Interval Prediction for Continuous-Time Systems with Parametric Uncertainties

The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all uncertainties take values in a given admissible set. Then an interval predictor is designed and its stability is guaranteed applying Lyapunov function with a novel structure. The conditions of stability are formulated in the form of linear matrix inequalities. Efficiency of the theoretical results is demonstrated in the application to safe motion planning for autonomous vehicles.Comment: 6 pages, CDC 2019. Website: https://eleurent.github.io/interval-prediction

Model-based prognosis of fatigue crack growth under variable amplitude loading

International audienceIn this paper, a model-based prognosis method using a particle filter that takes model uncertainty, measurement uncertainty and future loading uncertainty into account is proposed. A nonlinear analytical model of the degradation that depends on loading parameters is established, and then a particle filter is used to estimate and forecast these unknown inputs at the same time as the degradation state. Moreover, adding to this joint input-state estimation, a two-sided CUSUM algorithm is implemented to detect load variations. This would help the prognosis module to adapt to a change in the degradation state evolution, in order to correct the remaining useful life prediction. Real data from fatigue tests on fiber-reinforced metal matrix composite materials are used to demonstrate the efficiency of the proposed methodology for crack growth prognosis

Some recent results on interval observers design of uncertain systems

International audienceBased on the theory of positive systems, the goal of interval observers is to compute sets of admissible values of the state vector at each instant of time for systems subject to bounded uncertainties (noises, disturbances and parameters). The size of the estimated sets, which should be minimised, are proportional to the model uncertainties. An interval estimation can be seen as a conventional point estimation (the centre of the interval) with an estimation error given by the interval radius. The reliable uncertainties propgation performed in this context can be useful in several fields such as robust control, diagnosis and fault-tolerant control. This paper presents some recent results on interval observers for several dynami-cal systems classes such as continuous-time and switched systems

Supervision of Nonlinear Networked Control Systems Under Network Constraints

International audienceThe remote supervision for a class of nonlinear systems in the presence of additive disturbances and measurement noises is considered in this paper. The communication network may introduce time delays while exchanging data among sites connected to the network medium (i.e., the data acquisition site and the remote plant site). Two different approaches are presented in this paper. The first one uses a conventional estimator-based predictor when the uncertainties are supposed to be known. In the case of unknown but bounded uncertainties by known bounds, an interval estimation-based predictor evaluating the set of admissible values for the state is investigated. The state prediction techniques are used to compensate the effect of network-induced delays. Simulation results are introduced to illustrate the efficiency of the proposed techniques

Interval estimation of switched Takagi-Sugeno systems with unmeasurable premise variables

International audienceThis paper deals with interval observers design for nonlinear switched systems. The nonlinear modes are represented by the Takagi-Sugeno (T-S) fuzzy models with premise variables depending on unmeasurable terms, e.g. the state vector. This T-S structure can be used to represent exactly a nonlinear switched system in a compact set of the state space. The introduced method in this paper allows to compute the lower and upper bounds of the system state under the assumption that the disturbances as well as the measurement noises are unknown but bounded. First, the stability conditions of the proposed T-S interval observers are developed via Linear Matrix Inequality (LMI) formulations to ensure the convergence of the nonnegative observation error dynamics. Then, changes of coordinates are employed to relax the restrictive requirement of nonnegativity constraints. Theoretical results are applied to a numerical example to illustrate the effectiveness of the proposed method

Control of nonlinear and LPV systems: interval observer-based framework

International audienceThe problem of output stabilization of a class of nonlinear systems subject to parametric and signal uncertainties is studied. First, an interval observer is designed estimating the set of admissible values for the state. Next, it is proposed to design a control algorithm for the interval observer providing convergence of interval variables to zero, that implies a similar convergence of the state for the original nonlinear system. An application of the proposed technique shows that a robust stabilization can be performed for linear time-varying and Linear-Parameter-Varying (LPV) systems without assumption that the vector of scheduling parameters is available for measurements. Efficiency of the proposed approach is demonstrated through two examples

On interval observer design for continuous-time LPV switched systems

State estimation for switched systems with time-varying parameters has received a great attention during the past decades. In this paper, a new approach to design an interval observer for this class of systems is proposed. The scheduling vector is described by a convex combination so that the varying parameters belong into polytopes. The considered system is also subject to measurement noise and state disturbances which are supposed to be unknown but bounded. The proposed method guarantees both cooperativity and Input to State Stability (ISS) of the upper and lower observation errors. Sufficient conditions are given in terms of Linear Matrix Inequalities (LMIs) using a common quadratic Lyapunov function. Finally, a numerical example is provided to show the effectiveness of the designed observer

Robust output feedback MPC for LPV systems using interval observers

This work addresses the problem of robust output feedback model predictive control for discrete-time, constrained, linear parameter-varying systems subject to (bounded) state and measurement disturbances. The vector of scheduling parameters is assumed to be an unmeasurable signal taking values in a given compact set. The proposed controller incorporates an interval observer, that uses the available measurement to update the setmembership estimation of the states, and an interval predictor, used in the prediction step of the MPC algorithm. The resulting MPC scheme offers guarantees on recursive feasibility, constraint satisfaction, and input-to-state stability in the terminal set. Furthermore, this novel algorithm shows low computation complexity and ease of implementation (similar to conventional MPC schemes)

Robust Output Feedback MPC: An Interval-Observer Approach

International audienceIn this work, we address the problem of output-feedback Model Predictive Control (MPC) of constrained, linear, discrete-time systems corrupted by additive perturbations on both state and output. The use of estimated variables in MPC is challenging and computationally expensive due to constraint satisfaction. To overcome this issue, the proposed approach incorporates interval observers on the MPC scheme to cope with uncertainty, leading to a novel, simple and very intuitive methodology providing robust constraint satisfaction with reduced computational complexity