The interval turnpike property for adjoints
@article{Faulwasser2020TheIT, title={The interval turnpike property for adjoints}, author={Timm Faulwasser and Lars Grune and Jukka-Pekka Humaloja and Manuel Schaller}, journal={arXiv: Optimization and Control}, year={2020} }
In this work we derive an interval turnpike result for adjoints of finite- and infinite-dimensional nonlinear optimal control problems under the assumption of an interval turnpike on states and controls. We consider stabilizable dynamics governed by a generator of a semigroup with finite-dimensional unstable part satisfying a spectral decomposition condition and show the desired turnpike property under continuity assumptions on the first-order optimality conditions. We further give stronger…
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References
SHOWING 1-10 OF 40 REFERENCES
Steady-State and Periodic Exponential Turnpike Property for Optimal Control Problems in Hilbert Spaces
- MathematicsSIAM J. Control. Optim.
- 2018
This work designs an appropriate dichotomy transformation, based on solutions of the algebraic Riccati and Lyapunov equations, that establishes the steady-state (or periodic) exponential turnpike property of optimal control problems in Hilbert spaces.
An Exponential Turnpike Theorem for Dissipative Discrete Time Optimal Control Problems
- MathematicsSIAM J. Control. Optim.
- 2014
Two theorems illustrate how this boundedness condition can be concluded from structural properties like controllability and stabilizability of the control system under consideration of the class of strictly dissipative systems under consideration.
On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems
- MathematicsMathematical Control & Related Fields
- 2021
The paper is devoted to analyze the connection between turnpike phenomena and strict dissipativity properties for continuous-time finite dimensional linear quadratic optimal control problems. We…
The turnpike property in nonlinear optimal control — A geometric approach
- Economics, Mathematics2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019
First, it is shown that a turnpike-like property appears in general dynamical systems with hyperbolic equilibrium and then, apply it to optimal control problems to obtain sufficient conditions for the turnpikes occurs.
Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations
- Mathematics
- 2020
Integral and measure-turnpike properties for infinite-dimensional optimal control systems
- Mathematics, EconomicsMath. Control. Signals Syst.
- 2018
It is proved that strict strong duality, which is a classical notion in optimization, implies strict dissipativity, and measure-turnpike, and the property of the time average of the distance from any optimal solution to the turnpike set converges to zero, as the time horizon tends to infinity.
On turnpike and dissipativity properties of continuous-time optimal control problems
- Mathematics, EconomicsAutom.
- 2017
On the Turnpike Phenomenon for Optimal Boundary Control Problems with Hyperbolic Systems
- MathematicsSIAM J. Control. Optim.
- 2019
It is shown that for optimal boundary control problems with integer constraints for the controls the turnpike phenomenon occurs, and a numerical verification is given for a control problem in gas pipeline operations.
Long Time versus Steady State Optimal Control
- MathematicsSIAM J. Control. Optim.
- 2013
This paper analyzes the convergence of optimal control problems for an evolution equation in a finite time-horizon toward the limit steady state ones as T tends to infinity and shows that the optimal controls and states exponentially converge in the transient time.