Related papers: Synthesizing Control Laws from Data using Sum-of-S…
Computing a stabilizing static output-feedback (SOF) controller is an NP-hard problem, in general. Yet, these controllers have amassed popularity in recent years because of their practical use in feedback control applications, such as fluid…
In this paper we use SOS and SDP to design output feedback controllers for a class of one-dimensional parabolic partial differential equations with point measurements and point actuation. Our approach is based on the use of SOS to search…
This paper deals with fractional-order controllers. We outline mathematical description of fractional controllers and methods of their synthesis and application. Synthesis method is a modified root locus method for fractional-order systems…
Safety is closely related to set invariance for dynamical systems. However, synthesizing a safe invariant set and at the same time synthesizing the associated safe controller still remains challenging. In this note we introduce a simple…
The Sum-of-Squares (SOS) approximation method is a technique used in optimization problems to derive lower bounds on the optimal value of an objective function. By representing the objective function as a sum of squares in a feature space,…
In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…
The problem under consideration is the synthesis of a distributed controller for a nonlinear network composed of input affine systems. The objective is to achieve exponential convergence of the solutions. To design such a feedback law,…
This paper develops a data-driven safe control framework for linear systems possessing a known strict-feedback structure, but with most plant parameters, external disturbances, and input delay being unknown. By leveraging Koopman operator…
Recent advances in learning techniques have enabled the modelling of unknown dynamical systems directly from data. However, in many contexts, these learning-based methods are short of safety guarantee and strict stability verification. To…
In recent years data-driven analysis of dynamical systems has attracted a lot of attention and transfer operator techniques, namely, Perron-Frobenius and Koopman operators are being used almost ubiquitously. Since data is always obtained in…
This paper considers the problem of learning control laws for nonlinear polynomial systems directly from the data, which are input-output measurements collected in an experiment over a finite time period. Without explicitly identifying the…
In recent years, the success of the Koopman operator in dynamical systems analysis has also fueled the development of Koopman operator-based control frameworks. In order to preserve the relatively low data requirements for an approximation…
Automated proving of polynomial inequalities is a fundamental challenge in automated mathematical reasoning, where rich algebraic structure and a rapidly growing certificate search space hinder scalability. Purely symbolic approaches…
We present a new data-driven method to provide probabilistic stability guarantees for black-box switched linear systems. By sampling a finite number of observations of trajectories, we construct approximate Lyapunov functions and deduce the…
This paper presents a convex optimization-based solution to the design of state-feedback controllers for solving the linear quadratic regulator (LQR) problem of uncertain discrete-time systems with multiplicative noise. To synthesize a…
In this paper, we provide a systematic approach for the design of stabilizing feedback controllers for nonlinear control systems using the Koopman operator framework. The Koopman operator approach provides a linear representation for a…
In this paper, we study linearly constrained policy optimization over the manifold of Schur stabilizing controllers, equipped with a Riemannian metric that emerges naturally in the context of optimal control problems. We provide extrinsic…
This paper proposes novel approaches for designing control Lyapunov functions (CLFs) for constrained linear systems. We leverage recent configuration-constrained polyhedral computing techniques to devise piecewise affine convex CLFs.…
Koopman spectral theory has grown in the past decade as a powerful tool for dynamical systems analysis and control. In this paper, we show how recent data-driven techniques for estimating Koopman-Invariant subspaces with neural networks can…
This paper considers the problem of data-driven robust control design for nonlinear systems, for instance, obtained when discretizing nonlinear partial differential equations (PDEs). A robust learning control approach is developed for…