A learning- and scenario-based MPC design for nonlinear systems in LPV framework with safety and stability guarantees

In this paper, for the first time, a simultaneous design of a model predictive control plan and persistent dwell-time switching signal utilizing the conventional multiple Lyapunov–Krasovskii functional is proposed for linear delayed switched systems that are affected by physical constraints and exogenous disturbances. The conventional multiple Lyapunov–Krasovskii functional with a ‘jump high’ condition is used as a step forward to reduce the strictness of constraints on controller design compared with the switched Lyapunov–Krasovskii functional. However, a dwell-time constraint is inflicted on the switching signal by the ‘jump-high’ condition. Therefore, to decrease the dwell-time limit, the persistent dwell-time structure is used and compared with other structures. Also, a new online framework is proposed to reduce the number of constraints on controller design at each time step. Moreover, for the first time, exogenous disturbances are considered in the procedure of MPC design for delayed switched systems, and non-weighted H∞ performance is ensured. The simulation outcome demonstrates the great performance of the suggested plan and its ability to asymptotically stabilize the switched system.

Section: Resultsmentioning

confidence: 94%

Guaranteed H∞ Performance of Switched Systems with State Delays: A Novel Low-Conservative Constrained Model Predictive Control Strategy

Hassan,

Zarkani,

Alali

et al. 2024

“…Many problems in practice can be modeled using MNNs with random uncertainties. However, the mathematical formulation of these problems is difficult and needs more data-driven knowledge to clarify uncertainty bounds [23,24], which we will study in the near future.…”

Section: The Dynamic Model Of Cmnnsmentioning

confidence: 99%

Pinning Event-Triggered Scheme for Synchronization of Delayed Uncertain Memristive Neural Networks

Fan,

Ban,

Yuan

et al. 2024

To reduce the communication and computation overhead of neural networks, a novel pinning event-triggered scheme (PETS) is developed in this paper, which enables pinning synchronization of uncertain coupled memristive neural networks (CMNNs) under limited resources. Time-varying delays, uncertainties, and mismatched parameters are all considered, which makes the system more interpretable. In addition, from the low energy cost point of view, an algorithm for pinned node selection is designed to further investigate the newly event-triggered function under limited communication resources. Meanwhile, based on the PETS and following the Lyapunov functional method, sufficient conditions for the pinning exponential stability of the proposed coupled error system are formulated, and the analysis of the self-triggered method shows that our method can efficiently avoid Zeno behavior under the newly determined triggered conditions, which contribute to better PETS performance. Extensive experiments demonstrate that the PETS significantly outperforms the existing schemes in terms of solution quality.

“…where âi are class K functions for all x ∈ R n ⊂ D. The Lyapunov function V can be designed using a quadratic formulation, which satisfies the required criteria, or, alternately, using learning-based approaches, as conducted using a linear parameter-varying (LPV) framework in [18]. In the simulation example presented in our work below, a quadratic Lyapunov function is used, and extensive open-loop and closed-loop simulations are conducted to verify that the asymptotic stability assumption is met.…”

Section: Lyapunov-based Control Using An Rnn Modelmentioning

confidence: 99%

Machine Learning-Based Model Predictive Control of Two-Time-Scale Systems

Alnajdi,

Abdullah,

Suryavanshi

et al. 2023

In this study, we present a general form of nonlinear two-time-scale systems, where singular perturbation analysis is used to separate the dynamics of the slow and fast subsystems. Machine learning techniques are utilized to approximate the dynamics of both subsystems. Specifically, a recurrent neural network (RNN) and a feedforward neural network (FNN) are used to predict the slow and fast state vectors, respectively. Moreover, we investigate the generalization error bounds for these machine learning models approximating the dynamics of two-time-scale systems. Next, under the assumption that the fast states are asymptotically stable, our focus shifts toward designing a Lyapunov-based model predictive control (LMPC) scheme that exclusively employs the RNN to predict the dynamics of the slow states. Additionally, we derive sufficient conditions to guarantee the closed-loop stability of the system under the sample-and-hold implementation of the controller. A nonlinear chemical process example is used to demonstrate the theory. In particular, two RNN models are constructed: one to model the full two-time-scale system and the other to predict solely the slow state vector. Both models are integrated within the LMPC scheme, and we compare their closed-loop performance while assessing the computational time required to execute the LMPC optimization problem.