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.

[1]  Brigitte d'Andréa-Novel,et al.  The kinematic bicycle model: A consistent model for planning feasible trajectories for autonomous vehicles? , 2017, 2017 IEEE Intelligent Vehicles Symposium (IV).

[2]  Denis V. Efimov,et al.  Interval state observer for nonlinear time varying systems , 2013, Autom..

[3]  Denis V. Efimov,et al.  Design of interval observers for uncertain dynamical systems , 2016, Automation and Remote Control.

[4]  Denis Efimov,et al.  Approximate Robust Control of Uncertain Dynamical Systems , 2019, ArXiv.

[5]  A. Yu. Aleksandrov,et al.  Robust stability analysis and implementation of Persidskii systems , 2019, 2019 IEEE 58th Conference on Decision and Control (CDC).

[6]  Jean-Marie Flaus,et al.  Trajectory computation of dynamic uncertain systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[7]  Hal L. Smith,et al.  Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith , 1995 .

[8]  Leonid M. Fridman,et al.  Interval estimation for LPV systems applying high order sliding mode techniques , 2012, Autom..

[9]  Ali Zolghadri,et al.  Interval observer design for consistency checks of nonlinear continuous-time systems , 2010, Autom..

[10]  ChebotarevStanislav,et al.  Interval observers for continuous-time LPV systems with L 1 / L 2 performance , 2015 .

[11]  Luc Jaulin,et al.  Nonlinear bounded-error state estimation of continuous-time systems , 2002, Autom..

[12]  Uwe Helmke,et al.  Robust Positive Interval Observers for Uncertain Positive Systems , 2011 .

[13]  Jeff S. Shamma,et al.  Gain-Scheduled Missile Autopilot Design Using Linear Parameter Varying Transformations , 1993 .

[14]  Olivier Bernard,et al.  Near optimal interval observers bundle for uncertain bioreactors , 2007, 2007 European Control Conference (ECC).

[15]  Javad Mohammadpour,et al.  Control of linear parameter varying systems with applications , 2012 .

[16]  Christophe Combastel,et al.  Stable Interval Observers in BBC for Linear Systems With Time-Varying Input Bounds , 2013, IEEE Transactions on Automatic Control.

[17]  G. Balas,et al.  Development of linear-parameter-varying models for aircraft , 2004 .

[18]  Helbing,et al.  Congested traffic states in empirical observations and microscopic simulations , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  Eric Walter,et al.  Guaranteed Nonlinear State Estimator for Cooperative Systems , 2004, Numerical Algorithms.

[20]  Chun Hung Cheng,et al.  Tight robust interval observers: An LP approach , 2008, 2008 47th IEEE Conference on Decision and Control.

[21]  Denis V. Efimov,et al.  Some recent results on the design and implementation of interval observers for uncertain systems , 2018, Autom..

[22]  S. Rinaldi,et al.  Positive Linear Systems: Theory and Applications , 2000 .

[23]  Olivier Bernard,et al.  Interval observers for linear time-invariant systems with disturbances , 2011, Autom..

[24]  Denis Emov,et al.  Design of interval observers for uncertain dynamical systems , 2016 .

[25]  Denis V. Efimov,et al.  Interval State Estimation for a Class of Nonlinear Systems , 2012, IEEE Transactions on Automatic Control.

[26]  Jean-Luc Gouzé,et al.  Closed loop observers bundle for uncertain biotechnological models , 2004 .

[27]  Denis V. Efimov,et al.  Interval observers for continuous-time LPV systems with L1/L2 performance , 2015, Autom..

[28]  Denis V. Efimov,et al.  Control of Nonlinear and LPV Systems: Interval Observer-Based Framework , 2013, IEEE Transactions on Automatic Control.