This manuscript addresses the problem of data driven model based economic model predictive control (MPC) design. To this end, first, a data-driven Lyapunov-based MPC is designed, and shown to be capable of stabilizing a system at an unstable equilibrium point. The data driven Lyapunov-based MPC utilizes a linear time invariant (LTI) model cognizant of the fact that the training data, owing to the unstable nature of the equilibrium point, has to be obtained from closed-loop operation or experiments. Simulation results are first presented demonstrating closed-loop stability under the proposed data-driven Lyapunov-based MPC. The underlying data-driven model is then utilized as the basis to design an economic MPC. The economic improvements yielded by the proposed method are illustrated through simulations on a nonlinear chemical process system example.
In this work, we address the problem
of control of nonlinear systems to deliver a prescribed closed-loop
behavior. In particular, the framework allows for the practitioner
to first specify the nature and specifics of the desired closed-loop
behavior (e.g., first order with smallest time constant, second order
with no more than a certain percentage overshoot, etc.). An optimization
based formulation then computes the control action to deliver the
best attainable closed loop behavior. To decouple the problems of
determining the best attainable behavior and tracking it as closely
as possible, the optimization problem is posed and solved in two tiers.
In the first tier, the focus is on determining the best closed-loop
behavior attainable, subject to stability and tracking constraints.
In the second tier, the inputs are tweaked to possibly improve the
tracking of the optimal output trajectories given by the first tier.
The efficacy of the proposed method and the various specific formulations
needed are illustrated through implementation on a linear system subject
to output feedback, a nonlinear CSTR subject to uncertainty and rate
of change of input constraints, and a reactor separator system. The
simulation results demonstrate significantly improved adherence to
the prescribed performance criteria over a predictive controller representative
of existing approaches.
The present work addresses the problem
of loss of model validity
in batch process control via online monitoring and adaptation based
model predictive control. To this end, a state space subspace-based
model identification method suitable for batch processes is utilized
and then a model predictive controller is designed. To monitor model
performance, a model validity index is developed for batch processes.
In the event of poor prediction (observed via breaching of a threshold
by the model validity index), reidentification is triggered to identify
a new model and thus adapt the controller. In order to capture the
most recent process dynamics, the identification is appropriately
designed to emphasize more the recent process data. The efficacy of
the proposed method is demonstrated using an electric arc furnace
as a simulation test bed.
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