Data-driven dissipativity analysis with quadratic difference form supply-rate functions and its applications

Dissipativity property is a concept introduced in the early 70s by Jan C. Willems, to describe the input-output behaviour of a dissipative system. The main idea of this concept follows the energy conservation laws, where the rate change of a system's energy function, called storage function, is upper bounded by the power or work done to the system, commonly referred to as the supply-rate function. We call the inequality that describe this behavior as dissipativity inequality. As most real-world applications belong to the class of dissipative systems, investigating theoretical methods to analyse and deal with such systems can be the base of many practical solutions, for instance fault detection. In this thesis, we specifically investigate the verification of dissipativity properties of unknown LTI (linear time invariant) systems using input-output data and the application of the approach to a fault detection method. For validating our theoretical results, we apply the proposed methods in numerical simulations and practical real-world applications. The first practical application concerns to an educational two-degree-of-freedom planar manipulator from Quanser. Using data obtained from experiments using this manipulator, we are able to verify the dissipativity and subsequently apply the proposed fault detection algorithm and observe its advantages when comparing it to a standard principal component analysis algorithm. The second main practical study case is an ultra-high vacuum chemical vapor deposition (UHVCVD) process

Data-driven dissipative verification of LTI systems:Multiple shots of data, QDF supply-rate and application to a planar manipulator

We present a data-driven dissipative verification method for LTI systems based on using multiple input-output data. We assume that the supply-rate functions have a quadratic difference form corresponding to the general dissipativity notion known in the behavioural framework. We validate our approach in a practical example using a two-degree-of-freedom planar manipulator from Quanser, with which we demonstrate the applicability of multiple datasets over one-shot of data recently proposed in the literature

Direct data-driven signal temporal logic control of linear systems

Most control synthesis methods under temporal logic properties require a model of the system, however, identifying such a model can be a challenging task for complex systems. In this paper, we develop a direct data-driven controller synthesis method for linear systems subject to a temporal logic specification, which does not require this explicit modeling step. After collecting a single sequence of input-output data from the system, we construct a data-driven characterization of the system behavior. Using this data-driven characterization we show that we can synthesize a controller, such that the controlled system satisfies a signal temporal logic-based specification. The underlying optimization problem is solved by mixed-integer linear programming. We demonstrate applicability of the results through benchmark simulation examples.Comment: Submitted to the 62nd IEEE Conference on Decision and Control (CDC2023

Data-driven Economic NMPC using Reinforcement Learning

Reinforcement Learning (RL) is a powerful tool to perform data-driven optimal control without relying on a model of the system. However, RL struggles to provide hard guarantees on the behavior of the resulting control scheme. In contrast, Nonlinear Model Predictive Control (NMPC) and Economic NMPC (ENMPC) are standard tools for the closed-loop optimal control of complex systems with constraints and limitations, and benefit from a rich theory to assess their closed-loop behavior. Unfortunately, the performance of (E)NMPC hinges on the quality of the model underlying the control scheme. In this paper, we show that an (E)NMPC scheme can be tuned to deliver the optimal policy of the real system even when using a wrong model. This result also holds for real systems having stochastic dynamics. This entails that ENMPC can be used as a new type of function approximator within RL. Furthermore, we investigate our results in the context of ENMPC and formally connect them to the concept of dissipativity, which is central for the ENMPC stability. Finally, we detail how these results can be used to deploy classic RL tools for tuning (E)NMPC schemes. We apply these tools on both a classical linear MPC setting and a standard nonlinear example from the ENMPC literature

Guaranteed H∞\mathcal{H}_\infty performance analysis and controller synthesis for interconnected linear systems from noisy input-state data

The increase in available data and complexity of dynamical systems has sparked the research on data-based system performance analysis and controller design. Recent approaches can guarantee performance and robust controller synthesis based on noisy input-state data of a single dynamical system. In this paper, we extend a recent data-based approach for guaranteed performance analysis to distributed analysis of interconnected linear systems. We present a new set of sufficient LMI conditions based on noisy input-state data that guarantees $\mathcal{H}_\infty$ performance and have a structure that lends itself well to distributed controller synthesis from data. Sufficient LMI conditions based on noisy data are provided for the existence of a dynamic distributed controller that achieves $\mathcal{H}_\infty$ performance. The presented approach enables scalable analysis and control of large-scale interconnected systems from noisy input-state data sets

Distributed Learning of Neural Lyapunov Functions for Large-Scale Networked Dissipative Systems

This paper considers the problem of characterizing the stability region of a large-scale networked system comprised of dissipative nonlinear subsystems, in a distributed and computationally tractable way. One standard approach to estimate the stability region of a general nonlinear system is to first find a Lyapunov function for the system and characterize its region of attraction as the stability region. However, classical approaches, such as sum-of-squares methods and quadratic approximation, for finding a Lyapunov function either do not scale to large systems or give very conservative estimates for the stability region. In this context, we propose a new distributed learning based approach by exploiting the dissipativity structure of the subsystems. Our approach has two parts: the first part is a distributed approach to learn the storage functions (similar to the Lyapunov functions) for all the subsystems, and the second part is a distributed optimization approach to find the Lyapunov function for the networked system using the learned storage functions of the subsystems. We demonstrate the superior performance of our proposed approach through extensive case studies in microgrid networks