Abstract We provide a computer-assisted approach to ensure that a given discrete-time polynomial system is (asymptotically) stable. Our framework relies on constructive analysis together with formally certified sums of squares Lyapunov functions. The crucial steps are formalized within the proof assistant $$\texttt {Minlog}$$ Minlog . We illustrate our approach with an example issued from the control system literature.

Slip control is a common and crucial functionality for a number of vehicles ranging from cars to tractors and trucks. The purpose of slip control is to improve vehicle's traction and motion stability, prevent excessive wheel slippage and provide stable braking. Slip is a non-linear function of the vehicle's ground speed and wheel rotation frequency and as such depends on the internal state variables, such as wheel load torque, which are in turn unknown. A number of approaches exist to estimate the unknown state, one of the most used ones being based on Kalman filter. In the current study, we present experimental results of slip control for an electrical single wheel-drive tractor using an unscented Kalman filter, which is a variant of Kalman filter suitable for non-linear systems. To cope with the problems of state estimation for heavy-duty vehicles, the Kalman filter was augmented with a fuzzy-logic supervisor aimed at assessment of vehicle dynamics. The goal of the supervisor was to adapt the state noise covariance with the goal of improving tracking accuracy. Wheel slip reduction was observed and its mean stayed within the desired limit. Experiments were carried out under two different road conditions and the condition change was identified by the Kalman filter

SUMMARY: Often competing hypotheses for biochemical networks exist in the form of different mathematical models with unknown parameters. Considering available experimental data, it is then desired to reject model hypotheses that are inconsistent with the data, or to estimate the unknown parameters. However, these tasks are complicated because experimental data are typically sparse, uncertain, and are frequently only available in form of qualitative if-then observations. ADMIT (Analysis, Design and Model Invalidation Toolbox) is a MatLab(TM)-based tool for guaranteed model invalidation, state and parameter estimation. The toolbox allows the integration of quantitative measurement data, a priori knowledge of parameters and states, and qualitative information on the dynamic or steady-state behavior. A constraint satisfaction problem is automatically generated and algorithms are implemented for solving the desired estimation, invalidation or analysis tasks. The implemented methods built on convex relaxation and optimization and therefore provide guaranteed estimation results and certificates for invalidity. AVAILABILITY: ADMIT, tutorials and illustrative examples are available free of charge for non-commercial use at http://ifatwww.et.uni-magdeburg.de/syst/ADMIT/