# Robustness of optimal control when subject to control constraints

Topic: Optimal control | All

Thursday 6th January 2022, 4pm – 5pm (Paris time)

SPEAKER

François Chaplais, CAS, Mines Paris, France

ABSTRACT

Optimal control is introduced; the first order necessary conditions and second order sufficient conditions are explained. Model perturbations in optimal control are presented for unconstrained problems.

Then the necessary first order optimality condition for control constrained problems is recalled (Pontryagin minimum principle). The stationarity condition that was used in the previous perturbation analysis does not hold anymore. However, the solution of a control constrained optimal control problem can be approximated by a sequence of optimal control problems where the stationarity condition does hold (interior methods). For each of these approximate problems, we perform a perturbation analysis. We show then that the error bound holds when we go to the limit and finally obtain an error bound for the constrained problem. The final result is interpreted as a robustness result. We can solve a nominal constrained problem and derive the corresponding control. However there is some uncertainty on the model parameters. The errors in the model are bounded in magnitude, without additional details. The question arise of controlling the perturbed system with our nominal, computed, control. This theory exhibits a bound on the lack of performance of the computed control, versus what we could have achieved if we had completely known the perturbed system.

Bio

François Chaplais has been with CAS - Mines Paristech since 1981. His domains of interest are optimal control and time scales in dynamical systems.

You can download the slides

SPEAKER

François Chaplais, CAS, Mines Paris, France

ABSTRACT

Optimal control is introduced; the first order necessary conditions and second order sufficient conditions are explained. Model perturbations in optimal control are presented for unconstrained problems.

Then the necessary first order optimality condition for control constrained problems is recalled (Pontryagin minimum principle). The stationarity condition that was used in the previous perturbation analysis does not hold anymore. However, the solution of a control constrained optimal control problem can be approximated by a sequence of optimal control problems where the stationarity condition does hold (interior methods). For each of these approximate problems, we perform a perturbation analysis. We show then that the error bound holds when we go to the limit and finally obtain an error bound for the constrained problem. The final result is interpreted as a robustness result. We can solve a nominal constrained problem and derive the corresponding control. However there is some uncertainty on the model parameters. The errors in the model are bounded in magnitude, without additional details. The question arise of controlling the perturbed system with our nominal, computed, control. This theory exhibits a bound on the lack of performance of the computed control, versus what we could have achieved if we had completely known the perturbed system.

Bio

François Chaplais has been with CAS - Mines Paristech since 1981. His domains of interest are optimal control and time scales in dynamical systems.

You can download the slides