Huu-Thinh Do

Huu-Thinh Do, Ionela Prodan

The concept of positively invariant (PI) sets has proven effective in the formal verification of stability and safety properties for autonomous systems. However, the characterization of such sets is challenging for nonlinear systems in general, especially in the presence of constraints. In this work, we show that, for a class of feedback linearizable systems, called differentially flat systems, a PI set can be derived by leveraging a neural network approximation of the linearizing mapping. More specifically, for the class of flat systems, there exists a linearizing variable transformation that converts the nonlinear system into linear controllable dynamics, albeit at the cost of distorting the constraint set. We show that by approximating the distorted set using a rectified linear unit neural network, we can derive a PI set inside the admissible domain through its set-theoretic description. This offline characterization enables the synthesis of various efficient online control strategies, with different complexities and performances. Numerical simulations are provided to demonstrate the validity of the proposed framework.

Huu-Thinh Do, Ionela Prodan, Florin Stoican

Neural networks have proven practical for a synergistic combination of advanced control techniques. This work analyzes the implementation of rectified linear unit neural networks to achieve constrained control in differentially flat systems. Specifically, the class of flat systems enjoys the benefit of feedback linearizability, i.e., the systems can be linearized by means of a proper variable transformation. However, the price for linearizing the dynamics is that the constraint descriptions are distorted geometrically. Our results show that, by using neural networks, these constraints can be represented as a union of polytopes, enabling the use of mixed-integer programming tools to guarantee constraint satisfaction. We further analyze the integration of the characterization into efficient settings such as control Lyapunov function-based and model predictive control (MPC). Interestingly, this description also allows us to explicitly compute the solution of the MPC problem for the nonlinear system. Several examples are provided to illustrate the effectiveness of our framework.