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Abstract: In this paper, we consider a class of optimal control problem involving an impulsive systems in which some of its coefficients are subject to variation. We formulate this optimal control problem as a two-stage optimal control problem. We first formulate the optimal impulsive control problem with all its coefficients assigned to their nominal values. This becomes a standard optimal impulsive control problem and it can be solved by many existing optimal control computational techniques, such as the control parameterizations technique used in conjunction with the time scaling transform. The optimal control software package, MISER 3.3, is applicable. Then, we formulate the second optimal impulsive control problem, where the sensitivity of the variation of coefficients is minimized subject to an additional constraint indicating the allowable reduction in the optimal cost. The gradient formulae of the cost functional for the second optimal control problem are obtained. On this basis, a gradient-based computational method is established, and the optimal control software, MISER 3.3, can be applied. For illustration, two numerical examples are solved by using the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a nonlinear dynamic system with uncertain parameters. Our goal is to choose a control function for this system that balances two competing objectives: (i) the system should operate efficiently; and (ii) the system’s performance should be robust with respect to changes in the uncertain parameters. With this in mind, we introduce an optimal control problem with a cost function penalizing both the system cost (a function of the final state reached by the system) and the system sensitivity (the derivative of the system cost with respect to the uncertain parameters). We then show that the system sensitivity can be computed by solving an auxiliary initial value problem. This result allows one to convert the optimal control problem into a standard Mayer problem, which can be solved directly using conventional techniques. We illustrate this approach by solving two example problems using the software MISER3. [Copyright &y& Elsevier]

Abstract: We consider an optimal control problem with a nonlinear continuous inequality constraint. Both the state and the control are allowed to appear explicitly in this constraint. By discretizing the control space and applying a novel transformation, a corresponding class of semi-infinite programming problems is derived. A solution of each problem in this class furnishes a suboptimal control for the original problem. Furthermore, we show that such a solution can be computed efficiently using a penalty function method. On the basis of these two ideas, an algorithm that computes a sequence of suboptimal controls for the original problem is proposed. Our main result shows that the cost of these suboptimal controls converges to the minimum cost. For illustration, an example problem is solved. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a class of optimal control problems which is governed by nonsmooth functional inequality constraints involving convolution. First, we transform it into an equivalent optimal control problem with smooth functional inequality constraints at the expense of doubling the dimension of the control variables. Then, using the Chebyshev polynomial approximation of the control variables, we obtain an semi-infinite quadratic programming problem. At last, we use the dual parametrization technique to solve the problem. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a general class of optimal sensor scheduling problems in discrete time. There are sensors available for acquiring data so as to estimate the needed but unknown signal. Only out of the sensors can be turned on at any moment, while different weights can be assigned to different sensors. This problem is formulated as a discrete time deterministic optimal control problem involving both discrete and continuous valued controls. A computational method is developed for solving this discrete time deterministic optimal control problem based on a branch and bound method in conjunction with a gradient-based method. The branch and bound method is used to determine the optimal schedule of sensors, where a sequence of lower bound dynamic systems is introduced so as to provide effective lower bounds for the construction of the branching rules. Each of the branches is an optimal weight vector assignment problem and a gradient-based method is developed for solving this optimal control problem. For illustration, two numerical examples are solved. [Copyright &y& Elsevier]

In this article, we consider a class of optimal control problems involving dynamical systems described by impulsive integrodifferential equations. First, we approximate the integral kernel of the integral equation by a finite expansion of the shifted Chebyshev polynomial. Through this process, the optimal control problem is approximated by a sequence of optimal control problems involving only impulsive ordinary differential equations. Each of them can be viewed as a nonlinear optimization problem. For each of these approximated problems, the gradient formula of the cost functional can be derived and hence can be solved by many efficient optimization techniques. Consequently, the optimal control software, MISER, is applicable for the purpose. Then, we present some convergence results showing the relationship between the sequence of the optimal controls of the approximated problems and that of the original problem. Finally, a numerical example is presented to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: A mathematical model of the evaporation system in the form of a state space model with multiple time delays is constructed. On this basis, an optimal control of an industrial-scale alumina evaporation process is obtained, where the objective is to find a control such that the specific quality of the sodium aluminate solution control is met with the least energy usage and the constraints on the state and the control are satisfied. Then, a numerical algorithm is developed for solving this optimal control problem. It is applied to study the optimal control of a practical alumina evaporation process and the results obtained are highly satisfactory. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a class of the optimal state feedback control problems involving switched systems with state jumps. The planning time horizon is subdivided into subintervals, where the breakpoints are called the re-setting times. One system is used during each subinterval with a piecewise state feedback control form. The re-setting time, the feedback gain matrices and the heights of the state jumps at the re-setting times are considered as decision variables. It is shown, through a time scaling transform, that this class of optimal control problems is equivalent to an optimal parameter selection problem, where the varying re-setting time points are mapped into fixed time points. The gradient formula of the transformed cost function is derived. With this gradient formula, the optimal parameter selection problem can be solved as a nonlinear optimization problem, and the optimal control software MISER 3.3 can be used. Two illustrative examples are solved using the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, we establish the existence of the optimal control for an optimal control problem where the state of the system is defined by a variational inequality problem with monotone type mappings. Moreover, as an application, we get several existence results of an optimal control for the optimal control problem where the system is defined by a quasilinear elliptic variational inequality problem with an obstacle. [Copyright &y& Elsevier]