Controllability as a key to predictive control with guaranteed stability

• Applicant: Professor Dr. Moritz Schulze Darup
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: from 2014 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 265894868

Model predictive control (MPC) is an established and powerful tool for the control of dynamical systems.The control scheme excels in the intuitive measure of system performance and the straightforward inclusion of state and input constraints. From a technical point of view, MPC is based on the recurring solution of an optimal control problem (OCP) at each sampling instant. Despite the "optimized" system behavior, it is not necessarily guaranteed that the MPC-scheme is stable. Conventionally, stability is ensured based on the inclusion of a terminal set and a terminal cost in the formulation of the OCP.This workaround is suboptimal in two different aspects. First, the terminal set and the associated constraints restrain the feasibility of the OCP. Second, the terminal cost often dominates the objective function of the OCP with the consequence that the above-mentioned performance measure loses significance. Novel MPC-schemes provide stability guarantees without the usage of a terminal set or cost.Unfortunately, in order to apply these schemes, we need to quantify the controllability of the constrained system (controllability assumption). While the theory of stable MPC based on the controllability assumption is well-developed, the approach is lacking procedures for the practical verification of the mentioned assumption. Consequently, one goal of this research project is the design of methods for the verification of the controllability assumption of constrained systems. To solve this task, we combine tools from reachability analysis and rigorous global optimization with methods for the robust handling of nonlinearities.While the analysis of constrained controllability is demanding, there exist various concepts for the verification of controllability of unconstrained systems (e.g., Kalman's criterion for linear systems or the detection of flatness). Hence, a second goal of this project aims at the usage of unconstrained controllability for the predictive control of constrained systems. Roughly speaking, this approach requires the smart trajectory generation for the unconstrained system with the objective of providing trajectories that are, to some extent, viable for the constrained system. In principle, we are looking for a new approach for the systematic design of control Lyapunov functions (CLF).

• DFG Programme: Research Fellowships
• International Connection: United Kingdom
• Hosts: Professor Mark Cannon; Professor Stephen Duncan