arXiv subjects

Marco H. Terra

Publications and source records attributed to Marco H. Terra.

10 recordsLinked to original sources

arXiv2026

Set-based state estimation of nonlinear discrete-time systems using constrained zonotopes and polyhedral relaxations

This paper presents a new algorithm for set-based state estimation of nonlinear discrete-time systems. A key step in such algorithms is to propagate a set (often a zonotope or constrained zonotope) through a nonlinear function. Existing methods accomplish this through conservative linearization procedures that are known to lead to severe overestimation in many cases. Here, we propose an alternative that avoids linearization using the so-called factorable representation of nonlinear functions. We use a recursive polyhedral relaxation technique based on this representation that is well-established in the global optimization literature but has not previously been used for set-based estimation. This technique is combined with constrained zonotope (CZ) technology to avoid the limitations of recursive computations with polyhedra in halfspace representation. The resulting state estimation method is fully automated, has attractive computational complexity (with one caveat discussed herein), and can provide significantly tighter enclosures than those resulting from linearization procedures in many cases. Numerical examples highlight the advantages of this approach relative to existing CZ methods based on the Mean Value Theorem and Difference of Convex functions (DC) programming.

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arXiv2025

Reachability Analysis of Nonlinear Discrete-Time Systems Using Polyhedral Relaxations and Constrained Zonotopes

This paper presents a novel algorithm for reachability analysis of nonlinear discrete-time systems. The proposed method combines constrained zonotopes (CZs) with polyhedral relaxations of factorable representations of nonlinear functions to propagate CZs through nonlinear functions, which is normally done using conservative linearization techniques. The new propagation method provides better approximations than those resulting from linearization procedures, leading to significant improvements in the computation of reachable sets in comparison to other CZ methods from the literature. Numerical examples highlight the advantages of the proposed algorithm.

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arXiv2025

ZETA: a library for Zonotope-based EsTimation and fAult diagnosis of discrete-time systems

This paper introduces ZETA, a new MATLAB library for Zonotope-based EsTimation and fAult diagnosis of discrete-time systems. It features user-friendly implementations of set representations based on zonotopes, namely zonotopes, constrained zonotopes, and line zonotopes, in addition to a basic implementation of interval arithmetic. This library has capabilities starting from the basic set operations with these sets, including propagations through nonlinear functions using various approximation methods. The features of ZETA allow for reachability analysis and state estimation of discrete-time linear, nonlinear, and descriptor systems, in addition to active fault diagnosis of linear systems. Efficient order reduction methods are also implemented for the respective set representations. Some examples are presented in order to illustrate the functionalities of the new library.

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arXiv2020

Tube-based Guaranteed Cost Model Predictive Control Applied to Autonomous Driving Up to the Limits of Handling

The development of control techniques to maintain vehicle stability under possible loss-of-control scenarios is essential to the safe deployment of autonomous ground vehicles in public scenarios. In this paper, we propose a tube-based guaranteed cost model predictive controller for autonomous vehicles able to avoid front and rear tire saturation and to track a provided reference trajectory up to the limits of handling of the vehicle. Such an approach ensures the vehicle will remain within its safe operational envelope; therefore, guaranteeing both stability and performance of the vehicle, including highly dynamic maneuvers that may be necessary for emergency conditions. We also propose a new conservative approximation of the nonlinear vehicle dynamics to a linear system subject to norm bounded multiplicative uncertainties and a new maximal robust controllable invariant set for vehicle dynamics. It consists of a larger feasible state-space region when compared to previously proposed invariant sets. Finally, we present both simulation and in-vehicle results of the performance of the proposed approach.

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arXiv2020

Tube-based Guaranteed Cost Robust Model Predictive Control for Linear Systems Subject to Parametric Uncertainties

We propose a tube-based guaranteed cost model predictive controller considering a homothetic formulation for constrained linear systems subject to multiplicative structured norm-bounded uncertainties. It provides an upper bound to the general min-max model predictive control. The invariance property of the proposed tube holds for any arbitrary scaling. It yields a second-order cone programming problem which is less computationally expensive than standard semi-definite programming problems. We also present a numerical example with a comparative study among the proposed approach, an open-loop guaranteed cost model predictive controller, and a homothetic tube model predictive controller for linear difference inclusion systems.

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arXiv2019

Optimal Guaranteed Cost Control of Discrete-Time Linear Systems subject to Structured Uncertainties

In this paper, we propose state- and static output-feedback generalized guaranteed cost control (GCC) approaches for discrete-time linear systems subject to norm-bounded structured parametric uncertainties. This method enables the convex synthesis for a more general class of systems, where uncertainties are uncorrelated block diagonal, and no feed-through uncertainty is multiplicative with control input ones. It also provides necessary and sufficient conditions for state-feedback and sufficient conditions for static output-feedback. We also present a comparative study among the proposed controllers, standard Linear Quadratic Regulator, and Guaranteed Cost Controller found in the literature.

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arXiv2018

Computation of Extended Robust Kalman Filter for Real-Time Attitude and Position Estimation

This paper deals with the implementation of the extended robust Kalman filter (ERKF) which was developed considering uncertainties in the parameter matrices of the underlying state-space model. A key contribution of this work is the demonstration of a method for real-time computation of the filter on parallel computing devices. The solution of the filter is expressed as a set of simultaneous linear equations, which can then be evaluated based on QR decomposition using Givens rotation. This paper also presents the application of the ERKF in the development of an attitude and position reference system for a cargo transport vehicle. This work concludes by analyzing the performance of the ERKF and verifying the validity of the Givens rotation method.

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arXiv2017

Guaranteed Cost Approach to Robust Model Predictive Control of Uncertain Linear Systems

In this paper we propose a constrained guaranteed cost robust model predictive controller (GCMPC) for uncertain discrete time systems. This controller was developed based on a quadratic cost functional and guarantee robustness with respect to quadratically bound uncertainties. Such a class of problems is currently intractable by Min-Max Robust Model Predictive Controllers without polytopic approximations of the uncertainties. The proposed technique is computationally more efficient then an enumeration-based approach and requires only a Quadratically Constrained Quadratic Problem (QCQP) optimization, whereas LMI-based GCMPC approaches require a Semi-Definite Programming (SDP) optimization.

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arXiv2016

Guaranteed Cost Model Predictive Control-based Driver Assistance System for Vehicle Stabilization Under Tire Parameters Uncertainties

Road traffic crashes have been the leading cause of death among young people. Most of these accidents occur when the driver becomes distracted and a loss-of-control situation occurs. Steer-by-Wire systems were recently proposed as an alternative to mitigate such accidents. This technology enables the decoupling of the front wheel steering angles from the driver hand wheel angle and, consequently, the measurement of road/tire friction limits and the development of novel control systems capable of ensuring vehicle stabilization and safety. However, vehicle safety boundaries are highly dependent on tire characteristics which vary significantly with temperature, wear and the tire manufacturing process. Therefore, design of autonomous vehicle and driver assistance controllers cannot assume that these characteristics are constant or known. Thus, this paper proposes a Guaranteed Cost Model Predictive Controller Driver Assistance System able to avoid front and rear tire saturation and to track the drivers intent up to the limits of handling for a vehicle with uncertain tire parameters. Simulation results show the performance of the proposed approach under time-varying uniformly distributed disturbances.

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arXiv2016

Safely Optimizing Highway Traffic with Robust Model Predictive Control-based Cooperative Adaptive Cruise Control

Road traffic crashes have been the leading cause of death among young people. Most of these accidents occur when the driver becomes distracted due to fatigue or external factors. Vehicle platooning systems such as Cooperative Adaptive Cruise Control (CACC) are one of the results of the effort devoted to the development of technologies for decreasing the number of road crashes and fatalities. Previous studies have suggested such systems improve up to 273\% highway traffic throughput and fuel consumption in more than 15\% if the clearance between vehicles in this class of roads can be reduced to 2 meters. This paper proposes an approach that guarantees a minimum safety distance between vehicles taking into account the overall system delays and braking capacity of each vehicle. A $l\infty$-norm Robust Model Predictive Controller (RMPC) is developed to guarantee the minimum safety distance is not violated due to uncertainties on the lead vehicle behavior. A formulation for a lower bound clearance of vehicles inside a platoon is also proposed. Simulation results show the performance of the proposed approach compared to a nominal controller when the system is subject to both modeled and unmodeled disturbances.

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