On Average Performance and Stability of Economic Model Predictive Control

By David Angeli, R. Amrit, James B. Rawlings. IEEE Transactions on Automatic Control, 2012

628 citations recorded by the source corpus.

Control performance and cost optimization can be conflicting goals in the management of industrial processes. Even when optimal or optimization-based control synthesis tools are applied, the economic cost associated with plant operation is often only optimized according to static criteria that pick, among all feasible steady states, those with minimal cost. In mathematical terms, an economic cost functional differs from stage costs commonly adopted in model predictive control (MPC) as it need not be minimal at its best equilibrium. This note collects and illustrates some recent advances in receding horizon optimization of nonlinear systems that allow the control designer to simultaneously and dynamically optimize transient and steady-state economic performance. In particular, we show that average performance of economic MPC is never worse than the optimal steady-state operation. We introduce a dissipation inequality and supply function that extend previous sufficient conditions for asymptotic stability of economic MPC. Dissipativity is also shown to be a sufficient condition for concluding that steady-state operation is optimal. We show how to modify an economic cost function so that steady-state operation is asymptotically stable when that feature is deemed desirable. Finally, for the case when steady-state operation is not optimal, we develop two modified MPC controllers that asymptotically guarantee 1) improved performance compared to optimal periodic control and 2) satisfaction of constraints on average values of states and inputs.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/f268865638b0bc36d98c3b13f5eede53615c87d7

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In Control and Systems Engineering

Citations in the corpus

Asymptotic stability and transient optimality of economic MPC without terminal conditions (2014, methodology): “Note that our assumptions are not much more restrictive than those needed in [3] for proving stability for terminal constrained economic MPC.”
Fundamentals of economic model predictive control (2012, background): “To conclude this work, we present two examples to illustrate the concept of dissipativity and its relation to the tradeoff between stability and profitability, both of which are adapted from [26].”
Approximation Properties of Receding Horizon Optimal Control (2016, background): “Its importance for receding horizon control was first observed in [5,6].”
A tutorial review of economic model predictive control methods (2014, methodology): “Instead, the following is used for the definition of the asymptotic average in [6]:”
Model predictive control: Recent developments and future promise (2014, background): “It is shown in Angeli et al. (2012) that if (xr , ur) is defined as above (i.”
On the role of dissipativity in economic model predictive control (2015, methodology): “Namely, dissipativity with respect to a supply rate involving the employed stage cost function is both necessary and sufficient such that the optimal operating regime is stationary, i.e., at some steady-state (Angeli et al., 2012; Müller et al., 2013a, 2015; Faulwasser et al., 2014).”
Online Optimal Control with Linear Dynamics and Predictions: Algorithms and Regret Analysis (2019, background): “Recent years have seen a lot of attention on the optimality performance analysis of EMPC, under both time-invariant costs [17, 18, 19] and timevarying costs [20, 12, 14, 21, 22].”
Postface to “ Model Predictive Control : Theory and Design ” (2012, result): “This result is further generalized in the recent paper Angeli, Amrit, and Rawlings (2012).”
Single-layer economic model predictive control for periodic operation (2014, background): “In [2] an 50 economic MPC that guarantees that the asymptotic average economic cost of the controlled system is no worse that the average economic cost of the optimal trajectory has been presented.”