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Control Synthesis given Temporal Logic Specifications using Mixed Logic Dynamical Systems



Damian Frick, Tony Wood, Maryam Kamgarpour

    An approach to capture complex motion planning specifications for a dynamical system is to use the framework of automata theory. One can then synthesize a controller such that the state trajectory is accepted by the automaton, and thus, the required specification is satisfied. An example of such automaton is shown in the figure below where we capture the specification of reaching a goal set (G) after passing through an intermediate set (B) and while always staying inside safe subset (S) of the state space. The goal of this project is to develop a mixed logical dynamic system framework for control synthesis for specifications defined by automaton.

Project Description
    The specific tasks are as follows. First, the student will understand about temporal logic specifications and their connection with finite state automata. Then, she/he will translate general motion planning specifications, such as the one shown below, as automata. Next, a framework for representing the specification together with the dynamical system as a mixed logic dynamical (MLD) system will be developed. The student will research the theory and numerical algorithms for this class of systems. She/he will develop an approach to synthesize a controller that satisfies the specification using the MLD description, while minimizing an objective function. The objective function could be, for example, the time to satisfy the specification or the control effort. Additionally, we will explore inclusion of uncertainty in the dynamical system model or in the environment. Consequently, we will address solving a robust MLD problem, using branch & bound optimization technique. Finally, there is a potential to implement the developed framework on the IfA race car platform.

Required Skills
    control systems, optimization, Matlab.

Acquired Skills
    hybrid systems control, control synthesis based on automaton specification, robust control, numerical optimization

Weitere Informationen

Maryam Kamgarpour

Art der Arbeit:
Anzahl StudentInnen:
Status: taken