Interval Prediction for Continuous-Time Systems with Parametric Uncertainties

Abstract

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.

On interval prediction of COVID-19 development in France based on a SEIR epidemic model

“…where x t ∈ R + is a non-negative system state, whose initial conditions belong to a given interval x 0 ∈ [x 0 , x 0 ], a t ∈ R + and d t ∈ R are uncertain inputs, which also take values in known intervals a t ∈ [a t , a t ], d t ∈ [d t , d t ], for all t ∈ N. So, we assume that x 0 ≤ x 0 , 0 ≤ a t ≤ a t and d t ≤ d t are known for all t ∈ N. The imposed non-negativity constraints on x t and a t correspond to the case of the model (1). We wish to calculate the lower x t and upper x t predictions on the state x t of this system under the introduced hypotheses on all uncertain variables, which have to satisfy x t ≤ x t ≤ x t , ∀t ∈ N. The theory of interval observers and predictors [17], [22] answers this question, and a possible solution (that utilizes the non-negativity of x t and a t ) is as follows:…”

“…Remark 4. The boundedness of the state of (5) established in Theorem 3 does not imply the stability of the internal dynamics of the interval predictor (it is also a reason to impose the explicit saturation in ( 5)), which is a frequent and challenging problem for the predictors [16], [22]. Remark 5.…”

Robust stability analysis and implementation of Persidskii systems

“…circadian oscillations in [26] or chemostat [27]. An application of the proposed approach for analysis of stability of an interval predictor is given in [28].…”

Robust Output Feedback MPC: An Interval-Observer Approach

“…The design of IOs has been exhaustively studied, and the literature reports results on linear [8], linear parameter-varying [9], nonlinear [10], discrete-time [11], as well as on time-delay systems [12]. Recently an interval predictor (IP), sometimes also called framer, was presented in [13], [14] for systems in continuous time.…”