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We consider the problem of designing a feedback controller that guides the input and output of a linear time-invariant system to a minimizer of a convex optimization problem. The system is subject to an unknown disturbance that determines the feasible set defined by the system equilibrium constraints. Our proposed design enforces the Karush-Kuhn-Tucker optimality conditions in steady-state without incorporating dual variables into the controller. We prove that the input and output variables achieve optimality in equilibrium and outline two procedures for designing controllers that stabilize the closed-loop system. We explore key ideas through simple examples and simulations.
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This content will become publicly available on February 16, 2026
A Galerkin Approach to the Generalized Karush–Kuhn–Tucker Conditions for the Solution of an Elliptic Distributed Optimal Control Problem with Pointwise State and Control Constraints
Abstract We develop a convergence analysis for the simplest finite element method for a model linear-quadratic elliptic distributed optimal control problem with pointwise control and state constraints under minimal assumptions on the constraint functions.We then derive the generalized Karush–Kuhn–Tucker conditions for the solution of the optimal control problem from the convergence results of the finite element method and the Karush–Kuhn–Tucker conditions for the solutions of the discrete problems.
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- Award ID(s):
- 2208404
- PAR ID:
- 10604040
- Publisher / Repository:
- De Gruyter
- Date Published:
- Journal Name:
- Computational Methods in Applied Mathematics
- ISSN:
- 1609-4840
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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