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• A state-feedback controller is introduced for the chemical process optimal control problem. • A smoothing cost penalty function approach is introduced for the state and control constraints. • A gradient-based optimization algorithm is developed for solving this optimal control. • Convergence results indicate that the gradient-based optimization algorithm is convergent. • A sensitivity analysis method is developed for the chemical process optimal control problem. This paper considers an optimal control problem of chemical processes with a small perturbation in the system state and control input inequality constraints. Since open loop controls may not be robust in practice engineering applications, a general state-feedback controller is introduced for the biochemical process optimal control problem. Then, in order to obtain the optimal state-feedback parameters, a numerical optimization algorithm is proposed for solving this problem based on a novel smoothing cost penalty function approach. Compared with the existing methods, this algorithm has two advantages. One is the penalty parameter need not take a very big value or go to infinity. The other is guaranteed to converge to a local optimal solution without the requirement of the global solution being obtained at each step. More importantly, an effective sensitivity analysis method is also developed for the chemical process optimal control problem. Finally, three chemical process optimal control problems are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we solve an optimal control problem for switched stochastic systems using calculus of variations, where the objective is to minimize a cost functional defined on the state and the switching times are the sole control variables. In particular, we focus on the problem in which a pre-specified sequence of active subsystems is given. For one switching time case, the derivative of the cost functional with respect to the switching time is derived, which has an especially simple form and can be directly used in gradient descent algorithms to locate the optimal switching instant. Then, we propose an approach to deal with the problem with multi-switching times case. Finally, two numerical examples are given, highlighting the viability and advantages of the proposed methodology. [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]

In the paper, the optimal control problem of chemical process systems is considered. In general, it is very difficult to solve this problem analytically due to its nonlinear nature and the existence of control input constraints. To obtain the numerical solution, based on the time-scaling transformation technology and the control parameterization method, the problem is transformed into a parameter optimization problem with some variable bounds, which can be efficiently solved using the improved conjugate gradient algorithm developed by us. However, in spite of the improved conjugate gradient 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, a novel stochastic search method is developed. A large number of numerical experiments show that the novel stochastic search method is excellent in exploration, while bad in exploitation. In order to improve the exploitation, we propose a hybrid stochastic optimization approach to solve the problem based on the novel stochastic search method and the improved conjugate gradient algorithm. Convergence results indicate that any global optimal solution of the approximate problem is also a global optimal solution of the original problem. Finally, four chemical process system optimal control problems illustrate that the hybrid numerical optimization algorithm proposed by us is low CPU time and obtains a better cost function value than the existing approaches. [ABSTRACT FROM AUTHOR]