Linear quadratic zonotopic control of switched systems: application to autonomous vehicle path-tracking

Abstract

This letter proposes a zonotopic approach for the state feedback control problem of a class of uncertain switched systems subject to unknown but bounded disturbances and measurement noises. The proposed approach is the zonotopic analogous case of the switched Linear Quadratic Gaussian (LQG) control, in which the feedback loop is closed using the optimal estimates of a Switched Zonotopic Kalman Filter (SZKF) leading to a Switched Linear Quadratic Zonotopic (SLQZ) control scheme. In this context, first, a SZKF with offline filter gains design is proposed so that the unmeasurable system states can be estimated. Then, to tackle the synthesis of the SZKF and the state feedback controller, separation principle is proved so that the computation of the optimal controller and estimator can be done separately by finding the solutions to a finite set of Linear Matrix Inequalities (LMIs). At last, a reference path tracking controller of the vehicle lateral dynamics is designed to demonstrate the validity and performance of the proposed method.

This work has been co-financed by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERFD) through the project SaCoAV (ref. MINECO PID2020-114244RB-I00), by the European Regional Development Fund of the European Union in the framework of the ERDF Operational Program of Catalonia 2014–2020 (ref. 001-P-001643 Looming Factory), by the DGR of Generalitat de Catalunya (SAC group ref. 2017/SGR/482) and by the Chinese Scholarship Council (CSC) under grant (202006120006).

Peer Reviewed

Postprint (published version)