Zonotope parameter identification for piecewise affine systems

The problem of how to identify the piecewise affine system is studied in this paper, where this considered piecewise affine system is a special nonlinear system. The reason why it is not easy to identify this piecewise affine system is that each separated region and each unknown parameter vector are all needed to be determined simultaneously. Then, firstly, in order to achieve the identification goal, a multi-class classification process is proposed to determine each separated region. As the proposed multi-class classification process is the same with the classical data clustering strategy, the multi-class classification process can combine the first order algorithm of convex optimization, while achieving the goal of the classification process. Secondly, a zonotope parameter identification algorithm is used to construct a set, which contains the unknown parameter vector. In this zonotope parameter identification algorithm, the strict probabilistic description about the external noise is relaxed, and each unknown parameter vector is also identified. Furthermore, this constructed set is consistent with the measured output and the given bound corresponding to the noise. Thirdly, a sufficient condition about guaranteeing our derived zonotope not growing unbounded with iterations is formulated as an explicit linear matrix inequality. Finally, the effectiveness of this zonotope parameter identification algorithm is proven through a simulation example.

Inequalities for Zonotopes

The lower bound for the volume of the zonotope for John-basis had been given by Ball. In this paper, a simple proof of Ball＇s inequality was first provided, then the result of Ball was generalized from John-basis to a sequence of non-zero vectors which are full rank. Furthermore, the upper bound for the volumes of zonotopes was given. Finally the inequalities were deduced for the inradius and circumradius of a certain zonotope.

Safe Motion Planning and Control Framework for Automated Vehicles with Zonotopic TRMPC

Model mismatches can cause multi-dimensional uncertainties for the receding horizon control strategies of automated vehicles(AVs).The uncertainties may lead to potentially hazardous behaviors when the AV tracks ideal trajectories that are individually optimized by the AV's planning layer.To address this issue,this study proposes a safe motion planning and control(SMPAC)framework for AVs.For the control layer,a dynamic model including multi-dimensional uncertainties is established.A zonotopic tube-based robust model predictive control scheme is proposed to constrain the uncertain system in a bounded minimum robust positive invariant set.A flexible tube with varying cross-sections is constructed to reduce the controller conservatism.For the planning layer,a concept of safety sets,representing the geometric boundaries of the ego vehicle and obstacles under uncertainties,is proposed.The safety sets provide the basis for the subsequent evaluation and ranking of the generated trajectories.An efficient collision avoidance algorithm decides the desired trajectory through the intersection detection of the safety sets between the ego vehicle and obstacles.A numerical simulation and hardware-in-the-loop experiment validate the effectiveness and real-time performance of the SMPAC.The result of two driving scenarios indicates that the SMPAC can guarantee the safety of automated driving under multi-dimensional uncertainties.

车辆自主决策安全性验证方法

针对传统算法在车辆自主决策安全性验证中置信水平较低、验证结果不完备的问题,基于形式化的可达性方法分析车辆自主决策行为状态的可行性,并给出车辆自主决策的行为状态完备性集合。采用有向凸多面体算法对自主车辆非线性混合系统进行保守线性化处理,再利用迭代原理和Zonotope近似方法计算可达集。变道避碰的仿真实验表明,在初始状态集和传感器噪声边界条件下,自主车辆位置可达集和速度可达集给出了高置信水平的安全保证。

A Zonotopic-Based Watermarking Design to Detect Replay Attacks

This paper suggests the use of zonotopes for the design of watermark signals.The proposed approach exploits the recent analogy found between stochastic and zonotopic-based estimators to propose a deterministic counterpart to current approaches that study the replay attack in the context of stationary Gaussian processes.In this regard,the zonotopic analogous case where the control loop is closed based on the estimates of a zonotopic Kalman filter(ZKF)is analyzed.This formulation allows to propose a new performance metric that is related to the Frobenius norm of the prediction zonotope.Hence,the steadystate operation of the system can be related with the size of the minimal Robust Positive Invariant set of the estimation error.Furthermore,analogous expressions concerning the impact that a zonotopic/Gaussian watermark signal has on the system operation are derived.Finally,a novel zonotopically bounded watermark signal that ensures the attack detection by causing the residual vector to exit the healthy residual set during the replay phase of the attack is introduced.The proposed approach is illustrated in simulation using a quadruple-tank process.

Robust Fault Detection and Isolation Based on Finite-frequency H__/H_∞ Unknown Input Observers and Zonotopic Threshold Analysis

This work proposes a robust fault detection and isolation scheme for discrete-time systems subject to actuator faults,in which a bank of H_/H∞ fault detection unknown input observers(UIOs) and a zonotopic threshold analysis strategy are considered. In observer design, finite-frequency H_ index based on the generalized Kalman-Yakubovich-Popov lemma and H∞ technique are utilized to evaluate worst-case fault sensitivity and disturbance attenuation performance, respectively. The proposed H_/H∞ fault detection observers are designed to be insensitive to the corresponding actuator fault only, but sensitive to others.Then, to overcome the weakness of predefining threshold for FDI decision-making, this work proposes a zonotopic threshold analysis method to evaluate the generated residuals. The FDI decision-making relies on the evaluation with a dynamical zonotopic threshold. Finally, numerical simulations are provided to show the feasibility of the proposed scheme.

Brascamp-Lieb inequality for positive double John basis and its reverse

In this paper, we establish the Brascamp-Lieb inequality for positive double John basis and its reverse. As their applications, we estimate the upper and lower bounds for the volume product of two unit balls with the given norms. Moreover, the Loomis-Whitney inequality for positive double John basis is obtained.

New semidefinite programming relaxations for box constrained quadratic program

We establish in this paper optimal parametric Lagrangian dual models for box constrained quadratic program based on the generalized D.C.(difference between convex) optimization approach,which can be reformulated as semidefinite programming problems.As an application,we propose new valid linear constraints for rank-one relaxation.

Operational-space wrench and acceleration capability analysis for multi-link cable-driven robots

Multi-link cable-driven robots(MCDRs)have potential advantages in confined spaces exploration because of their redundancy and flexibility.Operational space wrench and acceleration capability analysis of MCDRs is important for their design,manipulability optimization,and motion planning.However,existing works mainly focus on capability analysis in the joint space.In this paper,we present a zonotope-based iterative method and a simplified capability zonotope to analyze the operational-space wrench and acceleration capability of MCDRs.In the iterative method,the capability generated by some cables can be iteratively added to the initial capability zonotope based on the Minkowski sum.In the simplified zonotope capability representation,a threshold is put forward to reduce redundant vertices and faces with little volume loss.Finally,simulations on a 24 DOFs MCDR are performed to verify the effectiveness of the developed method.The results demonstrate that our iterative algorithm can easily generate the capability zonotope with a few MB ROM,while traditional operational wrench capability evaluation without our iterative algorithm needs 18432 GB ROM.Furthermore,our simplified representation reduces the vertices and faces from 1260 and 2516 to 88 and 172,respectively,but with only 3.3%volume loss,which decreases the constraints of the robot and is conducive to manipulability optimization and motion planning.