Robust explicit model predictive control via regular piecewise-affine approximation

Abstract

This paper proposes an explicit model predictive control design approach for regulation of linear time-invariant systems subject to both state and control constraints, in the presence of additive disturbances. The proposed control law is implemented as a piecewise-affine function defined on a regular simplicial partition, and has two main positive features. Firstly, the regularity of the simplicial partition allows one to efficiently implement the control law on digital circuits, thus achieving extremely fast computation times. Moreover, the asymptotic stability (or the convergence to a set including the origin) of the closed-loop system can be enforced a-priori, rather than checked a-posteriori via Lyapunov analysis.

Explicit model predictive control through robust optimization

“…We assume that a matrix Φ consists of elements ϕ i,j , then jΦj consist of elements jϕ i,j j. In contrast to classic mpMPC formulations, the considered model is uncertain and depends on the scalars ϵ α and ϵ β that are used to form a box uncertainty set and is described in Equations ( 2)- (5). Specifically, apart from the deterministic B respectively.…”

“…In an effort to address this challenge within the mpMPC literature, strategies that account for additive and multiplicative (parametric) uncertainty have been developed. For models with additive uncertainty, the research focus of the contribution of Sakizlis et al 2 was on finding the worst‐case uncertainty value of the constraint set through the use of flexibility analysis tools, Kerrigan and Maciejowski 3 solved a min‐max problem to derive a robust solution, in Rodríguez‐Ayerbe and Olaru 4 a nominal explicit control law was found which is subsequently robustified to account for disturbances, while Rubagotti et al 5 created approximate robust control laws over simplicial partitions of the state space. Other contributions include the utilization of adjustable robust optimization 6 or tube MPC approaches that took advantage of multiparametric programming as part of the algorithmic procedure for their online implementation 7 .…”

Intelligent explicit model predictive control based on machine learning for microbial desalination cells

“…Originally, EMPC is proposed to be applied to the linear systems as discussed in previous works. [17][18][19] Similar as the other control algorithms, it is not easy to be expanded into the nonlinear EMPC except for some special nonlinear systems. For example, the optimal control law and stability guarantee can be realized for the unconstrained input-affine system.…”

Globally robust explicit model predictive control of constrained systems exploiting SVM‐based approximation

“…To remedy the first limitation, many approximate methods of EMPC have been proposed such as set membership approximation , vertex control strategy via simplex‐based partition , approximate convex programing , and regular piecewise affine approximation . Although the complexity of partitioning the critical regions is reduced dramatically, it still needs to exploit lookup table online to obtain the piecewise affine control law.…”

“…The first-order KKT conditions lead to a polyhedral feasible state space that usually cannot cover the whole constrained state space. Therefore, no control action exists in the infeasible state space.To remedy the first limitation, many approximate methods of EMPC have been proposed such as set membership approximation [18], vertex control strategy via simplex-based partition [19,20], approximate convex programing [21], and regular piecewise affine approximation [22]. Although the complexity of partitioning the critical regions is reduced dramatically, it still needs to exploit lookup table online to obtain the piecewise affine control law.…”