ISSN:0143-2087    

DOI:10.1002/oca.4660010102

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1980

数据来源: WILEY

摘要:

AbstractThis paper describes a maximum principle for distributed parameter systems, i.e. systems characterized by partial differential equations. The maximum principle is applied to solve the problem of a cattle rancher who must decide the number of cattle in different age groups to be bought and sold at each instant in order to maximize his profits.

ISSN:0143-2087    

DOI:10.1002/oca.4660010103

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1980

数据来源: WILEY

ISSN:0143-2087    

DOI:10.1002/oca.4660010104

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1980

数据来源: WILEY

摘要:

AbstractA two‐level hierarchical algorithm of the interaction prediction type is derived for the decentralized optimal control of linear systems with fixed terminal state, linear interactions, and a minimum energy criterion. The algorithm is noniterative at the infimal level and utilizes successive approximation with averaging for the coordination. Numerical experiments compare the effect of the interactions, sampling times, and time horizon on the convergence of the algorith

ISSN:0143-2087    

DOI:10.1002/oca.4660010105

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1980

数据来源: WILEY

摘要:

AbstractThrough proper design, it is possible to build an electromagnetic bearing system, using a ferromagnetic rotor, such that there exists an equilibrium position in the magnetostatic field which is unstable only in the axial direction. In order to achieve axial stability, a regulator may be employed to vary the current in the coils whenever the rotor is displaced from the equilibrium position. The idea is to vary the current in such a way that the resultant change in the magnetic, field produces a restoring force to the rotor.This study is devoted to an investigation of the relative merits of various control laws which could be implemented by the regulator. The rotor is to be maintained in the vicinity of the equilibrium point even if an external force is present which enters the system as an unknown but bounded function of the system state and time.Recent magnetic suspension systems have been designed using a regulator based on linear state variable feedback. It is shown here that asymptotic stability cannot be maintained for the system in the presence of an external force if linear feedback control is used. The effect of an unknown but bounded external force on the system is vividly demonstrated by using qualitative methods to find the boundary of the set reachable under this force. Linear state variable feedback can maintain partial controllability of the system to some neighbourhood of the equilibrium point provided a simple inequality relationship between the feedback parameters and the bounds on the external force is maintained. Finally, it is shown that a game theoretic approach may be used for a nonlinear regulator design which will result in an asymptotically stable system in the presence of an unknown but bounded external force.

ISSN:0143-2087    

DOI:10.1002/oca.4660010106

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1980

数据来源: WILEY

摘要:

AbstractA stochastic linear quadratic optimal control problem is considered in which some of the plant states may be measured without a measurement noise component. This set of states are assumed to be associated with the plant inputs and force transducers. The optimal controller is shown to include state feedback from this part of the system. The states which cannot be measured are assumed to be combined in noisy output signal. The optimal controller corresponding to this second subsystem is shown to include a Kalman filter and state‐estimate feedback.The combination of state and state‐estimate feedback has the advantage that the dimension of the Kalman filter is equal to that of the second subsystem mentioned above. In the conventional solution to this problem, no states are assumed measurable, and the dimension of the Kalman filter is equal to the dimension of the complete system. In many industrial control problems, the combined control law enables a significant reduction in the dimension of the filter to be achieved. The technique has been proposed for use in dynamic ship positioning control systems, and this problem is discus

ISSN:0143-2087    

DOI:10.1002/oca.4660010107

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1980

数据来源: WILEY

摘要:

AbstractIn this paper, a new member of the family of sequential gradient‐restoration algorithms for the solution of optimal control problems is presented. This is an algorithm of the conjugate gradient type, which is designed to solve two classes of optimal control problems, called Problem P1 and Problem P2 for easy indentification.Problem P1 involves minimizing a functionalIsubject to differential constraints and general boundary conditions. It consists of finding the statex(t), the controlu(t), and the parameter pi so that the functionalIis minimized, while the constraints and the boundary conditions are satisfied to a predetermined accuracy. Problem P2 extends Problem P1 to include non‐differential constraints to be satisfied everywhere along the interval of integration.The approach taken is a sequence of two‐phase cycles, composed of a conjugate gradient phase and a restoration phase. The conjugate gradient phase involves one iteration and is designed to decrease the value of the functional, while the constraints are satisfied to first order. The restoration phase involves one or more iterations; each restorative iteration is designed to force constraint satisfaction to first order, while the norm squared of the variations of the control, the parameter, and the missing components of the initial state is minimized. The resulting algorithm has several properties: (i) it produces a sequence of feasible solutions; (ii) each feasible solution is characterized by a value of the functionalIwhich is smaller than that associated with any previous feasible solution; and (iii) for the special case of a quadratic functional subject to linear constraints, the variations of the state, control, and parameter produced by the sequence of conjugate gradient phases satisfy various orthogonality and conjugacy conditions.The algorithm presented here differs from those of References 1‐4, in that it is not required that the state vector be given at the initial point. Instead, the initial conditions can be absolutely general. In analogy with References 1‐4, the present algorithm is capable of handling general final conditions; therefore, it is suitable for the solution of optimal control problems with general boundary conditions.The importance of the present algorithm lies in that many optimal control problems either arise naturally in the present format or can be brought to such a format by means of suitable transformations.5Therefore, a great variety of optimal control problems can be handled. This includes: (i) problems with control equality constraints, (ii) problems with state equality constraints, (iii) problems with state‐derivative equality constraints, (iv) problems with‐control inequality constraints, (v) problems with state inequality constraints, (vi) problems with state‐derivative inequality constraints, and (vii) Chebyshev minimax problems.Several numerical examples are presented in Part 2 (Reference 6) in order to illustrate the performance of the algorithm associated with Problem P1 and Problem P2. The numerical results show the feasibility as well as the convergence characteristics of the pr

ISSN:0143-2087    

DOI:10.1002/oca.4660010108

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1980

数据来源: WILEY

摘要:

AbstractA process for adjusting perturbation magnitude for accurate difference‐quotient estimation of derivatives is described in the following. The process is intended to be carried out sequentially, alternating with iterations of a parameter‐optimization algorithm. A more complex and computationally‐expensive scheme for occasional auxiliary use is also desc

ISSN:0143-2087    

DOI:10.1002/oca.4660010109

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1980

数据来源: WILEY

摘要:

AbstractThis paper presents a flexible, user‐oriented algorithm for the numerical implementation of the terminal point transversality conditions associated with optimal control problems. The method differs from the usual numerical implementation in that the constant Lagrange multipliers associated with terminal constraints are eliminated numerically during program execution rather than being eliminated analytically prior to program coding. This conceptual innovation gives the user considerable flexibility in specifying new sets of terminal boundary conditions without reprogrammin

ISSN:0143-2087    

DOI:10.1002/oca.4660010110

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1980

数据来源: WILEY

ISSN:0143-2087    

DOI:10.1002/oca.4660010111

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1980

数据来源: WILEY