arXiv subjects

Hossam S. Abbas

Publications and source records attributed to Hossam S. Abbas.

15 recordsLinked to original sources

arXiv2026

LPV Updates for Sequentially Linearized Moving Horizon Estimation of Nonlinear Systems

Moving horizon estimation (MHE) provides high precision state estimation for nonlinear systems, but it is often limited by the substantial computational demands of solving a nonlinear optimization problem at every sampling step. To address this issue, we develop an efficient MHE scheme based on linear parameter-varying (LPV) formulation, where the scheduling parameters are given by the estimated states of the system and used to construct inexact Jacobians. Due to the LPV representation, the Jacobian can be pre-specified offline in a structured form and then updated in the quadratic programming (QP) subproblem, which reduces computational cost commonly used in standard nonlinear programming (NLP) systems. We illustrate the performance by numerical simulations.

math.OC↗

arXiv2025

A Linear Parameter-Varying Approach to Data Predictive Control

By means of the linear parameter-varying (LPV) Fundamental Lemma, we derive novel data-driven predictive control (DPC) methods for LPV systems. In particular, we present output-feedback and state-feedback-based LPV-DPC methods with terminal ingredients, which guarantee exponential stability and recursive feasibility. We provide methods for the data-based computation of these terminal ingredients. Furthermore, an in-depth analysis of the application and implementation aspects of the LPV-DPC schemes is given, including application for nonlinear systems and handling noisy data. We compare and demonstrate the performance of the proposed methods in a detailed simulation example involving a nonlinear unbalanced disc system.

eess.SY↗

arXiv2025

Deadbeat Robust Model Predictive Control for Linear Parameter-Varying Systems

The concept of Deadbeat Robust Model Predictive Control (DRMPC) is to completely extinguish the effect of external disturbances within the first few steps of the prediction horizon. The benefit is that the remaining dynamics of the system can be planned with certainty. This means it is not necessary to employ a Robust Positive Invariant (RPI) set as a terminal condition, which is often complex or even intractable to compute. Recent work has shown that it is possible to obtain full system theoretic guarantees in the case of linear systems, including recursive feasibility of all constraints and input-to-state stability. This paper extends this contribution to linear time-varying (LTV) or parameter-varying systems (LPV) systems with bounded parametric uncertainty and additive disturbances. Full system-theoretic guarantees can also be provided for these cases. Numerical simulation results demonstrate that the performance of the proposed LPV-DRMPC scheme, with the origin as the terminal set and a slightly increased prediction horizon, is almost comparable to that of other LPV-MPC schemes with an RPI terminal set constraint, despite a lower computational complexity. Besides avoiding the computation of RPI terminal sets, LPV-DRMPC allows to shift a significant portion of the computations offline.

math.OC↗

arXiv2025

Efficient Nonlinear MPC by Leveraging LPV Embedding and Sequential Quadratic Programming

In this paper, we present efficient solutions for the nonlinear program (NLP) associated with nonlinear model predictive control (NMPC) by leveraging the linear parameter-varying (LPV) embedding of nonlinear models and sequential quadratic programming (SQP). The corresponding quadratic program (QP) subproblem is systematically constructed and efficiently updated using the scheduling parameter from the LPV embedding, enabling fast convergence while adapting to the behavior of the controlled system. Furthermore, the approach provides insight into the problem, its connection to SQP, and a clearer understanding of the differences between solving NMPC as an NLP and using the LPV-MPC approach, compared to similar methods in the literature. The efficiency of the proposed approach is demonstrated against state-of-the-art methods, including NLP algorithms, in control benchmarks and practical applications.

math.OC↗

arXiv2024

Direct Data-Driven State-Feedback Control of Linear Parameter-Varying Systems

The framework of linear parameter-varying (LPV) systems has shown to be a powerful tool for the design of controllers for complex nonlinear systems using linear tools. In this work, we derive novel methods that allow to synthesize LPV state-feedback controllers directly from only a single sequence of data and guarantee stability and performance of the closed-loop system. We show that if the measured open-loop data from the system satisfies a persistency of excitation condition, then the full open-loop and closed-loop input-scheduling-state behavior can be represented using only the data. With this representation we formulate data-driven analysis and synthesis problems, where the latter yields controllers that guarantee stability and performance in terms of infinite horizon quadratic cost, generalized $\mathcal{H}_2$-norm and $\ell_2$-gain of the closed-loop system. The controllers are synthesized by solving a semi-definite program. Additionally, we provide a synthesis method to handle noisy measurement data. Competitive performance of the proposed data-driven synthesis methods is demonstrated w.r.t. model-based synthesis in multiple simulation studies, including a nonlinear unbalanced disc system.

eess.SY↗

arXiv2024

Stochastic Error Bounds in Nonlinear Model Predictive Control with Gaussian Processes via Parameter-Varying Embeddings

This study utilized the Gaussian Processes (GPs) regression framework to establish stochastic error bounds between the actual and predicted state evolution of nonlinear systems. These systems are embedded in the linear parameter-varying (LPV) formulation and controlled using model predictive control (MPC). Our main focus is quantifying the uncertainty of the LPVMPC framework's forward error resulting from scheduling signal estimation mismatch. We compared our stochastic approach with a recent deterministic approach and observed improvements in conservatism and robustness. To validate our analysis and method, we solved the regulator problem of an unbalanced disk.

math.OC↗

arXiv2024

Obstacle Avoidance of Autonomous Vehicles: An LPVMPC with Scheduling Trust Region

Reference tracking and obstacle avoidance rank among the foremost challenging aspects of autonomous driving. This paper proposes control designs for solving reference tracking problems in autonomous driving tasks while considering static obstacles. We suggest a model predictive control (MPC) strategy that evades the computational burden of nonlinear nonconvex optimization methods after embedding the nonlinear model equivalently to a linear parameter-varying (LPV) formulation using the so-called scheduling parameter. This allows optimal and fast solutions of the underlying convex optimization scheme as a quadratic program (QP) at the expense of losing some performance due to the uncertainty of the future scheduling trajectory over the MPC horizon. Also, to ensure that the modeling error due to the application of the scheduling parameter predictions does not become significant, we propose the concept of scheduling trust region by enforcing further soft constraints on the states and inputs. A consequence of using the new constraints in the MPC is that we construct a region in which the scheduling parameter updates in two consecutive time instants are trusted for computing the system matrices, and therefore, the feasibility of the MPC optimization problem is retained. We test the method in different scenarios and compare the results to standard LPVMPC as well as nonlinear MPC (NMPC) schemes.

eess.SY↗

arXiv2024

Closed-Loop Identification and Tracking Control of a Ballbot

Identifying and controlling an unstable, underactuated robot to enable reference tracking is a challenging control problem. In this paper, a ballbot (robot balancing on a ball) is used as an experimental setup to demonstrate and test proposed strategies to tackle this control problem. A double-loop control system, including a state-feedback gain in the outer-loop and a Proportional-Integral-Derivative (PID) controller in the inner-loop, is presented to balance the system in its unstable equilibrium. Once stability is reached, the plant's response to a designed excitation signal is measured and interpreted to identify the system's dynamics. Hereby, the parameters of a linearized model of the ballbot are identified with prior knowledge about the structure of the nonlinear dynamics of the system. Based on an identified linear time-invariant (LTI) state-space model, a double-loop control strategy is considered to balance the real system and to allow reference tracking. A linear quadratic regulator (LQR) is designed offline and implemented in the inner-loop to ensure balance. In the outer-loop, the estimated dynamics forecast the system's behavior online using a model-predictive-control (MPC) design to find the optimal control input for reference tracking. The experimental results demonstrate the applicability of the proposed strategies.

math.OC↗

arXiv2024

Parameter Refinement of a Ballbot and Predictive Control for Reference Tracking with Linear Parameter-Varying Embedding

In this study, we implement a control method for stabilizing a ballbot that simultaneously follows a reference. A ballbot is a robot balancing on a spherical wheel where the single point of contact with the ground makes it omnidirectional and highly maneuverable but with inherent instability. After introducing the scheduling parameters, we start the analysis by embedding the nonlinear dynamic model derived from first principles to a linear parameter-varying (LPV) formulation. Continuously, and as an extension of a past study, we refine the parameters of the nonlinear model that enhance significantly its accuracy. The crucial advantages of the LPV formulation are that it consists of a nonlinear predictor that can be used in model predictive control (MPC) by retaining the convexity of the quadratic optimization problem with linear constraints and further evades computational burdens that appear in other nonlinear MPC methods with only a slight loss in performance. The LPVMPC control method can be solved efficiently as a quadratic program (QP) that provides timing that supports real-time implementation. Finally, to illustrate the method, we test the control designs on a two-set point 1D non-smooth reference with sudden changes, to a 2D nonstationary smooth reference known as Lissajous curves, and to a single-set point 1D non-smooth reference where for this case theoretical guarantees such as stability and recursive feasibility are provided.

math.OC↗

arXiv2023

On the Design of Nonlinear MPC and LPVMPC for Obstacle Avoidance in Autonomous Driving

In this study, we are concerned with autonomous driving missions when a static obstacle blocks a given reference trajectory. To provide a realistic control design, we employ a model predictive control (MPC) utilizing nonlinear state-space dynamic models of a car with linear tire forces, allowing for optimal path planning and tracking to overtake the obstacle. We provide solutions with two different methodologies. Firstly, we solve a nonlinear MPC (NMPC) problem with a nonlinear optimization framework, capable of considering the nonlinear constraints. Secondly, by introducing scheduling signals, we embed the nonlinear dynamics in a linear parameter varying (LPV) representation with adaptive linear constraints for realizing the nonlinear constraints associated with the obstacle. Consequently, an LPVMPC optimization problem can be solved efficiently as a quadratic programming (QP) that constitutes the main novelty of this work. We test the two methods for a challenging obstacle avoidance task and provide qualitative comparisons. The LPVMPC shows a significant reduction in terms of the computational burden at the expense of a slight loss of performance.

eess.SY↗

arXiv2023

Direct data-driven LPV control of nonlinear systems: An experimental result

We demonstrate that direct data-driven control of nonlinear systems can be successfully accomplished via a behavioral approach that builds on a Linear Parameter-Varying (LPV) system concept. An LPV data-driven representation is used as a surrogate LPV form of the data-driven representation of the original nonlinear system. The LPV data-driven control design that builds on this representation form uses only measurement data from the nonlinear system and a priori information on a scheduling map that can lead to an LPV embedding of the nonlinear system behavior. Efficiency of the proposed approach is demonstrated experimentally on a nonlinear unbalanced disc system showing for the first time in the literature that behavioral data-driven methods are capable to stabilize arbitrary forced equilibria of a real-world nonlinear system by the use of only 7 data points.

eess.SY↗

arXiv2023

A Learning- and Scenario-based MPC Design for Nonlinear Systems in LPV Framework with Safety and Stability Guarantees

This paper presents a learning- and scenario-based model predictive control (MPC) design approach for systems modeled in linear parameter-varying (LPV) framework. Using input-output data collected from the system, a state-space LPV model with uncertainty quantification is first learned through the variational Bayesian inference Neural Network (BNN) approach. The learned probabilistic model is assumed to contain the true dynamics of the system with a high probability and used to generate scenarios which ensure safety for a scenario-based MPC. Moreover, to guarantee stability and enhance performance of the closed-loop system, a parameter-dependent terminal cost and controller, as well as a terminal robust positive invariant set are designed. Numerical examples will be used to demonstrate that the proposed control design approach can ensure safety and achieve desired control performance.

eess.SY↗

arXiv2022

A real-time GP based MPC for quadcopters with unknown disturbances

Gaussian Process (GP) regressions have proven to be a valuable tool to predict disturbances and model mismatches and incorporate this information into a Model Predictive Control (MPC) prediction. Unfortunately, the computational complexity of inference and learning on classical GPs scales cubically, which is intractable for real-time applications. Thus GPs are commonly trained offline, which is not suited for learning disturbances as their dynamics may vary with time. Recently, state-space formulation of GPs has been introduced, allowing inference and learning with linear computational complexity. This paper presents a framework that enables online learning of disturbance dynamics on quadcopters, which can be executed within milliseconds using a state-space formulation of GPs. The obtained disturbance predictions are combined with MPC leading to a significant performance increase in simulations with jMAVSim. The computational burden is evaluated on a Raspberry Pi 4 B to prove the real-time applicability.

eess.SY↗

arXiv2022

Data-Driven Predictive Control for Linear Parameter-Varying Systems

Based on the extension of the behavioral theory and the Fundamental Lemma for Linear Parameter-Varying (LPV) systems, this paper introduces a Data-driven Predictive Control (DPC) scheme capable to ensure reference tracking and satisfaction of Input-Output (IO) constraints for an unknown system under the conditions that (i) the system can be represented in an LPV form and (ii) an informative data-set containing measured IO and scheduling trajectories of the system is available. It is shown that if the data set satisfies a persistence of excitation condition, then a data-driven LPV predictor of future trajectories of the system can be constructed from the IO data set and online measured data. The approach represents the first step towards a DPC solution for nonlinear and time-varying systems due to the potential of the LPV framework to represent them. Two illustrative examples, including reference tracking control of a nonlinear system, are provided to demonstrate that the data-based LPV-DPC scheme, achieves similar performance as LPV model-based predictive control.

eess.SY↗

arXiv2021

LPV Modeling of Nonlinear Systems: A Multi-Path Feedback Linearization Approach

This paper introduces a systematic approach to synthesize linear parameter-varying (LPV) representations of nonlinear (NL) systems which are described by input affine state-space (SS) representations. The conversion approach results in LPV-SS representations in the observable canonical form. Based on the relative degree concept, first the SS description of a given NL representation is transformed to a normal form. In the SISO case, all nonlinearities of the original system are embedded into one NL function, which is factorized, based on a proposed algorithm, to construct an LPV representation of the original NL system. The overall procedure yields an LPV model in which the scheduling variable depends on the inputs and outputs of the system and their derivatives, achieving a practically applicable transformation of the model in case of low order derivatives. In addition, if the states of the NL model can be measured or estimated, then a modified procedure is proposed to provide LPV models scheduled by these states. Examples are included to demonstrate both approaches.

eess.SY↗