Related papers: Koopman-based control using sum-of-squares optimiz…
This paper delves into the challenges posed by the increasing complexity of modern control systems, specifically focusing on bilinear systems, a prevalent subclass of non-linear systems characterized by state dynamics influenced by the…
This paper introduces an input-output bilinear Koopman realization with an optimization algorithm of lifting functions. For nonlinear systems with inputs, Koopman-based modeling is effective because the Koopman operator enables a…
We solve the problem of output feedback stabilization of a class of nonlinear systems, which may have unstable zero dynamics. We allow for any globally stabilizing full state feedback control scheme to be used as long as it satisfies a…
This work focuses on developing a data-driven framework using Koopman operator theory for system identification and linearization of nonlinear systems for control. Our proposed method presents a deep learning framework with recursive…
A high order optimal control strategy implemented in the Koopman operator framework is proposed in this work. The new technique exploits the Koopman representation of the solution of the equations of motion to develop an energy optimal…
In this paper, we present a computational approach to certify almost sure reachability for discrete-time polynomial stochastic systems by turning drift--variant criteria into sum-of-squares (SOS) programs solved with standard semidefinite…
This paper develops a semidefinite-programming-based method for online feedback control of nonlinear systems using a state-dependent representation. We formulate sequences of time-varying SDPs whose optimal solutions jointly yield a…
Safety guarantees are valuable in the control of walking robots, as falling can be both dangerous and costly. Unfortunately, set-based tools for generating safety guarantees (such as sums-of-squares optimization) are typically restricted to…
Koopman liftings have been successfully used to learn high dimensional linear approximations for autonomous systems for prediction purposes, or for control systems for leveraging linear control techniques to control nonlinear dynamics. In…
Modularized Koopman Bilinear Form (M-KBF) is presented to model and predict the transient dynamics of microgrids in the presence of disturbances. As a scalable data-driven approach, M-KBF divides the identification and prediction of the…
The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify…
Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…
This paper offers a data-driven approach for designing adaptive suboptimal second-order sliding mode (ASSOSM) controllers for single-input nonlinear systems, characterized by perturbed strict-feedback structures with unknown dynamics. The…
In this paper we use optimization-based methods to design output-feedback controllers for a class of one-dimensional parabolic partial differential equations. The output may be distributed or point-measurements. The input may be distributed…
This paper presents an indirect data-driven output feedback controller synthesis for nonlinear systems, leveraging Structured State-space Models (SSMs) as surrogate models. SSMs have emerged as a compelling alternative in modelling…
The modeling of nonlinear dynamics based on Koopman operator theory, which is originally applicable only to autonomous systems with no control, is extended to non-autonomous control system without approximation to input matrix B. Prevailing…
This paper proposes a dynamic quantum-assisted co-design framework for nonlinear closed-loop systems in which controller parameters and Lyapunov-certificate parameters are redesigned jointly at successive decision epochs. Unlike…
This paper introduces an efficient first-order method based on the alternating direction method of multipliers (ADMM) to solve semidefinite programs (SDPs) arising from sum-of-squares (SOS) programming. We exploit the sparsity of the…
In this paper, we address the problem of safety verification of nonlinear hybrid systems. A hybrid symbolic-numeric method is presented to compute exact inequality invariants of hybrid systems efficiently. Some numerical invariants of a…
Uncertainty in state or model parameters is common in robotics and typically handled by acquiring system measurements that yield information about the uncertain quantities of interest. Inputs to a nonlinear dynamical system yield outcomes…