Control theory is a field of applied mathematics concerned with the modeling and control of dynamics in physical and man-made processes and systems. Control theory has applications in engineering, life sciences, economics, sociology, and operation research. Under the broad spectrum of control theory, our focus is on developing new methods for stability, robustness, and optimization-based control of (i) hybrid dynamical systems (in particular, impulsive and switched systems), (ii) systems governed by partial differential equations, (iii) nonlinear systems, (iv) stochastic systems, and (v) time-delay systems. Motivated by modern mathematical methods enabled by the unprecedented availability of data and computational resources, we are also interested in data-driven approaches for complex systems that are not amenable to empirical models or derivations based on first-principles.
Nonlinear systems theory is an active research area, where such questions as stability, robustness, and optimal control are important issues interesting both from theoretical and practical viewpoints. Hybrid systems combine continuous and discontinuous behavior. An important property of hybrid systems is stability that is decisive for their performance and sustainability. In this project, we are focused on developing new non-conservative tools for stability verification.
In many real-world processes, there is an interplay between software and physical components. These processes are vulnerable to malicious cyber-attacks. Attackers can gain access to the network layer and manipulate system measurement data and control input commands to severely compromise system performance. We aim to develop efficient control architectures that foil these malicious sensor and actuator attacks caused by adversarial entities controlling the measurement and actuator devices and recover the system performance.
Impulsive systems are a class of hybrid systems with continuous-time states, the flow, that are exposed to discrete changeovers in time, called jumps. This research proposes an MPC that schedules the optimal jumps at arbitrary discrete times, generating non-periodic jumps for impulsive linear systems. These systems with non-fixed jump times are important due to their ability to model i.a. cyber-physical systems, as for instance multi-agent communication systems.
Efficient implementations of symbolic computation with computer algebra tools presents an important research aspect for the analysis and design of control systems. The goal follows this line by formulating algebraic condition to the system stability and then applying more efficient semi-algebraic techniques to compute the stability region of system in parameter space.
The framework of Linear Parameter Varying (LPV) systems has proven to be a systematic way to model nonlinear real-world phenomena and synthesize gain-scheduled controllers for nonlinear systems. The applications of LPV systems include the automotive industry, turbofan engines, robotics, and aerospace systems.