\(\mathrm{L}^1\)-minimization for mechanical systems (Q2807332)
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scientific article; zbMATH DE number 6583294
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(\mathrm{L}^1\)-minimization for mechanical systems |
scientific article; zbMATH DE number 6583294 |
Statements
20 May 2016
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\(L^1\)-minimization
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optimal control
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mechanical systems
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sufficient optimality conditions
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Jacobi field
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conjugate points
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\(\mathrm{L}^1\)-minimization for mechanical systems (English)
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The paper deals with the optimal control of mechanical system in a potential field, where the mass of the body depends dynamically on the control. The \(L^1\)-norm of the control is minimized.NEWLINENEWLINESufficient conditions of optimality for the system are established. In the first place, it is pointed out that the system does not admit abnormal extremals. Then, sufficient conditions of optimality using the Jacobi field of extremals and conjugate points are established. Regular extremals correspond to controls whose norm is bang-bang. The sufficient conditions hold also for the case of broken controls, where conjugate moments happen both at or between switches of the control.NEWLINENEWLINEThe result is illustrated on two examples from space mechanics including the numerical computation of the fuel-minimizing control of the system with two-body potential.
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