The concept of a fuzzy controller, first introduced by E.H. Mamdani in 1974, was revolutionary and created a new and powerful knowledge-based model-free control paradigm. The underlying idea was to construct a nonlinear controller without a mathematical model of the system to be controlled. Instead, fuzzy sets, fuzzy logic, fuzzy rules, and fuzzy reasoning are used to intuitively capture, represent, and process a human operator's control strategy in order to build a controller. This is sensible because system behavior and dynamics are reflected in human control expertise and therefore implicitly utilized in the controller design. This paradigm has proven to be successful in a variety of real-world applications and commercial products since the early 1980s. 

Not requiring a mathematical model in controller design significantly reduces product development time and cost, making the paradigm more practically useful than model-based control approaches. It is challenging to attain an accurate mathematical model for any real-world system, and modeling efforts are typically time-consuming and costly. This is partially because finding a plausible mathematical model structure is a difficult task to begin with, and validating it is another challenge. This explains why the PID controller, a simple, century-old model-free controller, is controlling more than 90% of control system applications worldwide, despite the existence of numerous model-based control theories developed over many decades.

The knowledge-based model-free approach, while practical, lacks mathematical rigor, which has limited its acceptance. A fuzzy controller is widely treated as a black box whose input-output analytical structure is unknown. To bridge this gap, we have developed a mathematical model-free fuzzy control theory that provides a rigorous and insightful perspective on the behavior and effectiveness of fuzzy controllers.

In this presentation, we will explore the benefits of our approach by discussing example type-1 and interval type-2 fuzzy controllers, and demonstrating how to derive their analytical structures. With this information, we can gain a deeper understanding of how and why fuzzy controllers work and identify connections between fuzzy controllers and conventional controllers. We will also examine the differences between type-1 and interval type-2 fuzzy controllers, and their relative merits and pitfalls. With this approach, we can encourage acceptance of fuzzy control in safety-critical fields, such as medicine and nuclear engineering, where black box controllers are not currently acceptable.

Complemented with other fuzzy control approaches, our model-free fuzzy control theory
is mathematically rigorous and offers unique analysis and design tools not available elsewhere.

Rule based fuzzy systems have progressed from using type-1 fuzzy sets, to interval type-2 fuzzy sets, to general type 2 fuzzy sets, etc. In this talk I will highlight the potential benefits for using (why use?) each of these fuzzy systems, and will then focus on why it
may/should be possible to obtain even better performance out of type-1 and interval type-
2 fuzzy systems than is currently demonstrated. This is important because designers of
more advanced fuzzy systems arguably need to compare performance from such
advanced fuzzy systems with the best designed simpler kind of fuzzy system. Why?
Because advanced fuzzy systems are more complicated to understand and design, so their use in real world applications must be fully justified. More needs to be done, and some
suggestions will be provided.

Optimization problems are ubiquitous, finding applications in numerous real-life situations. Multi-objective optimization problems (MOPs) are ones that require simultaneous optimization of multiple conflicting objectives such that improving solutions in terms of one objective leads to deterioration in terms of one or more of the other objectives. In MOPs, the target is to arrive at the best trade-off surface, called the Pareto optimal front. Population based metaheuristics find favor in solving MOPs because of their ability to work with multiple solutions at the same time. Multi-modal MOPs (MMMOPs) are those where a many-to-one mapping exists from solution space to objective space. As a result, multiple subsets of the Pareto-optimal set could independently generate the same Pareto-Front. The discovery of such equivalent solutions across the different subsets is essential during decision-making to facilitate the analysis of their non-numeric, domain-specific attributes. 

In this talk, we will first provide a brief introduction to MOPs and discuss some metaheuristics for solving them. Applications in clustering and in drug design will be demonstrated. We will then discuss the basic concept of multi-modality in MOPs and describe the crowding illusion problem. A method for solving MMMOPs with a graph Laplacian-based Optimization using Reference vector assisted Decomposition (LORD) will thereafter be described. The talk will conclude with the brief discussion of an application of MMMOPs to the problem of building energy optimization.