Controls, Dynamical Systems and Estimation

Why controls, dynamical systems and estimation?

Control has been a critical technology for aerospace systems since the  very birth of  aviation:  the Wright brothers' first powered flight was successful only because of the presence of warpable wings allowing the pilot to continuously control an otherwise unstable aircraft... Today, control theory, i.e., the principled use of feedback loops and algorithms to steer a system to its goal, is the prime enabler for the design of autonomous vehicle (autopilots, drones, robots, self-driving `smart cars'...), but also the regulation of transportation infrastructures.

Dynamical Systems is an active areas of modern mathematics that deals with the long-term qualitative behavior of trajectories of evolving systems. Bifurcations are “tipping points” where the behavior of a system changes dramatically even though the system's control parameters have changed only slightly. Stochastic bifurcation theory describes the qualitative changes in parameterized families of random dynamical systems (e.g., those generated by a family of stochastic differential equations).

Estimation is concerned with blending the information from observations with the information from dynamical models to estimate the current state of the system or the model parameters. This is also called data assimilation or filtering.

What is going on in dynamical systems & controls research at Illinois AE?

The research conducted in the field of Control in the department ranges from the theoretical to the applied. Several ongoing projects focus on the design of algorithms for the coordination and distributed control of multi-party systems. Others focus on the design of secure guidance and navigation protocols, which can perform adequately even in the presence of possible cyber-breaches.  More theoretical projects are concerned with modeling and data assimilation tools for complex nonlinear systems, as well as game and distributed control theory.

A major part of the research in dynamical systems focuses on developing methods to unravel complex interactions between noise and nonlinearities, using a mix of multidisciplinary approaches from theory, modeling, and simulation. Practical applications of these results are beginning to appear across the entire spectrum of engineering; for example, vibration absorbers, rotating systems, panel flutter, energy harvesters, variable speed machining processes, and mixing and transport phenomena in fluid mechanics. Other ongoing projects study the dynamics and stability of randomly perturbed non-linear oscillators, which find applications, e.g.,  in the design of efficient energy harvesters as well as in improving the stability of the power grid.

Who are the faculty members in the area?

Courses in this Area

• AE 454 - Systems Dynamics & Control
• AE455 - Estimation and Data Assimilation
• AE 483 - Unmanned Aerial Vehicle (UAV) Navigation and Control
• AE 504 - Optimal Aerospace Systems
• AE 554 - Dynamical Systems Theory
• AE555 - Multivariable Control Design
• AE 556 - Robust Control
• ECE 515 - Control System Theory & Design
• ECE 555 - Control of Stochastic Systems
• ME 546 - Analysis of Nonlinear Systems
• ME 561 - Convex Methods in Control