the novel stochastic search method and the improved Broyden-Fletcher-Goldfarb-Shanno algorithm. Convergence results indicate that any global optimal solution of the approximate problem is also a global optimal solution of the original problem. Finally, two bioprocess system optimal control problems illustrate that the hybrid numerical optimization algorithm proposed by us is low time-consuming and obtains a better cost function value than the existing approaches. [ABSTRACT FROM AUTHOR]

In this paper, we consider an optimal control problem of switched systems with a continuous-time inequality constraint. Because of the complexity of this constraint, it is difficult to solve this problem by standard optimization techniques. To overcome this difficulty, the problem is divided into a bi-level optimization problem involving a combination of a continuous-time optimal control problem and a discrete optimization problem. Then, a modified Broyden-Fletcher-Goldfarb-Shanno algorithm and a discrete filled function method is first proposed to solve this bi-level optimization problem. Finally, a numerical example is presented to illustrate the efficiency of our method. [ABSTRACT FROM PUBLISHER]

Abstract: This paper considers an optimal sensor scheduling problem in continuous time. In order to make the model more close to the practical problems, suppose that the following conditions are satisfied: only one sensor may be active at any one time; an admissible sensor schedule is a piecewise constant function with a finite number of switches; and each sensor either doesn’t operate or operates for a minimum non-negligible amount of time. However, the switching times are unknown, and the feasible region isn’t connected. Thus, it’s difficult to solve the problem by conventional optimization techniques. To overcome this difficulty, by combining a binary relaxation, a time-scaling transformation and an exact penalty function, an algorithm is developed for solving this problem. Numerical results show that the algorithm is effective. [Copyright &y& Elsevier]

This paper investigates the control synthesis problem for discrete-time switched linear systems with input saturation. Based on minimal dwell time approach, state feedback controller and dynamic output feedback controller are respectively designed in terms of LMIs. The corresponding optimization problems are formulated to obtain a bigger attractive region. Compared with previous results, our proposed results can recover part of attractive region. Finally, numerical example is presented to illustrate the effectiveness and value of our obtained results. [ABSTRACT FROM AUTHOR]

This paper considers an optimal control problem of switched dynamical systems with control input and system state constraints. Unlike in traditional switched dynamical systems, the switching times cannot be specified directly and they are governed by a state-dependent switching condition. Thus, the existing methods cannot be directly used to solve this problem. To overcome this difficulty, the switching conditions are transformed into a continuous-time inequality constraint by introducing an integer constraint. Further, the original optimal control problem is approximated by using a sequence of constrained non-convex nonlinear parameter optimization problems by using a relaxation method, a control vector parameterization technique, and a time-scaling transformation. Following that, a penalty function-based intelligent optimization algorithm is proposed for obtaining a global optimal solution based on a more effective penalty function method and a more effective intelligent optimization algorithm. The convergence results show that the proposed method is globally convergent. Numerical simulation results show that the proposed method is lower time-consuming, has faster convergence speed, can obtain a better objective function value than the existing typical algorithms, and can achieve a stable and robust performance when considering the small perturbations in constraint conditions or the small perturbations of the model parameters. • The switching times cannot be specified directly and they are governed by a state-dependent switching condition. • The switching conditions are transformed into a continuous-time inequality constraint by introducing an integer constraint. • A penalty function-based intelligent optimization algorithm is developed for solving this optimal control problem. • The convergence results show that this algorithm is globally convergent. • A drug therapy problem is provided to illustrate the effectiveness of the method developed by this paper. [ABSTRACT FROM AUTHOR]

Highlights • A novel piecewise state feedback controller is introduced. • The chemical process optimal control problem is formulated as an optimal control problem of switched dynamical systems. • A gradient-based parallel optimization algorithm is developed for solving the optimal control. • Convergence results indicate that the gradient-based parallel optimization algorithm is global convergent. • Three chemical process optimal control problems are given to illustrate the effectiveness of the proposed algorithm. Abstract This paper considers an optimal control problem of chemical processes with a novel piecewise state-feedback controller. Firstly, the chemical process optimal control problem is formulated as a switched dynamical system optimal control problem, which can be transformed into a parameter optimization problem. Next, to achieve rapid convergence from remote starting points, we propose a novel gradient-based optimization algorithm, which is suitable to a parallel implementation because the step is improved by updating its direction as well as its length simultaneously before moving to the next iteration, and the step computation involves only the inner products of vectors. Then, the convergent properties of the parameter optimization problem to the original optimal control problem are discussed. Finally, the numerical simulation results show that the gradient-based parallel optimization algorithm is an effective alternative method for solving the chemical process optimal control problems. [ABSTRACT FROM AUTHOR]

Abstract: Many practical control systems can be modeled as switched linear systems with stabilizable and unstabilizable subsystems. In this paper, control synthesis for such a class of systems with actuator saturation is well investigated in the continuous-time and discrete-time cases. Based on the time-dependent switching signals and multiple Lyapunov function method, stabilization conditions are established in terms of LMIs. To obtain an attractive region as large as possible, the optimization problems are formulated. As the applications, the asynchronously switched control and intermittent control under actuator saturation are discussed. Numerical examples and simulations are presented to illustrate the feasibility and values of the proposed results. [Copyright &y& Elsevier]

In traditional graph-based optimization framework for salient object detection, an image is over-segmented into superpixels and mapped to one single graph. The saliency value of each superpixel is then computed based on the similarity between connected nodes and the saliency related queries. When applying the traditional graph-based optimization framework to the salient object detection problem in natural scene images, we observe at least two limitations: only one graph is employed to describe the information contained in an image and no cognitive property about visual saliency is explicitly modeled in the optimization framework. In this work, we propose a novel graph-based optimization framework for salient object detection. Firstly, we employ multiple graphs in our optimization framework. A natural scene image is usually complex, employing multiple graphs from different image properties can better describe the complex information contained in the image. Secondly, we model one popular cognitive property about visual saliency (visual rarity) in our graph-based optimization framework, making this framework more suitable for saliency detection problem. Specifically, we add a regularization term to constrain the saliency value of each superpixel according to visual rarity in our optimization framework. Our experimental results on four benchmark databases with comparisons to fifteen representative methods demonstrate that our graph-based optimization framework is effective and computationally efficient. [ABSTRACT FROM AUTHOR]

Point predictions of wind speed can hardly be reliable and accurate when the uncertainty level increases in data. Prediction intervals (PIs) provide a solution to quantify the uncertainty associated with point predictions. In this paper, we adopt radial basis function (RBF) neural networks to perform interval forecasting of the future wind speed. A two-step method is proposed to determine the RBF connection weights in a multi-objective optimization framework. In the first step, the centers of the RBF are determined using the K -means clustering algorithm and the hidden-output weights of the RBF are pre-trained using the least squares algorithm. In the second step, the hidden-output weights are further adjusted by the non-dominated sorting genetic algorithm-II (NSGA-II), which aims at concurrently minimizing the width and maximizing the coverage probability of the constructed intervals. We test the performance of the proposed method on three real data sets, which are collected from different wind farms in China. The experimental results indicate that the proposed method can provide higher quality PIs than the conventional multi-layer perceptron (MLP) based methods. [ABSTRACT FROM AUTHOR]