Abstract
In this paper, we consider the problem of minimum-norm control of the double integrator with bilateral inequality constraints for the output. We approximate the constraints by piecewise linear functions and prove that the Langrange multipliers associated with the state constraints of the approximating problem are discrete measures, concentrated in at most two points in every interval of discretization. This allows us to reduce the problem to a convex finite-dimensional optimization problem. An algorithm based on this reduction is proposed and its convergence is examined. Numerical examples illustrate our approach. We also discuss regularity properties of the optimal control for a higher-dimensional state-constrained linear regulator problem.
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Communicated by T. L. Vincent
The first author was supported by the National Science Foundation, Grant No. DMS-9404431. The second author was supported by a François-Xavier Bagnoud Doctoral Fellowship and by NSF Grants DMS-9404431 and MSS-9114630.
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Dontchev, A.L., Kolmanovsky, I.V. State constraints in the linear regulator problem: Case study. J Optim Theory Appl 87, 323–347 (1995). https://doi.org/10.1007/BF02192567
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DOI: https://doi.org/10.1007/BF02192567