Search results for "Optimal control"
showing 10 items of 209 documents
Optimal Control Under Fuzzy Conditions for Dynamical Systems Associated with the Second Order Linear Differential Equations
2020
This paper is devoted to an optimal trajectory planning problem with uncertainty in location conditions considered as a problem of constrained optimal control for dynamical systems. Fuzzy numbers are used to incorporate uncertainty of constraints into the classical setting of the problem under consideration. The proposed approach applied to dynamical systems associated with the second order linear differential equations allows to find an optimal control law at each \(\alpha \)-level using spline-based methods developed in the framework of the theory of splines in convex sets. The solution technique is illustrated by numerical examples.
Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model
2008
The special functions are intensively used in mathematical physics to solve differential systems. We argue that they should be most useful in economic dynamics, notably in the assessment of the transition dynamics of endogenous economic growth models. We illustrate our argument on the famous Lucas-Uzawa model, which we solve by the means of Gaussian hypergeometric functions. We show how the use of Gaussian hypergeometric functions allows for an explicit representation of the equilibrium dynamics of all variables in level. The parameters of the involved hypergeometric functions are identified using the Pontryagin conditions arising from the underlying optimization problems. In contrast to th…
Dynamic analysis of a five degree of freedom robotic arm using MATLAB-Simulink Simscape
2021
In this paper, a dynamic analysis for a 5 degree of freedom (DOF) robotic arm with serial topology is presented. The dynamic model of the robot is based on importing a tri-dimensional CAD model of the robot into Simulink®-Simscape™-Multibody™. The dynamic model of the robot in Simscape is a necessary and important step in development of the mechanical structure of the robot. The correct choice of the electric motors is made according to the resistant joint torques determined by running the dynamic analysis. One can import complete CAD assemblies, including all masses, inertias, joints, constraints, and tri-dimensional geometries, into the model block. The first step for executing a dynamic …
Monotonically convergent optimal control theory of quantum systems under a nonlinear interaction with the control field
2008
We consider the optimal control of quantum systems interacting non-linearly with an electromagnetic field. We propose new monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured by a non-standard choice of the cost which is not quadratic in the field. These algorithms can be constructed for pure and mixed-state quantum systems. The efficiency of the method is shown numerically on molecular orientation with a non-linearity of order 3 in the field. Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well-approximated by pulses that could be implemented ex…
Abstract Estimates of the Rate of Convergence for Optimal Control Problems
1997
A method for solving optimal control problems with general elliptic operators is presented and analyzed. Especially, estimates of the rate of convergence for the control problems with the proposed approach are derived independently of the underlying approximation method. Some numerical experiments with the proposed method are included.
Minimum Losses Reconfiguration of MV Distribution Networks through Local Control of Tie Switches
2002
This paper deals with the problem of optimal reconfiguration of radial distribution networks for minimum loss operation. The proposed control strategy of the open-closed status of the tie-switches is distributed, since every MV/LV node is provided with local controllers having some measured entities as input. It also does not prevent the system from the future implementation of centralized control; instead it may represent the first step toward a complete automation of the distribution system. The proposed strategy is indeed organized in hierarchic levels, the highest of which may be in the future a central control. After introducing the general problem of networks reconfiguration, a review…
Control strategy analysis of the hydraulic hybrid excavator
2015
Abstract Applying the electric hybrid technique on the off-road vehicle is one popular method to reduce the fuel consumption. However, the high cost, low energy conversion efficiency and disposal of used batteries are still the main problems. This paper is focusing on one alternative choice which is hydraulic hybrid off-road vehicles. Among the most typical off-road vehicles, the excavator is chosen as the prototype to study the control strategy. First, the basic principle of the hydraulic hybrid excavator based on Common Pressure Rail is introduced. Then, the mathematical model of the whole excavator is created. Moreover, the dynamic programming algorithm is used to solve the optimal contr…
Time-Optimal Synthesis for Three Relevant Problems: The Brockett Integrator, the Grushin Plane and the Martinet Distribution
2015
We construct the time-optimal synthesis for 3 problems that are linear in the control and with polytopic constraints in the controls. Namely, the Brockett integrator, the Grushin plane, and the Martinet distribution. The main purpose is to illustrate the steps in solving an optimal control problem and in particular the use of second order conditions. The Grushin and the Martinet case are particularly important: the first is the prototype of a rank-varying distribution, the second of a non-equiregular structure.
A polynomial algorithm solving a special class of hybrid optimal control problems
2006
Hybrid optimal control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions [5]. In this paper, we identify a special class of hybrid optimal control problems which are easy to solve. We do this by using a paradigm borrowed from the Operations Research field. As main result, we present a solution algorithm that converges to the exact solution in polynomial time. Our approach consists in approximating the hybrid optimal control problem via an integer-linear programming reformulation. The integer-linear programming problem is a Set-covering one with a totally unimodular constraint matrix and therefore solving the S…
Integrated Approach to Part Scheduling and Inspection Policies for a Job Shop Manufacturing System
2007
The quality of a product greatly depends on the quality of its components. This requires that manufacturing specifications have to be met in the manufacturing environment and as a consequence inspection stations are present in many manufacturing systems and inspection policies must be adopted. One problem, which has been widely investigated, concerns the detection of the inspection points in the hypothesis that the action to be taken is known when a defective part is detected. If different jobs are to be produced, then operation scheduling becomes yet another complex problem needing to be solved. And while the problem of scheduling has received a great amount of attention from researchers, …