Long time versus steady state optimal control
A Porretta, E Zuazua - SIAM Journal on Control and Optimization, 2013 - SIAM
SIAM Journal on Control and Optimization, 2013•SIAM
This paper analyzes the convergence of optimal control problems for an evolution equation
in a finite time-horizon 0,T toward the limit steady state ones as T→∞. We focus on linear
problems. We first consider linear time-independent finite-dimensional systems and show
that the optimal controls and states exponentially converge in the transient time (as T tends
to infinity) to the ones of the corresponding steady state model. For this to occur suitable
observability assumptions need to be imposed. We then extend the results to infinite …
in a finite time-horizon 0,T toward the limit steady state ones as T→∞. We focus on linear
problems. We first consider linear time-independent finite-dimensional systems and show
that the optimal controls and states exponentially converge in the transient time (as T tends
to infinity) to the ones of the corresponding steady state model. For this to occur suitable
observability assumptions need to be imposed. We then extend the results to infinite …
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 . We focus on linear problems. We first consider linear time-independent finite-dimensional systems and show that the optimal controls and states exponentially converge in the transient time (as tends to infinity) to the ones of the corresponding steady state model. For this to occur suitable observability assumptions need to be imposed. We then extend the results to infinite-dimensional systems including the linear heat and wave equations with distributed controls.
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