Optimal control of a rotary crane

This paper is concerned with the optimal control of a rotary crane, which makes two kinds of motion (rotation and hoisting) at the same time. The optimal control which transfers a load to a desired place as fast as possible and minimizes the swing of the load during the transfer, as well as the swing at the end of transfer, is calculated on the basis of a dynamic model. A new computational technique is employed for computing the optimal control, and several numerical results are presented.The authors wish to thank Professor D. G. Hull and the reviewers for their valuable comments and suggestions.     

Optimal control for parabolic systems with competitive interactions

We consider a two-dimensional parabolic system with general competitive interactions as a two-player game with conflicting objectives and with controls on the inhomogencous (source) terms. We show the existence of an optimal solution of the game as the saddle point of a suitable objective functional.     

Optimal sliding mode control for nonlinear systems with time-delay

This paper is concerned with the sliding mode control (SMC) for a class of nonlinear systems with time-delay. A novel optimal sliding mode is proposed by using the successive approximation approach (SAA). The stability of the nonlinear sliding mode is analyzed. The switching manifold ensures that the state trajectories of the closed-loop system converge to zero in an optimal fashion on the ideal sliding surface. Furthermore, the convergence velocity of every state trajectory on the ideal sliding surface can be adjusted through choosing the parameters of the quadratic performance index. A numerical simulation is given to show the effectiveness of the proposed design approach.     

Optimal control for nonlinear systems calculated with small computers

Using Ritz's procedure of representing the control functions of an optimal control problem by a function series with parameters to be optimized, it is shown that, from the well-known gradient procedure for dynamic problems, a simple iteration formula for the optimization of these parameters can be derived. Using an example with a technical background, the effectiveness of the program realization of this approach is demonstrated and is compared with the results of unrestricted dynamic optimization.This work was performed at the Technische Hochschule in Darmstadt, West Germany, with financial support from the DFG (Deutsche Forschungs-Gemeinschaft).     

Optimal stationary control for dynamic systems with Markov perturbations

Affine continuous and discrete-time dynamic systems with homogeneous jump Markov perturbations are considered and the existence of an optimal stationary control under a quadratic cost is discussed. In order to solve this problem some new stability results for linear systems with Markov perturbations are given.     

Optimal control problems with state constraints for semilinear distributed-parameter systems

We consider optimal control problems for distributed-parameter systems described by semilinear equations, with constraints on the control and on the state, and an exact pointwise target condition. As an application of a general theory of nonlinear programming problems in Banach spaces, a version of the Pontryagin maximum principle is obtained.This research was partly supported by the National Science Foundation under Grant DMS-92-21819.     

Optimal control computation for nonlinear time-lag systems

In this paper, a computational scheme using the technique of control parameterization is developed for solving a class of optimal control problems involving nonlinear hereditary systems with linear control constraints. Several examples have been solved to test the efficiency of the technique.     

Optimal feedback control for constrained mechanical systems

An approach to minimize the control costs and ensuring a stable deviation control is the Riccati controller and we want to use it to control constrained dynamical systems (differential algebraic equations of Index 3). To describe their discrete dynamics, a constrained variational integrators [1] is used. Using a discrete version of the Lagrange-d’Alembert principle yields a forced constrained discrete Euler-Lagrange equation in a position-momentum form that depends on the current and future time steps [2]. The desired optimal trajectory (q_opt, p_opt) and according control input u_opt is determined solving the discrete mechanics and optimal control (DMOC) algorithm [3] based on the variational integrator. Then, during time stepping of the perturbed system, the discrete Riccati equation yields the optimal deviation control input u_R. Adding u_opt and u_R to the discrete Euler-Lagrange equation causes a structure preserving trajectory as both DMOC and Riccati equations are based on the same variational integrator. Furthermore, coordinate transformations are implemented (minimal, redundant and nullspace) enabling the choice of different coordinates in the feedback loop and in the optimal control problem. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal control of time-delay systems with distributed parameters

An optimal control problem with a prescribed performance index for parabolic systems with time delays is investigated. A necessary condition for optimality is formulated and proved in the form of a maximum principle. Under additional conditions, the maximum principle gives sufficient conditions for optimality. It is also shown that the optimal control is unique. As an illustration of the theoretical consideration, an analytic solution is obtained for a time-delayed diffusion system.The author wishes to express his deep gratitude to Professors J. M. Sloss and S. Adali for the valuable guidance and constant encouragement during the preparation of this paper.     

Optimal control of differential-difference systems with intragroup symmetry

A decomposition method of finding the optimal control of differential-difference systems with intragroup symmetry is presented. The introduction of two forms of motions of coordinates of separate groups allows us to reduce the original optimal control problem to the solution of optimal control problems of order less than the order of the initial problem.     

Optimal control and stabilization for nonlinear systems

The optimal control and stabilization of nonlinear systems ofthe form = A(x)x + B(x)u is considered andexplicit expressions for the control are developed. Excellentresults have been obtained when we apply the technique presentedhere to an anaytical nonlinear model of the F-8 fighter aircraft.     

Optimal singular control for systems involving parameters

What we shall take into consideration is represented by the problems of singular optimal control when the index of performance, the differential constraints and the final conditions contain parameters. What is determined is the trajectory of the neighboring extremal for the initial point perturbed at the constraints of the perturbed final manifold. The present study evaluates the variation of the command on the extremal. This one allows obtaining the second variation in the singular case. The sufficient conditions of minimum are a result of imposing the non-negativity of the second variation. The application made analysis the optimality of the singular control for a system in the class of affine differential systems. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal control of parabolic systems with time-varying lags

Various optimal control problems for linear parabolic systemswith time-varying lags are considered. Necessary and sufficientconditions of optimality are derived for the Neumann problem.The optimal control is obtained in the feedback form. Makinguse of the results of Schwart's, the representation of the optimalfeedback control is given.     

Optimal control of parameter distributed systems with impulses

This paper concerns optimal control problems with impulses. The optimal magnitude of impulses and the spatial position of impulses are studied. We obtain maximum principles for these problems.     

Optimal control of switched systems with time delay

In this note, we develop a computational method for solving an optimal control problem which is governed by a switched dynamical system with time delay. Our approach is to parameterize the switching instants as a new parameter vector to be optimized. Then, we derive the required gradient of the cost function which is obtained via solving a number of delay differential equations forward in time. On this basis, the optimal control problem can be solved as a mathematical programming problem.