Robust economic model predictive control based on a periodicity constraint

Abstract

This paper proposes robust economic model predictive control based on a periodicity constraint for linear systems subject to unknown-but-bounded additive disturbances. In this economic MPC design, a periodic steady-state trajectory is not required and thus assumed unknown, which precludes the use of enforcing terminal state constraints as in other standard economic formulations. Instead, based on the desired periodicity of system operation, we optimize the economic performance over a set of periodic trajectories that include the current state. To achieve robust constraint satisfaction, we use a tube-based technique in the economic MPC formulation. The mismatches between the nominal model and the closed-loop system with perturbations are limited using a local control law. With the proposed robust tube-based strategy, recursive feasibility is guaranteed. Moreover, under a convexity assumption, the closed-loop convergence of the closed-loop system is analyzed, and an optimality certificate is provided to check if the closed-loop trajectory reaches a neighborhood of the optimal nominal periodic steady trajectory using Karush-Kuhn-Tucker optimality conditions. Finally, through numerical examples, we show the effectiveness of the proposed approach.KEYWORDS convex optimization, economic MPC, linear uncertain systems, periodic operation 3296

Robust Economic Model Predictive Control Based on a Zonotope and Local Feedback Controller for Energy Dispatch in Smart-Grids Considering Demand Uncertainty

“…The two proposed robust economic MPC strategies the Open-loop and Closed-loop approaches as well as the nominal approach (i.e., neglecting uncertain demands) have been implemented with YALMIP [14,32] using CPLEX solver in the Matlab environment. The local contol law K defined in (43) for the Robust Closed-loop approach is computed using the LQR method as proposed in [33] obtaining K = 0.0667 0 0 0 0 0 0 0 0 0 0.0667 0 0 0 0 0 0 0 (68) Two different Cases have been taken into account in the simulations: Case 1 (low and medium demand uncertainty) and Case 2 (high demand uncertainty). Demand uncertainty bounds ∆θ 1 = ∆θ 2 = 0.4 kW and ∆θ 1 = ∆θ 2 = 0.7 kW were considered in Case 1 and Case 2 respectively.…”

Advances in State Estimation, Diagnosis and Control of Complex Systems

“…Also under convexity assumption, robust stability of the closed-loop system is analyzed using KKT optimality conditions and an optimality certificate is provided to check if the closed-loop trajectories reach a neighborhood of optimal nominal periodic steady trajectories. The contributions of this chapter have been published and submitted to [157] and [136], respectively.…”

A New Observer-based Model- Reference Approach for Nonlinear Discrete-Time Systems with Application to Power Systems

“…Model-reference adaptive control design techniques have been recently developed and applied to many practical control systems such as robotics [1], economics [2], neural networks [3], power systems [4] …etc. The main idea of the approaches presented in the literature is to stabilize the error between the system of interest and the model to be followed to the zero steady states while using different design strategies [5].…”