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Optimality, stability, and convergence in nonlinear control

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Abstract

Sufficient optimality conditions for infinite-dimensional optimization problems are derived in a setting that is applicable to optimal control with endpoint constraints and with equality and inequality constraints on the controls. These conditions involve controllability of the system dynamics, independence of the gradients of active control constraints, and a relatively weak coercivity assumption for the integral cost functional. Under these hypotheses, we show that the solution to an optimal control problem is Lipschitz stable relative to problem perturbations. As an application of this stability result, we establish convergence results for the sequential quadratic programming algorithm and for penalty and multiplier approximations applied to optimal control problems.

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Authors and Affiliations

  1. Mathematical Reviews, 416 Fourth Street, 48107, Ann Arbor, MI, USA

    A. L. Dontchev

  2. Department of Mathematics, University of Florida, 32611, Gainesville, FL, USA

    W. W. Hager

  3. Department of Mathematics, Colorado State University, 80523, Fort Collins, CO, USA

    A. B. Poore

  4. Department of Mathematics, West Virginia Tech, 25136, Montgomery, WV, USA

    Bing Yang

Authors
  1. A. L. Dontchev
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  2. W. W. Hager
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  3. A. B. Poore
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  4. Bing Yang
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Additional information

Communicated by I. Lasiecka

This research was supported by the U.S. Army Research Office under Contract. Number DAAL03-89-G-0082, by the National Science Foundation under Grant Number DMS 9404431, and by Air Force Office of Scientific Research under Grant Number AFOSR-88-0059. A. L. Dontchev is on leave from the Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria.

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Dontchev, A.L., Hager, W.W., Poore, A.B. et al. Optimality, stability, and convergence in nonlinear control. Appl Math Optim 31, 297–326 (1995). https://doi.org/10.1007/BF01215994

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  • DOI: https://doi.org/10.1007/BF01215994

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