Finally, we consider an example of the duality for the second-order linear optimal control problem.
📌 3 Key Takeaways
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Objective & Hypothesis:The present paper is devoted to the duality theory for the convex optimal control problem of second-order differential inclusions with periodic boundary conditions.
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Key Findings & Data:Then, we concentrate on the duality that exists in periodic boundary conditions to establish a dual problem for the differential problem and prove that Euler-Lagrange inclusions are duality relations for both primal and dual problems.
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Conclusion & Impact:Finally, we consider an example of the duality for the second-order linear optimal control problem.
The present paper is devoted to the duality theory for the convex optimal control problem of second-order differential inclusions with periodic boundary conditions. First, we use an auxiliary problem with second-order discrete-approximate inclusions and focus on formulating sufficient conditions of optimality for the differential problem. Then, we concentrate on the duality that exists in periodic boundary conditions to establish a dual problem for the differential problem and prove that Euler-Lagrange inclusions are duality relations for both primal and dual problems. Finally, we consider an example of the duality for the second-order linear optimal control problem.
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