Publication Date


Document Type


Committee Members

Kuldip Rattan (Committee Chair); Matthew Clark (Committee Member); Marian Kazimierczuk (Committee Member)

Degree Name

Master of Science in Electrical Engineering (MSEE)


Modern aircraft with nonlinear flight envelopes predominately utilize gain scheduled controllers to provide stability of flight. Using gain scheduled control techniques, nonlinear envelopes can be linearized into collections of linear systems that operate under various system dynamics. Linear controllers approximate the nonlinear response over setpoints of operating conditions which allow traditional linear theory to be applied to maintain stability. Techniques to prove linear stability are well understood and realized in control systems, but when controllers are switched, interpolation methods must be used. Interpolation is necessary as gain scheduled systems do not have foundational switching paradigms as part of their realization and therefore can not naturally guarantee smooth (or stable) transitions. To ensure stability between linear controllers, empirical data must be obtained through test and simulation which adds significant time and fiscal cost to development. This work examines if fuzzy controllers can provide similar response to that of gain scheduled controllers. By representing controllers as fuzzy representations, transitions between the designed linear setpoints can be smoothed by adding membership functions between defined linear controllers. However, fuzzy control lacks analytical tools to find the stability margins to test the stability of fuzzy systems. In order to provide assurance of stability and performance concerns, fuzzy controllers are translated into hybrid automata representations. Hybrid Automata (HA) theory, which is gaining popularity to represent cyber-physical systems (CPS), is an extension of finite state machines (finite automata) which blends continuous dynamics with discrete switching conditions. The hybrid representation of the fuzzy system allows reachability tools and formal methods to examine stability and desired performance characteristics. This provides evidence that a fuzzy controller can produce, at a minimum, an equally effective controller. The goal of this effort is to establish a process to use fuzzy controller design and reachability tools to provide evidence of control system key attributes. The work primarily focuses on using two reachability tools which capture flow-pipe construction in linear models. The first, SpaceEx, uses representations of continuous sets to compute an overapproximation of the reachable states. The second, HyLAA, provides a simulation-equivalent reachability representation. Through reachability evidence generated by these tools, the tested fuzzy systems show that they maintain stability over the entire range of normalized input signal.

Page Count


Department or Program

Department of Electrical Engineering

Year Degree Awarded