共查询到20条相似文献,搜索用时 15 毫秒
1.
J. P. Kernevez 《Journal of Optimization Theory and Applications》1973,12(1):43-52
The aim of this paper is to show that the simple gradient method is efficient when applied to the optimal control of a distributed parameter system. The system is a model of a biological membrane (with enzymes), and the problem is to approach a desired flux of substrate entering the membrane by acting on an inhibitor's concentration at the boundary of the membrane.This paper was presented at the 4th IFIP Symposium, Los Angeles, California, 1971.The author thanks Professor J. L. Lions for his guidance and supervision in this work. He also thanks Messieurs R. Glowinsky, M. Nedelec, L. Tartar, and J. P. Yvon for a number of very helpful discussions on the subject of this paper. This work was done in collaboration with the Laboratory of Medical Biochemistry, Charles Nicolle Hospital, Rouen, France. The author is much indebted to Dr. D. Thomas who suggested this problem. 相似文献
2.
M. Corless 《Journal of Optimization Theory and Applications》1990,64(3):481-494
For systems described by ordinary differential equations, we introduce the notion of exponential convergence to a ball containing the origin of the state space. For two specific classes of uncertain systems, controllers are presented which assure this behavior. For one of the system classes, the rate of exponential convergence can be made arbitrarily large.This paper is based on research supported by the National Science Foundation under Grant MSM-87-06927.The author is grateful to Professors G. Leitmann, F. Garofalo, and B. R. Barmish for useful discussions on this topic. 相似文献
3.
H. Mete Soner 《Journal of Optimization Theory and Applications》1988,57(3):429-437
This paper is concerned with a certain class of distributed parameter control problems. The value function of these problems
is shown to be the unique viscosity solution of the corresponding Hamiltonian-Jacobi-Bellman equation. The main assumption
is the existence of an increasing sequence of compact invariant subsets of the state space. In particular, this assumption
is satisfied by a class of controlled delay equations.
This research was partly supported by the Institute for Mathematics and Its Applications with funds provided by the National
Science Foundation and the Office of Naval Research.
The author is indebted to Professor P. L. Lions for stimulating discussions and helpful suggestions. 相似文献
4.
Walter Benz 《Journal of Geometry》1979,12(2):146-151
W. LEISSNER proved in [2] that an arbitrarily given affine BARBILIAN PLANE must be isomorphic to a plane affine geometry over a Z-ring R and moreover did he establish the converse theorem among other results in [3]. One of the fundamental notions in this axiomatic approach of ring geometry is that of a BARBILIAN DOMAIN (BARBILIANBEREICH). The aim of our note is to present sufficient conditions in case of commutative rings R which guarantee that R admits exactly one BARBILIAN DOMAIN. If for instance R is an euclidean ring, then R admits exactly one BARBILIAN DOMAIN (P.M.COHN [1], corollary to Theorem 3 of our note).The author is indebted to Professor LEISSNER for several helpful discussions during the preparation of this note. 相似文献
5.
F. Blanchini 《Journal of Optimization Theory and Applications》1991,71(3):465-484
The linear state feedback synthesis problem for uncertain linear systems with state and control constraints is considered. We assume that the uncertainties are present in both the state and input matrices and they are bounded. The main goal is to find a linear control law assuring that both state and input constraints are fulfilled at each time. The problem is solved by confining the state within a compact and convex positively invariant set contained in the allowable state region.It is shown that, if the controls, the state, and the uncertainties are subject to linear inequality constraints and if a candidate compact and convex polyhedral set is assigned, a feedback matrix assuring that this region is positively invariant for the closed-loop system is found as a solution of a set of linear inequalities for both continuous and discrete time design problems.These results are extended to the case in which additive disturbances are present. The relationship between positive invariance and system stability is investigated and conditions for the existence of positively invariant regions of the polyhedral type are given.The author is grateful to Drs. Vito Cerone and Roberto Tempo for their comments. 相似文献
6.
B. Shahian 《Journal of Optimization Theory and Applications》1988,57(1):151-159
The problem of reduced-order, observer-based control of systems with controllers having different information about the system is considered. The set of necessary conditions for optimality is obtained, and then the breakdown of the separation principle is demonstrated. The necessary conditions are simplified, and it is shown that a suboptimal control law based on separation can be obtained to satisfy the necessary conditions.The author is indebted to Professor C. T. Leondes for his continuous support, guidance, and stimulating discussions. 相似文献
7.
This article investigates the delay‐dependent robust dissipative sampled‐data control problem for a class of uncertain nonlinear systems with both differentiable and non‐differentiable time‐varying delays. The main purpose of this article is to design a retarded robust control law such that the resulting closed‐loop system is strictly (Q, S, R)‐dissipative. By introducing a suitable Lyapunov–Krasovskii functional and using free weighting matrix approach, some sufficient conditions for the solvability of the addressed problem are derived in terms of linear matrix inequalities. From the obtained dissipative result, we deduce four cases namely, H∞ performance, passivity performance, mixed H∞, and passivity performance and sector bounded performance of the considered system. From the obtained result, it is concluded that based on the passivity performance it is possible to obtain the controller with less control effort, and also the minimum H∞ performance and the maximum allowable delay for achieving stabilization conditions can be obtained via the mixed H∞ and passivity control law. Finally, simulation studies based on aircraft control system are performed to verify the effectiveness of the proposed strategy. © 2015 Wiley Periodicals, Inc. Complexity 21: 142–154, 2016 相似文献
8.
W. M. Getz 《Journal of Optimization Theory and Applications》1979,28(4):585-602
The problem of harvesting two competing populations is formulated in an optimal control setting. The maximum sustained rent (MSR) solution is introduced and is shown to be not only totally singular, but also to play a central role in solutions to the harvesting problem. It is further shown that nonsingular extremal subarcs must in general approach and leave the MSR along partially singular curves. A numerical example is introduced to demonstrate this phenomenon. In the case where the populations are driven onto the MSR in minimum time, however, the optimal control is shown to be bang-bang with at most one switch.The author is indebted to Professor D. H. Jacobson and Dr. D. H. Martin for helpful discussions during the preparation of this paper. 相似文献
9.
Manlio Bordoni 《Mathematische Annalen》1994,298(1):693-718
Supported by funds of M.U.R.S.T. (Italy). The author is grateful to S. Gallot for his encouragement and for helpful discussions and to G. Besson for some interesting remarks 相似文献
10.
F. Wirl 《Journal of Optimization Theory and Applications》1996,91(2):299-320
The purpose of this paper is to characterize pathways to Hopf bifurcation in continuous time, concave, two-dimensional optimal control models. It is shown that essentially two pathways exist: control-state interaction and growth. The knowledge of such pathways provides a criterion at the stage of modelling on the potential complexity of optimal trajectories.The author knowledges the many discussions with Professor Gustav Feichtinger. 相似文献
11.
H. Zhu 《Journal of Optimization Theory and Applications》1992,75(1):155-181
Upon introducing a finite-fuel constraint in a stochastic control system, the convex duality formulation can be set up to represent the original singular control problem as a minimization problem over the space of vector measures at each level of available fuel. This minimization problem is imbedded tightly into a related weak problem, which is actually a mathematical programming problem over a convex,w*-compact space of vector-valued Radon measures. Then, through the Fenchel duality principle, the dual for the finite-fuel control problems is to seek the maximum of smooth subsolutions to a dynamic programming variational inequality. The approach is basically in the spirit of Fleming and Vermes, and the results of this paper extend those of Vinter and Lewis in deterministic control problems to the finite-fuel problems in singular stochastic control. Meanwhile, we also obtain the characterization of the value function as a solution to the dynamic programming variational inequality in the sense of the Schwartz distribution.The author is much indebted to Professor Wendell H. Fleming for his constant support and many helpful discussions during the preparation of this paper. 相似文献
12.
Kai Zheng Aik-Hong Lee Joseph Bentsman Philip T. Krein 《Nonlinear Analysis: Theory, Methods & Applications》2006
A robust induction motor control should provide the desired performance in the face of both plant model and controller model uncertainty. In a recent work, Bottura and co-workers, using the field orientation principle, introduced a representation of a nonlinear time-varying induction motor model that admits robust induction motor controller synthesis in the linear H∞ framework. The present work considers the use of the approach of Bottura et al. for attaining robust performance of the main operating modes–tracking and disturbance rejection–of an induction motor control system under implementation constraints on the control signal magnitude. This approach requires two distinct mode-specific controllers with gains that cannot be bridged without considerable performance degradation. To address this problem, a multi-objective hybrid control design methodology is developed that employs the corresponding mode-specific controller in each mode, and organizes a rapid and smooth steady-state switching, or transfer, between these controllers to permit sequencing of the operating modes, as necessary. Simulation shows that the technique proposed yields controllers with performance minimally affected by an imprecise modeling of an induction motor, as well as a reduced cost controller implementation throughout the entire induction motor operating sequence. 相似文献
13.
H. X. Phu 《Journal of Optimization Theory and Applications》1992,72(2):319-332
A macroeconomic model on the relation between economic growth and the environment is investigated with the aim of illustrating how the method of region analysis can be used in solving practical problems formulated as regular optimal control problems with state constraints.This paper was written when the author was invited by Professor R. Bulirsch to work at the Munich University of Technology with the assistance of the Alexander Von Humboldt Foundation. The author would like to express his sincere gratitude to the Alexander Von Humboldt Foundation and to Professor Bulirsch. 相似文献
14.
K. A. Lurie 《Journal of Optimization Theory and Applications》1992,72(3):553-575
This paper suggests a procedure of direct construction of the minimal extension of a constrained optimization problem for a heat equation containing controls in the coefficients. For a somewhat simpler problem, this approach has been initiated in Ref. 1.This research has been supported by AFOSR Grant No. 90-0268. The author acknowledges discussions with Dr. Janos Turi. 相似文献
15.
In 2004, Bertsimas and Sim proposed a robust approach that can control the degree of conservatism by applying a limitation Γ to the maximum number of parameters that are allowed to change. However, the robust approach can become extremely conservative even when Γ is relatively small. In this paper, we provide a theoretical analysis to explain why this extreme conservatism occurs. We further point out that the robust approach does not reach an extremely conservative state when Γ is less than k, where k is the number of nonzero components of the optimal solution of the extremely conservative robust approach. This research also shows that care must be taken when adjusting the value of Γ to control the degree of conservatism because the approach may result in greater conservatism than was intended. We subsequently apply our analysis to additive combinatorial optimization problems. Finally, we illustrate our results on numerical simulations. 相似文献
16.
研究了具有饱和因子的非线性奇异时滞系统的鲁棒保性能控制问题.目的是设计一个鲁棒控制器和保成本控制器,通过线性矩阵不等式方法(LMI)得出了鲁棒控制器和保性能控制器存在的充分条件.当这些LMI方法是可解时,分别给出了鲁棒控制器和保性能控制器的解析表达式. 相似文献
17.
G. S. Virk 《Journal of Optimization Theory and Applications》1985,45(2):295-312
In this paper, we present a convergent extension of the first-order strong-variational algorithm by Mayne and Polak (Ref. 1) for solving optimal control problems with control constraints to delay systems. Although the algorithm is similar to the one presented in Ref. 1, the proof of convergence is different, since the differential dynamic techniques used by Mayne and Polak are not applicable.This work forms part of the author's PhD Dissertation and was conducted at the Imperial College of Science and Technology under a studentship awarded by the UK Science and Engineering Research Council. This assistance is gratefully acknowledged. The author also wishes to thank Dr. R. B. Vinter for his encouragement and help. 相似文献
18.
Geometric methods for nonlinear optimal control problems 总被引:1,自引:0,他引:1
J. Baillieul 《Journal of Optimization Theory and Applications》1978,25(4):519-548
It is the purpose of this paper to develop and present new approaches to optimal control problems for which the state evolution equation is nonlinear. For bilinear systems in which the evolution equation is right invariant, it is possible to use ideas from differential geometry and Lie theory to obtain explicit closed-form solutions.The author wishes to thank Professor A. Krener for many stimulating discussions and in particular for suggesting Theorem 3.3. Also, special thanks are due to the author's thesis advisor Professor R. W. Brockett under whose direction most of the research was done. Finally, the author thanks two anonymous referees for suggestions which have improved the exposition. 相似文献
19.
O. Hájek 《Journal of Optimization Theory and Applications》1979,29(3):409-436
In a linear control system over a fixed time interval, we treat steering to the origin by controls (i) having realistic constraints on their values, while minimizing theL
1-cost of control, (ii) without such constraints, and (iii) minimizing the coordinate bound, with or without a givenL
1-cost restriction. Existence (also, nonexistence) results are obtained, together with further necessary conditions for control optimality.The author was introduced to these problems by Professors P. Hagedorn and W. Krabs and profited much by discussions with them and with other workers at the TH Darmstadt. The incisive idea that feedback controls still exist if state space is augmented by one dimension (see Example, Section 1) is due to Professor Hagedorn and obviously merits further treatment. Professor E. N. Chukwu pointed out an error in a preprint version of this paper, and the present formulation of Theorem 4.6 is the result of discussions with him. In a colloquium at Würzburg University, Professor P. C. Parks made the point that a portion ofmodern control theory is implicit in the work of Achiezer: in connection with the present material, the so-called M-moment problem, and our Theorem 4.6. The referee kindly pointed out the reference for the example in Section 1. This paper is a revised version of a report, Preprint No. 279, prepared while the author held a Humboldt Award at the TH Darmstadt. 相似文献