Skip to main content

Affine control processes

  • Invited Lectures
  • Conference paper
  • First Online:
Conference on the Theory of Ordinary and Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 280))

  • 445 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. A. Antosiewicz, Linear control systems, Arch. Rat. Mech. Anal. 12 (1963), 313–324

    Article  MATH  Google Scholar 

  2. A. V. Balakrishnan, Optimal control problems in Banach spaces, J.SIAM Control A, 3 (1965), 152–180

    MathSciNet  MATH  Google Scholar 

  3. R. Conti, Contributions to linear control theory, J. Diff. Eqs., 1 (1965), 427–444

    Article  MathSciNet  MATH  Google Scholar 

  4. R. Conti, Problems in linear control theory, Acta Fac. Rer. Nat. Univ. Comenianae, (Bratislava), Math. 17 (1967), 73–80

    MATH  Google Scholar 

  5. R. Conti, On some aspects of linear control theory, Math. Theory of Control, edited by A.V. Balakrishnan and Lucien W. Neustadt, Acad. Press 1967, 285–300

    Google Scholar 

  6. R. Conti, Time optimal solution of a linear evolution equation in Banach spaces, J. Opt. Theory & Applsol 2 (1968), 277–280

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Conti, A convex programming problem in Banach spaces and applications to optimum control theory, J. Comp. Syst. Sci., 4 (1970), 38–48

    Article  MathSciNet  MATH  Google Scholar 

  8. M. C. Delfour, Generalized controllability for perturbed linear systems, SRC-68-5, Case Western Reserve Univ., June 1968

    Google Scholar 

  9. M. C. Delfour-S.K. Mitter, Reachability of perturbed systems and min sup properties, J. SIAM Control, 7 (1969), 521–533

    Article  MathSciNet  MATH  Google Scholar 

  10. Yu. V. Egorov, Necessary conditions for optimum controls in Banach spaces (Russian), Matem. Sbornik, 64 (1964), 79–101

    MATH  Google Scholar 

  11. P. L. Falb, Infinite dimensional control problems. I: On the closure of the set of attainable states for linear systems, J. Math. Anal. & Appls., 9 (1964), 12–22

    Article  MathSciNet  MATH  Google Scholar 

  12. H. O. Fattorini, Control in finite time of differential equations in Banach space, Comm. on pure & appl. Math., 19 (1966), 17–34

    Article  MathSciNet  MATH  Google Scholar 

  13. H.O. Fattorini, On Jordan operators and rigidity of linear control systems, Revista Un. Mat. Argentina, 23 (1967), 67–75

    MathSciNet  MATH  Google Scholar 

  14. H. O. Fattorini, A remark on the "Bang-Bang" principle for linear control systems in infinite dimensional space, J. SIAM Control, 6 (1968), 109–113

    Article  MathSciNet  MATH  Google Scholar 

  15. H. O. Fattorini, On complete controllability of linear systems, J. Diff. Eqs., 3(1967), 391–402

    Article  MathSciNet  MATH  Google Scholar 

  16. H. O. Fattorini, Some remarks on complete controllability, J. SIAM Control A, 4 (1966), 686–694

    Article  MathSciNet  MATH  Google Scholar 

  17. H. O. Fattorini, Controllability of higher order linear systems, Conference on the Math. Theory of Control, L.A. 1967, edited by A.V.Balakrishnan and Lucien W. Neustadt, Acad. Press 1967, 301–311

    Google Scholar 

  18. H. O. Fattorini, Boundary control systems, J. SIAM Control, 6 (1968), 349–385

    Article  MathSciNet  MATH  Google Scholar 

  19. A. Friedman, Optimal control in Banach spaces, J. Math. Anal. & Appls, 19 (1967), 35–55

    Article  MATH  Google Scholar 

  20. R. Gabasov-F. M. Kirillova, The solution of some problems in the theory of optimal processes (Russian), Avtom. i Telem. 25 (1964), 1058–1066; engl. transl. in Autom. & Remote Control, 25, 945–955

    MathSciNet  MATH  Google Scholar 

  21. H. Halkin, A generalization of LaSalle's "Bang-Bang" principle, J. SIAM Control A, 2 (1965), 199–202

    MathSciNet  MATH  Google Scholar 

  22. H. Hermes, On the closure and convexity of attainable sets in finite and infinite dimensions, J. SIAM Control, 5 (1967), 409–417

    Article  MathSciNet  MATH  Google Scholar 

  23. H. Hermes-J.P.LaSalle, Functional Analysis and Time Optimal Control, Academic Press,1969

    Google Scholar 

  24. R. E. Kalman, Contributions to the theory of optimal control, Symp. Intern. de Ecuaciones diferenciales ordinarias (1959, publ. 1961; 102–119

    Google Scholar 

  25. R. E. Kalman-Y.C. Ho-K. S. Narendra, Controllability of linear dynamical systems, Contribs. to Diff. Eqs., 1 (1963), 189–213

    MathSciNet  MATH  Google Scholar 

  26. V. Klee, Separation and support properties of convex sets. A Survey., Control Theory and the Calculus of Variations, edited by A.V. Balakrishnan, U.C.L.A., July 1968, Academic Press,1969, 235–303

    Google Scholar 

  27. N. N. Krasovskii, On the theory of optimal regulation, (Russian), Prikl. Mat. i Meh., 23 (1969), 625–639; engl. transl. J. Appl. Math. Mech., 23, 899–919

    MathSciNet  Google Scholar 

  28. N. N. Krasovskii, Control theory of motion. Linear systems. (Russian) Izd. Nauka, Moscow, 1968

    Google Scholar 

  29. E. Kreindler, Contributions to the theory of time optimal control, J. Franklin Inst., 275 (1963), 314–344

    Article  MathSciNet  MATH  Google Scholar 

  30. L. M. Kuperman-Yu. M. Repin, On controllability in infinite dimensional spaces (Russian), Dokl. Akad. Nauk SSSR, 200 (1971), 767–769

    MathSciNet  MATH  Google Scholar 

  31. A. B. Kurjanskii, On controllability in Banach spaces (Russian), Diff. Uravnenia, 5 (1969), 1715–1718

    Google Scholar 

  32. J. P. LaSalle, The time optimal control problem, Contrs. to the Theory of Non-lin. Oscill., 5 (1960), 1–24

    MathSciNet  MATH  Google Scholar 

  33. E. B. Lee-L. Markus, Foundations of Optimal Control Theory, J. Wiley & Sons, 1967

    Google Scholar 

  34. N. Levinson, Minimax, Liapunov and "Bang-Bang", J. Diff. Eqs., 2 (1966), 218–241

    Article  MathSciNet  MATH  Google Scholar 

  35. C. Marchiò, Unpublished paper

    Google Scholar 

  36. L. Markus, Optimal control of limit cycles, Three Lectures on Control Theory, Warwick Control Theory Centre, July 1971, Report 1, 1–26

    Google Scholar 

  37. W. L. Miranker, Approximate controllability for distributed linear systems, J. Math. Anal. Appls., 10 (1965), 378–387

    Article  MathSciNet  MATH  Google Scholar 

  38. S. K. Mitter, Theory of inequalities and the controllability of linear systems, Math. Theory of Control, edited by A.V.Balakrishnan and Lucien W. Neustadt, Academic Press,1967, 203–212

    Google Scholar 

  39. L. W. Neustadt, Optimization, a moment problem, and nonlinear programming, J. SIAM Control A, 2 (1964), 33–53

    MathSciNet  MATH  Google Scholar 

  40. W. A. Porter, On the optimal control of distributed systems, J. SIAM Control, 4 (1966), 466–472

    Article  MATH  Google Scholar 

  41. G. Pulvirenti-G. Santagati, Controlli lineari negli spazi di Orlicz Ann. di Mat. pura ed appl., (4) 76 (1967), 165–202

    Article  MathSciNet  MATH  Google Scholar 

  42. G. Pulvirenti-G. Santagati, Sulla teoria dei controlli lineari negli spazi di Orlicz di funzioni a valori vettoriali, Ann. di Mat. pura ed appl., (4) 78 (1968), 279–322

    Article  MathSciNet  MATH  Google Scholar 

  43. W. T. Reid, Ordinary linear differential operators of minimum norm, Duke Math. J., 29 (1962), 591–606

    Article  MathSciNet  MATH  Google Scholar 

  44. P. Santoro, Condizioni di non controllabilità per i sistemi lineari, Boll. Un. Mat. Ital., (3) 19 (1964), 400–406

    MathSciNet  MATH  Google Scholar 

  45. J. Schmets, Sur le principe du "Bang-Bang", Revue Roum. de Math. pures et appl., 15 (1970), 633–641

    MathSciNet  MATH  Google Scholar 

  46. F. A. Sholokovitch, On controllability in Hilbert space (Russian), Diff. Uravnenia, 3 (1967), 479–484

    Google Scholar 

  47. L. M. Sonneborn-F. S. Van Vleck, The Bang-Bang principle for linear control systems, J. SIAM Control A, 2 (1965), 151–159

    MathSciNet  MATH  Google Scholar 

  48. I. Tarnove, A controllability problem for nonlinear systems, Math. Theory of Control, edited by A.V. Balakrishnan and Lucien W. Neustadt, Academic Press, 1967, 170–179

    Google Scholar 

  49. K. Tsujioka, Remarks on controllability of second order evolution equations in Hilbert spaces, J. SIAM Control, 8 (1970), 90–99.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

W. N. Everitt B. D. Sleeman

Rights and permissions

Reprints and permissions

Copyright information

© 1972 Springer-Verlag

About this paper

Cite this paper

Conti, R. (1972). Affine control processes. In: Everitt, W.N., Sleeman, B.D. (eds) Conference on the Theory of Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066917

Download citation

  • DOI: https://doi.org/10.1007/BFb0066917

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05962-2

  • Online ISBN: 978-3-540-37618-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics