12 research outputs found
An economic MPC formulation with offset-free asymptotic performance
This paper proposes a novel formulation of economic MPC for nonlinear discrete-time systems that is able to drive the closed-loop system to the (unknown) optimal equilibrium, despite the presence of plant/model mismatch. The proposed algorithm takes advantage of: (i) an augmented system model which includes integrating disturbance states as commonly used in offset-free tracking MPC; (ii) a modifier-adaptation strategy to correct the asymptotic equilibrium reached by the closed-loop system. It is shown that, whenever convergence occurs, the reached equilibrium is the true optimal one achievable by the plant. An example of a CSTR is used to show the superior performance with respect to conventional economic MPC and a previously proposed offset-free MPC still based on a tracking cost. The implementation of this offset-free economic MPC requires knowledge of plant input-output steady-state map gradient, which is generally not available. To this aim a simple linear identification procedure is explored numerically for the CSTR example, showing that convergence to a neighborhood of the optimal equilibrium is possible
Implementation of an economic MPC with robustly optimal steady-state behavior
Designing an economic model predictive control (EMPC) algorithm that asymptotically achieves the optimal performance in presence of plant-model mismatch is still an open problem. Starting from previous work, we elaborate an EMPC algorithm using the offset-free formulation from tracking MPC algorithms in combination with modifier-adaptation technique from the real-time optimization (RTO) field. The augmented state used for offset-free design is estimated using a Moving Horizon Estimator formulation, and we also propose a method to estimate the required plant steady-state gradients using a subspace identification algorithm. Then, we show how the proposed formulation behaves on a simple illustrative example
A Dissipativity Characterization of Velocity Turnpikes in Optimal Control Problems for Mechanical Systems
Turnpikes have recently gained significant research interest in optimal
control, since they allow for pivotal insights into the structure of solutions
to optimal control problems. So far, mainly steady state solutions which serve
as optimal operation points, are studied. This is in contrast to time-varying
turnpikes, which are in the focus of this paper. More concretely, we analyze
symmetry-induced velocity turnpikes, i.e. controlled relative equilibria,
called trim primitives, which are optimal operation points regarding the given
cost criterion. We characterize velocity turnpikes by means of dissipativity
inequalities. Moreover, we study the equivalence between optimal control
problems and steady-state problems via the corresponding necessary optimality
conditions. An academic example is given for illustration
Optimal control of membrane filtration systems
International audienceThis paper studies an optimal control problem related to membrane filtration processes. A generic mathematical model of membrane fouling is used to capture the dynamic behavior of the filtration process which consists in the attachment of matter onto the membrane during the filtration period and the detachment of matter during the cleaning period. We consider the maximization of the net water production of a membrane filtration system (i.e. the filtrate) over a finite time horizon, where the control variable is the sequence of filtration/backwashing cycles over the operation time of process. Based on the Pontryagin Maximum Principle, we characterize the optimal control strategy and show that it exhibits a singular arc. Moreover we prove the existence of an additional switching curve before reaching the terminal state, and also the possibility of having a dispersal curve as a locus where two different strategies are both optimal
Optimal and Sub-optimal Feedback Controls for Biogas Production
International audienceWe revisit the optimal control problem of maximizing biogas production in continuous bio-processes in two directions: 1. over an infinite horizon, 2. with sub-optimal controllers independent of the time horizon. For the first point, we identify a set of optimal controls for the problems with an averaged reward and with a discounted reward when the discount factor goes to 0 and we show that the value functions of both problems are equal. For the finite horizon problem, our approach relies on a framing of the value function by considering a different reward for which the optimal solution has an explicit optimal feedback that is time-independent. In particular, we show that this technique allows us to provide explicit bounds on the sub-optimality of the proposed controllers. The various strategies are finally illustrated on Haldane and Contois growth functions