Summary This article aims to address state and sensor fault estimation issue for a class of continuous‐time nonlinear switched systems, modelled as Takagi‐Sugeno (T‐S) models with nonlinear consequent parts and subject to norm bounded disturbances. This modelling approach helps to prevent Unmeasured Premise Variables (UPVs) problem. The primary contribution of this study consists of proposing robust asynchronous switched observers to simultaneously estimate state and sensor faults under state‐dependent switching. Based on a candidate multiple Lyapunov function, the design of the proposed observer is formulated in terms of Linear Matrix Inequalities (LMIs) conditions. These conditions are dwell‐time‐independent and less conservative compared with similar previous studies, thanks to some usual relaxation techniques and the incremental quadratic constraints applied on unmeasured nonlinear consequent parts. Another contribution consists to perform the estimation of the attraction domain of the estimation error using an optimization procedure. In order to illustrate the effectiveness of the proposed design approach, two simulation examples are considered. The first one concerns the conservatism reduction brought by our proposal compared with previous studies, while the second one is dedicated to show through an illustrative example the performance of the proposed switched T‐S observers under mismatching switching laws.
Summary This paper investigates the design of asynchronous switched nonlinear filters for a class of continuous‐time nonlinear switched systems with mismatching switching laws and norm‐bounded disturbances. In this context, the switched nonlinear system is modelled as a switched Takagi–Sugeno (T‐S) model with nonlinear consequent parts, that is, where unmeasured nonlinear terms are kept in the nonlinear consequent parts in order to circumvent the occurrence of unmeasured premise variables, which is usually faced in conventional T‐S modeling without nonlinear consequent parts. In this framework, asynchronous switched T‐S filters with unmeasured nonlinear consequent parts are proposed to estimate unmeasured and/or disturbed system's outputs, even when the filter's switching law mismatches the switched nonlinear system's one, which can be in practice unknown or imprecisely measured. Based on a candidate multiple Lyapunov function, combined with a criterion, conditions are proposed in terms of Linear Matrix Inequalities for the design of the considered asynchronous switched T‐S filters with unmeasured nonlinear consequent parts. Compared with previous related works, these conditions have the advantage of being dwell‐time‐independent and less conservative, thanks to the incremental quadratic constraints employed to deal with the unmeasured nonlinear consequent parts. Furthermore, acknowledging that T‐S models are only representing nonlinear ones on subsets of their state space, an optimization procedure to estimate the filtering error's domain of attraction is developed. Two illustrative examples are considered to validate the proposed results. An academic one is presented to illustrate the improvements brought in terms of conservatism by the proposed switched T‐S filter design methodology with regards to previous related studies. Then, a case study illustrates the effectiveness of this proposal from a switched nonlinear mass‐spring system inspired from related literature.
International audience
International audience
International audience
This paper aims to present a model predictive controller based on discrete state-space modeling, where the future control trajectory is approximated by a set of discrete-time Laguerre functions instead of shift forward operators. The benefit of using these orthonormal Laguerre functions is that they have fewer parameters to adjust in the optimization problem and the computation load is significantly lower than the standard predictive control. The effectiveness of this controller is illustrated through the quadruple tank process, which is a highly interacted, multivariable and constrained system.
National audience
National audience
This paper deals with a new non-cooperative distributed controller for linear large-scale systems based on designing multiple local Model Predictive Control (MPC) algorithms using Laguerre functions to enhance the global performance of the overall closed-loop system. In this distributed control scheme, that does not require a coordinator, local MPC algorithms might transmit and receive information from other sub-controllers by means of the communication network to perform their control decisions independently on each other. Thanks to the exchanged information, the sub-controllers have in this way the ability to work together in a collaborative manner towards achieving a good overall system performance. To decrease drastically the computational load in the small-size optimization problem with a short prediction horizon, discrete-time Laguerre functions are used to tightly approximate the optimal control sequence. For evaluating the proposed distribution control framework, a simulation example is proposed to show the effectiveness of the proposed scheme and its applicability for large-scale interconnected systems. The obtained simulation results are provided to demonstrate clearly that the proposed Non-Cooperative Distributed MPC (NC-DMPC) outperforms Decentralized MPC (De-MPC) and achieves performance comparable to centralized MPC with a reduced computing time. The system performance of the proposed distributed model predictive control is given.
The objective of this thesis is to develop methods for designing observers and H∞ filters for continuous-time switched nonlinear systems with Takagi–Sugeno (T-S) fuzzy models representing the nonlinear system in each mode. These estimation tech- niques are investigated under state-dependent switching laws (dwell-time-independent), bounded disturbances, and asynchronous switching, where the observer’s or filter’s active switching mode does not necessarily match that of the switched T-S system. First, switched T-S observers are proposed along with Lipschitz constraints, which allow state estimations when the systems’ premise variables are not necessarily measurable. However, due to the conservatism that might arise from the Lipschitz constraint, an inter- esting approach to dealing with unmeasured premise variables is investigated instead in the second part of this thesis in the context of H∞ filtering. Thus, the switched T-S system is modelled as a switched T-S model with nonlinear consequent parts, in which the unmeasured nonlinearities are kept in the nonlinear consequent parts. Thanks to the incremental quadratic constraint employed to deal with unmeasured nonlinearities, the obtained conditions are less conservative compared to the Lipschitz constraint. Further- more, acknowledging that T-S models only represent nonlinear ones on subsets of their state space, an optimization procedure to estimate the filtering error’s domain of attraction is developed. To deal with the asynchronous switching modes, multiple Lyapunov function candidates are considered, along with a H∞ criterion to minimize the transfer between the input/output disturbances and state estimation/filtering errors. Moreover, the proposed design conditions are formulated in terms of Linear Matrix Inequalities (LMI). Several illustrative examples are used throughout the manuscript to validate the proposed observers and filters, as well as the obtained results.
