Propositional logic in control and monitoring problems

doi:10.1016/S0005-1098(98)00198-8

Automatica

Volume 35, Issue 4, April 1999, Pages 565-582

https://doi.org/10.1016/S0005-1098(98)00198-8 Get rights and content

Abstract

By using linear constraints on integer variables, logical inference can be incorporated within model predictive control and model-based detection problems resulting in mixed integer quadratic or mixed integer linear programming problems. Qualitative knowledge can be used to prioritize control objectives, or to improve performance of detection schemes. This article demonstrates some capabilities of combining logic using integer variables with quantitative models.

References (0)

Cited by (104)

Lexicographic optimization for economic model predictive control with zone tracking
2023, Chemical Engineering Research and Design
Tracking model predictive control (MPC) and economic model predictive control (EMPC) are essential techniques in process control. Economic model predictive control with zone tracking offers an effective means of concurrently addressing both tracking MPC and EMPC objectives. However, the aggregated conflicting objectives do not always align with the prioritization of critical tasks, such as safety, stability, quality, and economy. To address this issue, this study introduces a lexicographic approach for EMPC with zone tracking, which aims at balancing the competing zone tracking and economic objectives. The work also explores a generalized lexicographic multi-objective MPC (MoMPC) formulation and presents lexicographic zone economic model predictive control to accommodate multiple tracking and economic objectives. The advantages, disadvantages, and effectiveness of the proposed approach are validated and showcased through extensive simulation experiments.
Lexicographic multi-objective MPC for constrained nonlinear systems with changing objective prioritization
2021, Automatica
This paper proposes a new lexicographic multi-objective model predictive control (MoMPC) scheme for constrained nonlinear systems with changing objective prioritization. The lexicographic optimization-based receding horizon optimal control problem is firstly formulated to accommodate the concern on prioritized control of multiple (economic) objectives. Then an elaborate generic function and the notion of general terminal constraints are introduced to regain feasibility of lexicographic MoMPC in the presence of constraints and changing objective prioritization. Moreover, the LaSalle invariance set theorem is used to establish stability of the closed-loop system with the lexicographic MoMPC. An example of a coupled-tank level control problem with three conflicting objectives is adopted to demonstrate the effectiveness of the proposed scheme.
Propositional logic concept for fault diagnosis in complex systems
2020, Engineering Science and Technology, an International Journal
Citation Excerpt :
The propositional logic is used in many areas in the industry and it is also a logical representation of the system especially in complex structures [1–4].
A great number of monitoring technologies have been developed especially for complex systems within the critical zones such as electric power substations, nuclear energy systems. But also, there is no single instruction or standardization in fault-focused on-line/off-line monitoring applications due to the acceleration of technological developments. Field experts have difficulty in choosing which test and measurement systems should be used in which stage of the complex systems. In this study, the propositional logic-based concept is presented, which field experts can use to manage this process. In this concept, test and measurement systems can be grouped according to the priority-order. According to the results of the graded groups on this concept, the suspected fault is verified by the cause of the occurrence. The applicability of the proposed concept has been tried to be explained by creating possible failure scenarios on the transformer. The theoretically validated concept can be used for even more fault situations. This concept can also be used in another complex systems with a large number of T&M systems where very different fault conditions can occur. 2009 Elsevier Ltd. All rights reserved.
Optimizing multi-modal cancer treatment under 3D spatio-temporal tumor growth
2019, Mathematical Biosciences
In this paper we introduce a new mixed-integer linear programming (MIP) model that explicitly integrates the spread of cancer cells into a spatio-temporal reaction-diffusion (RD) model of cancer growth, while taking into account treatment effects. This linear but non-convex model appears to be the first of its kind by determining the optimal sequence of the typically prescribed cancer treatment methods—surgery (S), chemotherapy (C), and radiotherapy (R)—while minimizing the newly generated tumor cells for early-stage breast cancer in a unique three-dimensional (3D) spatio-temporal system. The quadratically-constrained cancer growth dynamics and treatment impact formulations are linearized by using linearization as well as approximation techniques. Under the supervision of medical oncologists and utilizing several literature resources for the parameter values, the effectiveness of treatment combinations for breast cancer specified with different sequences (i.e., SRC, SCR, CR, RC) are compared by tracking the number of cancer cells at the end of each treatment modality. Our results provide the optimal dosages for chemotherapy and radiation treatments, while minimizing the growth of new cancer cells.
Lexicographic MPC with multiple economic criteria for constrained nonlinear systems
2018, Journal of the Franklin Institute
Many control problems in process systems feature multi-objective optimization problems that involve several and often conflicting objective functions, such as economic profit and environmental concerns. In this paper, we consider a class of multi-objective model predictive control (MO-MPC) problems where nonlinear systems are subject to state and control constraints and multiple economic criteria are conflicting. Using the lexicographic optimization, we propose a prioritized MO-MPC scheme with guaranteed stability for economic optimization. At each sampling time, the MPC action is computed by solving a set of sequentially ordered single objective optimized control problems. Some sufficient conditions are established to ensure recursive feasibility and asymptotic stability of the MO-MPC in the context of economic criteria optimization. Two examples of multi-objective control of a coupled-tank system and a free-radical polymerization process are exploited to illustrate the effectiveness of the proposed MPC scheme and to evaluate the performance by some comparison experiments.
Robust tube-based MPC of constrained piecewise affine systems with bounded additive disturbances
2017, Nonlinear Analysis: Hybrid Systems
Citation Excerpt :
In recent years, control of hybrid systems using Model Predictive Control (MPC) schemes has received an increased attention [1]. Firstly, in [2], and then in [3], it was set out to establish a framework for modeling and controlling of hybrid systems, namely mixed logical dynamical (MLD) models, that can be used in model predictive control. Another popular type of model for hybrid systems used in MPC is piecewise affine (PWA) model [4,5].
In this article, we propose a robust tube-based MPC formulation for a class of hybrid systems, namely autonomously switched PWA systems, with bounded additive disturbances. The term tube-based refers to those control techniques whose objective is to maintain all possible trajectories of the uncertain system inside a tube which is a set around the nominal (or reference) system trajectory, that is free from disturbances. Common methods in tube-based control systems consider an error dynamical system as the difference between the state of the nominal system and the state of the perturbed system. However, this definition of the error dynamical system leads to a complicated switched affine system for PWA systems. Therefore, we use a new notion of the reference system similar to the nominal system except that the switching between the various modes of the PWA system is driven by the state of the real system. Using this reference system instead of the nominal system leads us to an error dynamical system that can be modeled as a switched linear system. We employ a switched linear controller to stabilize this error system under arbitrary switching. This auxiliary controller forces the states of the uncertain system to remain in a tube confined to the invariant set around the state of the reference system. We add new constraints and tighten some other constraints of the nominal hybrid MPC for the reference system, in order to ensure convergence of the uncertain system and to guarantee robust exponential stability of the closed-loop system.

View all citing articles on Scopus

^☆: This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor P. Fleming under the direction of Editor S. Skogestad.

¹: Supported by Fannie and John Hertz Foundation.

View full text

Propositional logic in control and monitoring problems☆

Abstract