Recent advances on optimization for control, observation, and safety

Abstract

Mathematical optimization is the selection of the best element in a set with respect to a given criterion. Optimization has become one of the most commonly used tools in modern control theory to compute control laws, adjust the controller parameters (tuning), estimate unmeasured states, find suitable conditions to fulfill a given closed-loop property, carry out model fitting, among others. Optimization is also used in the design of fault detection and isolation systems, due to the complexity of automated installations and to prevent safety hazards and huge production losses that require the detection and identification of any kind of fault, as early as possible, as well as the minimization of their impacts by implementing real-time fault detection and fault-tolerant operations systems where optimization algorithms play an important role. Recently, it has been proved that many optimization problems with convex objective functions and linear matrix inequality (LMI) constraints can be solved efficiently using existing software, which increases the flexibility and applicability of the control algorithms. Therefore, real-world control systems need to comply with several conditions and constraints that have to be taken into account in the problem formulation, which represents a challenge in the application of the optimization algorithms. This special issue aims at offering an overview of the state-of-the-art of the most advanced (online and offine) optimization techniques and their applications in control engineering.