×

zbMATH — the first resource for mathematics

Projection series for retarded functional differential equations with applications to optimal control problems. (English) Zbl 0331.34059

MSC:
34K05 General theory of functional-differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
49K99 Optimality conditions
49M15 Newton-type methods
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Anderson, C.H, The linear differential-difference equation with constant coefficients, J. math. anal. appl., 40, 122-130, (1972) · Zbl 0245.34055
[2] Banks, H.T; Kent, G.A, Control of functional differential equations to target sets in function space, SIAM J. control, 10, 567-593, (1972) · Zbl 0266.49014
[3] Banks, H.T; Jacobs, M.Q, An attainable sets approach to optimal control of functional differential equations with function space terminal conditions, J. differential equations, 13, 127-149, (1973) · Zbl 0256.49044
[4] Banks, H.T; Jacobs, M.Q; Langenhop, C.E, Characterization of the controlled states in W2(1) of linear hereditary systems, SIAM J. control, 12, 611-649, (1974) · Zbl 0269.93005
[5] Bellman, R; Cooke, K.L, Differential-difference equations, (1963), Academic Press New York · Zbl 0115.30102
[6] Cameron, R.H; Martin, W.T, An unsymmetric Fubini theorem, Bull. amer. math. soc., 47, 121-125, (1941) · Zbl 0025.15201
[7] Canon, M.D; Cullum, C.D; Polak, E, Theory of optimal control and mathematical programming, (1970), McGraw-Hill New York · Zbl 0264.49001
[8] Daniel, J.W, The approximate minimization of functionals, (1971), Prentice-Hall Englewood Cliffs, NJ · Zbl 0208.42901
[9] Dunford, N; Schwartz, J.T, Linear operators, part I, (1958), Interscience New York
[10] Gabasov, R; Kirillova, F, Qualitative theory of optimal processes, (1971), Nauka Press Moscow · Zbl 0236.49001
[11] Hale, J.K, Linear functional differential equations with constant coefficients, Contributions to differential equations, 2, 291-319, (1963) · Zbl 0143.30702
[12] Hale, J.K, Functional differential equations, (1971), Springer-Verlag New York · Zbl 0213.36901
[13] Hale, J.K, Forward and backward continuation for neutral functional differential equations, J. differential equations, 9, 168-181, (1971) · Zbl 0213.36901
[14] Hastings, S.P, Backward existence and uniqueness for retarded functional differential equations, J. differential equations, 5, 441-451, (1969) · Zbl 0172.12202
[15] Henry, D, Small solutions of linear autonomous functional differential equations, J. differential equations, 8, 494-501, (1970) · Zbl 0228.34044
[16] Jacobs, M.Q; Kao, T.J, An optimum settling problem for time-lag systems, J. math. anal. appl., 40, 1-21, (1972) · Zbl 0211.46403
[17] Lasiecka, I, On the application of the method of moments to optimal control of systems with delays, ()
[18] Lions, J.L, Optimal control of systems governed by partial differential equations, (1971), Springer-Verlag New York · Zbl 0203.09001
[19] Luenberger, D.G, Optimization by vector space methods, (1969), Wiley New York · Zbl 0176.12701
[20] Markushin, E.M, On the convergence of a series of exponentials, Ural. GoS. univ., mat. zap., 5, 71-73, (1965), (tetrad 2)
[21] Markushin, E.M; Shimanov, S.N, The convergence of the optimal control of a countable system of differential equations, Differentsial’nye uravneniya, 2, 314-323, (1966) · Zbl 0194.45701
[22] Markushin, E.M; Shimanov, S.N, Approximate solution of the problem of analytical design of a controller for a time-lag equation, Differentsial’nye uravneniya, 2, 1018-1026, (1966) · Zbl 0194.45701
[23] Markushin, E.M; Shimanov, S.N, Approximate solution of analytical regulator problem for systems with delay, Automation and remote control, 29, 367-374, (1968) · Zbl 0181.16303
[24] Mostowski, A; Stark, M, Introduction to higher algebra, (1964), Pergamon Press Oxford · Zbl 0108.25102
[25] Neustadt, L.W, Optimization, a moment problem, and nonlinear programming, SIAM J. control, 2, 33-53, (1964) · Zbl 0133.36701
[26] Pitt, H.R, On a class of linear integro-differential equations, (), 153-163 · Zbl 0029.04401
[27] Poljak, B.T, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Dokl. akad. nauk SSSR, 166, 287-290, (1966) · Zbl 0171.09501
[28] Royden, H.L, Real analysis, (1968), Macmillan New York · Zbl 0197.03501
[29] Shimanov, S.N, On the theory of linear differential equations with retardations, Differentsial’nye uravneniya, 1, 102-116, (1965) · Zbl 0196.46201
[30] Swiger, J.M, Application of the theory of minimum normed operators to optimum control system problems, Advances in control systems, 3, 151-218, (1966) · Zbl 0196.46402
[31] Taylor, A.E, Introduction to functional analysis, (1958), Wiley New York · Zbl 0081.10202
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.