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In this paper we show how to extend KEM, a tableau-like proof system for normal modal logic, in order to deal with classes of non-normal modal logics, such as monotonic and regular, in a uniform and modular way.

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In this chapter, we directly design a state feedback controller that stabilizes a class of uncertain nonlinear systems solely based on input-state data collected from a finitelength experiment. Necessary and sufficient conditions are derived to guarantee that the system is absolutely stabilizable and a controller is designed. Results derived under some relaxed prior information about the system, strengthened data assumptions are also discussed. All the results are based on semi-definite programs that depend on input-state data only, which -once solved -directly return controllers. As such they represent end-to-end solutions to the problem of learning control from data for an important class of nonlinear systems. Numerical examples illustrate the method with different levels of prior information.This chapter has been published in "On data-driven stabilization of systems with nonlinearities satisfying quadratic constraints.

We consider the problem of designing an invariant set using only a finite set of input-state data collected from an unknown polynomial system in continuous time. We consider noisy data, i.e., corrupted by an unknown-but-bounded disturbance. We derive a data-dependent sum-of-squares program that enforces invariance of a set and also optimizes the size of the invariant set while keeping it within a set of user-defined safety constraints; the solution of this program directly provides a polynomial invariant set and a state-feedback controller. We numerically test the design on a system of two platooning cars.