A technique to design controllers for nonlinear systems from data consists of letting the controllers learn the nonlinearities, cancel them out and stabilize the closed-loop dynamics. When control and nonlinearities are unmatched, the technique leads to an approximate cancellation and local stability results are obtained. In this paper, we show that, if the system has some structure that the designer can exploit, an iterative use of the data leads to a globally stabilizing controller even when control and nonlinearities are unmatched.@en

We consider data-driven control of input-affine systems via approximate nonlinearity cancellation. Data-dependent semi-definite program is developed to characterize the stabilizer such that the linear dynamics of the closed-loop systems is stabilized and the influence of the nonlinear dynamics is decreased. Because of the additional nonlinearity brought by the state-dependent input vector field, nonlinearity cancellation is more difficult to achieve. We show that under some assumptions on the nonlinearity, the nonlinearity cancellation control approach can render the equilibrium locally asymptotically stable even if the additional nonlinearity is neglected. Data-based estimation of the region of the attraction is also presented.@en

We consider continuous-time equilibrium seeking in a class of aggregative games with strongly convex cost functions and affine coupling constraints. We propose simple, semi-decentralized integral dynamics and prove their global asymptotic convergence to a variational generalized aggregative or Nash equilibrium. The proof is based on Lyapunov arguments and invariance techniques for differential inclusions.@en

Lyapunov’s indirect methodLyapunovindirect method is one of the oldest and most popular approaches to model-based controller design for nonlinear systemsNonlinearsystem. When the explicit model of the nonlinear systemNonlinearsystem is unavailable for designing such a linear controller, finite-length off-line data is used to obtain a data-based representation of the closed-loop system, and a data-driven linear control law is designed to render the considered equilibrium locally asymptotically stable. This work presents a systematic approach for data-driven linear stabilizer design for continuous-time and discrete-time general nonlinear systemsNonlinearsystem. Moreover, under mild conditions on the nonlinear dynamics, we show that the region of attractionRegion of attraction of the resulting locally asymptotically stable closed-loop system can be estimated using data.@en

This paper outlines a method in which the heat production of a geothermal system is controlled in relation to the demand from a district-heating network. A model predictive control strategy is designed, which uses volume measurements in the storage tank, and predictions of the demand, to regulate the production of the geothermal system in real time. The implications of such time-varying production for the reservoir are investigated using a 2D reactive transport reservoir model. As a case study, the Groningen geothermal project is considered. The numerical data generated by the controller, in closed loop with a modelled district-heating network, are used as inputs for the reservoir simulations. The latter make use of discrete parameter analyses to evaluate the effect of pressure depletion, reservoir permeability, flow rate, re-injection temperature and injection pH on the geothermal reservoir, and also mitigate possible risks during development. Using a model predictive control does not create adverse geochemical effects in the reservoir; instead, the controller is able to improve the efficiency of the geothermal heat extraction. The findings pave the way for stronger integration between elements of heat networks and a more sustainable development of geothermal resources.@en

This paper outlines a method in which the heat production of a geothermal system is controlled in relation to the demand from a district-heating network. A model predictive control strategy is designed, which uses volume measurements in the storage tank, and predictions of the demand, to regulate the production of the geothermal system in real time. The implications of such time-varying production for the reservoir are investigated using a 2D reactive transport reservoir model. As a case study, the Groningen geothermal project is considered. The numerical data generated by the controller, in closed loop with a modelled district-heating network, are used as inputs for the reservoir simulations. The latter make use of discrete parameter analyses to evaluate the effect of pressure depletion, reservoir permeability, flow rate, re-injection temperature and injection pH on the geothermal reservoir, and also mitigate possible risks during development. Using a model predictive control does not create adverse geochemical effects in the reservoir; instead, the controller is able to improve the efficiency of the geothermal heat extraction. The findings pave the way for stronger integration between elements of heat networks and a more sustainable development of geothermal resources.@en

This paper outlines a method in which the heat production of a geothermal system is controlled in relation to the demand from a district-heating network. A model predictive control strategy is designed, which uses volume measurements in the storage tank, and predictions of the demand, to regulate the production of the geothermal system in real time. The implications of such time-varying production for the reservoir are investigated using a 2D reactive transport reservoir model. As a case study, the Groningen geothermal project is considered. The numerical data generated by the controller, in closed loop with a modelled district-heating network, are used as inputs for the reservoir simulations. The latter make use of discrete parameter analyses to evaluate the effect of pressure depletion, reservoir permeability, flow rate, re-injection temperature and injection pH on the geothermal reservoir, and also mitigate possible risks during development. Using a model predictive control does not create adverse geochemical effects in the reservoir; instead, the controller is able to improve the efficiency of the geothermal heat extraction. The findings pave the way for stronger integration between elements of heat networks and a more sustainable development of geothermal resources.@en

This paper outlines a method in which the heat production of a geothermal system is controlled in relation to the demand from a district-heating network. A model predictive control strategy is designed, which uses volume measurements in the storage tank, and predictions of the demand, to regulate the production of the geothermal system in real time. The implications of such time-varying production for the reservoir are investigated using a 2D reactive transport reservoir model. As a case study, the Groningen geothermal project is considered. The numerical data generated by the controller, in closed loop with a modelled district-heating network, are used as inputs for the reservoir simulations. The latter make use of discrete parameter analyses to evaluate the effect of pressure depletion, reservoir permeability, flow rate, re-injection temperature and injection pH on the geothermal reservoir, and also mitigate possible risks during development. Using a model predictive control does not create adverse geochemical effects in the reservoir; instead, the controller is able to improve the efficiency of the geothermal heat extraction. The findings pave the way for stronger integration between elements of heat networks and a more sustainable development of geothermal resources.@en

In this paper, we consider continuous-time semidecentralized dynamics for the equilibrium computation in a class of aggregative games. Specifically, we propose a scheme where decentralized projected-gradient dynamics are driven by an integral control law. To prove global exponential convergence of the proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov function argument. We derive a sufficient condition for global convergence that we position within the recent literature on aggregative games, and in particular we show that it improves on established results.@en

In this paper, we consider continuous-time semidecentralized dynamics for the equilibrium computation in a class of aggregative games. Specifically, we propose a scheme where decentralized projected-gradient dynamics are driven by an integral control law. To prove global exponential convergence of the proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov function argument. We derive a sufficient condition for global convergence that we position within the recent literature on aggregative games, and in particular we show that it improves on established results.@en

Continuous-time gradient-based Nash equilibrium seeking algorithms enjoy a passivity property under a suitable monotonicity assumption, which has been exploited to design distributed Nash equilibrium seeking algorithms. We further exploit the passivity property to interconnect the algorithms with distributed nonlinear averaging integral controllers that tune on-line the weights of the communication graph. The main advantage is to guarantee convergence to a Nash equilibrium without requiring a strong coupling condition on the algebraic connectivity of the communication graph over which the players exchange information, nor a global fixed high-gain.@en