Tube‐based robust economic model predictive control with practical and relaxed stability guarantees and its application to smart grid

Abstract

This article deals with an improved scheme of tube-based robust economic model predictive control (TEMPC). The controller is robust to unknown but bounded disturbances where guarantees recursive feasibility, robust stability, and convergence to the economically optimal operating point. Time-varying economic criteria are considered in the stage cost function of the control design. Initial states of the nominal-nondisturbed-system are considered as decision variables. It lets the controller know more information about the real-disturbance affected-system to take advantage of the recursive horizon approach. It also increases the control degree of freedom and enlarges the region of attraction. Making the closed-loop system work at the economically optimal operating point contradicts with the economic behavior. A convex optimization

On the design of efficient optimal tube‐based robust model predictive control: Quasi‐H∞ approach

“…Example 1. Disturbance affected dynamic system (12) with hard constraints (13) and disturbance bounds (14), discussed as a motivating example in Section 2.1, is again considered. We show how the Quasi-H ∞ optimal TMPC scheme overcomes the described challenges.…”

“…To better show how the TMPC design has been improved in the Quasi-H ∞ optimal TMPC scheme, we investigate the properties of the first, second, and optimal cases over dynamic model (12) with constraints (13) and disturbance bounds (14). The maximum terminal regions of the three cases are computed as Figure 12 and they are considered as the terminal region constraints in the attributed MPC optimization problems.…”

“…In [17], TMPC has been combined with multi‐stage MPC to benefit from the non‐conservatism of the latter approach. TMPC schemes have been recently applied to various fields of industry including process control ([18] and [19]), wind turbine power control [20], robotics [21], autonomous driving [22] and microgrid energy management [14].…”

“…Stochastic TMPC approaches have been designed in [12] and [13] to stabilize linear systems with multiplicative uncertainty or model mismatch besides exogenous disturbances. TMPC has been combined with economic MPC in [14,15], and [16] to directly consider economic criteria within the MPC stage cost function. In [17], TMPC has been combined with multi-stage MPC to benefit from the nonconservatism of the latter approach.…”

Energy shaping dynamic tube-MPC for underactuated mechanical systems

“…A tube-based NMPC for autonomous mobile robots with tire-terrain interactions is presented in [45]. A tube-based MPC with relaxed stability for smart grid is prensented in [49]. A sliding-mode control (SMC) for constrained MPC of non-linear systems is employed in [21].…”