A control algorithm based on the instantaneous Optimal control method is presented for on-line control of structures subjected to earthquake excitations. This algorithm employs the digital state-space equation to discretize the continuous dynamical equation of motion, and named discrete instantaneous Optimal control method. Based on the Lyapunov stability method, a procedure to obtain a discrete stable weighting matrix is developed. To demonstrate the precision and the efficiency of the proposed control algorithm an 8-story shear-type building frame equipped with one active mass damper/driver (AMD) mechanism is used. Behavior of different weighting matrices is also examined.

Government incomes include tax incomes and non-tax incomes that tax incomes can be considered as a more stable source of in come for government. In each country, tax incomes is regarderd as the basic unit of covering government costs؛ and developed economies take advantage of this tool to progress and achieve economic growth. In this study, Optimal control theory was used to access the amount and the rout of Optimal tax incomes to achieve economic growth during 1973-2007. For the analysis, a simultaneous system of general equilibrium of economics was designed and estemated by three stage least squares method (3SLS) using the information of Iran Central Bank time series and yearbook management and planning. Then the route of Optimal tax incomes and finally its values were specified by Optimal control theory and scenario planning that access to this values is crucial for economic growth. The results suggest a direct relationship between tax incomes and economic growth

We present the quantum equation and synthesize an Optimal control proce dure for this equation. We develop a theoretical method for the analysis of quantum Optimal control system given by the time depending Schrödinger equation. The Legendre wavelet method is proposed for solving this problem. This can be used as an efficient and accurate computational method for obtaining numerical solutions of different quantum Optimal control problems. The distinguishing feature of this paper is that it makes the method, previously used to solve non-quantum control equations based on Legendre wavelets, usable by using a change of variables for quantum control equations.

In this paper we consider the Time Optimal control Problem with Bounded state (TOCPB). By means of a process of embedding and using measure theory, this problem is replaced by another, in which we seek to minimize a linear form over a subset of a measure space defined by linear equalities. The theory allows us to convert the new problem to an infinite-dimensional linear programming problem. Afterwards, the infinite-dimensional linear programming problem is approximated by a finite dimensional one. Then by the solution of the final linear programming problem one can find an approximate value of the trajectory function x (0), control function u (0) and Optimal time T as well. AMS classification (49A).

In this paper, we present an efficient method to solve linear time-delay Optimal control problems with a quadratic cost function. In this regard, first, by employing the Pontryagin maximum principle to time-delay systems, the original problem is converted into a sequence of two-point boundary value problems (TPBVPs) that have both advance and delay terms. Then, using the continuous Runge–Kutta (CRK) method, the resulting sequences are recursively solved by the shooting method to obtain an Optimal control law. This obtained Optimal control consists of a linear feedback term, which is obtained by solving a Riccati matrix differential equation, and a forward term, which is an infinite sum of adjoint vectors, that can be obtained by solving sequences of delay TPBVPs by the shooting CRK method. Finally, numerical results and their comparison with other available results illustrate the high accuracy and efficiency of our proposed method.

In this paper, we solve Hamilton-Jocobi-Bellman (HJB) equations arising in Optimal control problems using Homotopy Perturbation Transform method (HPTM). The proposed method is a combined form of the Laplace Transformation method with the Homotopy Perturbation method to produce a highly effective method to handle many problems. Applying the HPTM, solution procedure becomes easier, simpler and more straightforward. Some illustrative examples are given to demonstrate the simplicity and efficiency of the proposed method.

Optimal control theory is a branch of mathematics. It is developed to find Optimal ways to control a dynamic system. In 1957, R.Bellman applied dynamic programming to solve Optimal control of discrete-time systems. His procedure resulted in closed-loop,  generally nonlinear, and feedback schemes. Optimal control problems which will be tackled involve the minimization of a cost function subject to constraints on the state vector and the control. Lagrange multipliers provide a method of converting a constrained minimization problem into an unconstrained minimization problem of higher order. The necessary condition for Optimality can be obtained as the solution of the unconstrained optimization problem of the Lagrange function and the bordered Hessian matrix is used for the second-derivative test. A spectral method for solving Optimal control problems is presented. The method is based on Bernoulli polynomials approximation. By using the Bernoulli operational matrix of integration and the Lagrangian function, stochastic Optimal control is transformed into an optimisation problem, where the unknown Bernoulli coefficients are determined by using Newton's iterative method. The convergence analysis of the proposed method is given. The simulation results based on the Monte-Carlo technique prove the performance of the proposed method. Some error estimations are provided and illustrative examples are also included to demonstrate the efficiency and applicability of the proposed method.

In many countries, railways, including intercity, urban railway (metro), tram, monorail, and other lines, have played a vital role in passenger and freight transportation in the past. The problem of optimizing energy and reducing air pollution has always been a very important issue in transportation systems. Given that trains are faster and more accessible for passenger and freight transportation and consume less energy compared to other public transportation vehicles, the use of railway lines has gained significant attention from many countries, individuals, and various companies. Nowadays, with the limitation of resources, the importance of Optimal energy consumption has received a lot of attention from researchers, and various methods have been proposed in this regard. As is well known, trains travel on railway lines based on speed profiles and control tables designed by the interlocking system, which have a close relationship with energy consumption. In recent years, investment in providing methods for designing train speed profiles with the aim of optimizing energy consumption in railway transportation systems has increased. There are various methods for optimizing speed profiles, among which the use of Optimal control theory can be mentioned. In this article, the multiple-phase Optimal control theory has been used to design train speed profiles. First, the train movement is divided into several phases based on the route layout, and then for each phase, dynamic equations and cost functions have been written to optimize energy consumption. In the next step, the solution to this multiple-phase problem will be done using pseudo-spectral methods and the GPOPS software. Finally, the designed speed profile for trains has been used for the Tehran-Mashhad path in the Abardej-Kavir section, and the level of energy consumption and optimization using this method has been discussed and investigated.