ProfessorEricKerrigan

CONTROL THEORY AND OPTIMIZATION

My primary focus revolves around developing innovative methods for two critical areas:

(i) Designing Optimization-Based Controllers: I specialise in developing novel approaches for creating controllers that leverage the power of optimization techniques.

(ii) Optimizing Closed-Loop Systems: I'm also interested in optimizing the entire closed-loop system by applying optimization principles.

Model Predictive Control (MPC): Imagine MPC as the rockstar of advanced control methods in various industries. Why? Because it's the ideal tool for handling constraints and nonlinearities in a systematic and optimal fashion. But here's the catch – implementing MPC involves solving a series of real-time challenges. Think of it like solving a complex puzzle on a tight schedule. To tackle these puzzles, we need more powerful computing resources compared to most other control methods. My unique expertise lies in developing novel numerical optimization methods and computer architectures, specially designed to solve the demanding problems posed by constrained and nonlinear optimal control and estimation tasks in real-time.

Optimal Cyber-Physical Co-Design: Here is where things get really interesting. When you consider not just the design of the controller, but also include the parameters of both the computer and physical systems as design variables, magic happens. You can achieve significantly superior performance compared to solely focusing on the controller's design. This is where mathematical optimization shines. It enables us to take a systematic approach to co-design, reducing both the time and cost of the design process. My interest lies in developing innovative multi-objective optimization methods that help us strike the perfect balance between optimization-based control algorithms, computer architectures, and physical designs to meet our performance goals.

APPLICATIONS

My theory and methods are supported by cross-disciplinary applications. The aim is to not only use control and optimization to develop new fundamental insights and open up possibilities in these application areas, but also to use these applications to motivate the development of novel control and optimization methods.

Information systems: Consider the scheduling of multi-processor computer and communication networks. These complex systems can often be boiled down to constrained, nonlinear optimal control problems. My focus is on creating optimal control methods that integrate the computation, communication, and propulsion for aerial robotic information-gathering networks. We're breaking new ground in solving problems that traditional approaches cannot solve.

Aerospace systems: From reducing aerodynamic drag to mitigating gust loads on wind turbine blades, from small satellites to energy-harvesting autonomous gliders, aerospace is a playground for innovation. In this arena, we're developing efficient optimization methods tailored for MPC, crafting models that blend physics-based knowledge with data for streamlined design, and devising optimization techniques that combine controller design with physical parameter design, such as aerofoil shape and the sizing and placement of energy sources, sensors, and actuators.

More on Optimal Co-design and Control

Cyber-physical systems (CPS) are a fusion of the physical and digital worlds, where computations influence physical processes and vice versa, creating a closed-loop system.

The key questions in CPS design are when, where, and how to measure, compute, communicate, and store data. My team is on a mission to answer these questions by developing control systems theory and mathematical optimization methods. These cutting-edge approaches allow us to seamlessly design algorithms, computer architecture, and physical systems together, resulting in smarter, more efficient, and environmentally friendly CPSs. This is in stark contrast to traditional methods where subsystems are independently designed and optimized.

The challenge in CPS co-design is bridging the gap between physics and computer science. Physics relies on differential equations and continuous mathematics, while computer science thrives on logical operations, discrete mathematics, and digital data. Furthermore, during computation, time keeps ticking, and the system continues evolving based on the laws of physics. This demands a delicate trade-off between system performance, robustness, physical resources, and the timing and accuracy of measurements, communications, computations, and model fidelity.

Our ongoing efforts are geared towards:

(i) Understanding and Leveraging Hybrid and Real-Time Nature: CPS is a complex blend of continuous and discrete elements, and we're crafting methods to harness this hybrid and real-time nature.

(ii) Tackling Non-Smooth and Uncertain Mathematical Optimization Problems: During co-design, we often encounter mathematical optimization problems that are anything but straightforward. Our goal is to model and solve these problems effectively.

(iii) Real-Time Optimization on Embedded and Distributed Computing Systems: We're developing solutions to enable real-time execution of constrained and nonlinear optimization algorithms, even on embedded and distributed computing systems.

In essence, our team members combine theory, innovation, and practical applications to redefine what's possible in the realm of control theory and optimization.

Software

ICLOCS: Solves nonlinear optimal control problems subject to constraints.