Hossam Seddik Abbas

The concept of Deadbeat Robust Model Predictive Control (DRMPC) has recently been established for linear systems, providing full system theoretic guarantees, while reducing the computational and conceptual complexity. This article extends DRMPC to systems with multiplicative uncertainty (“robust linear”) and systems that depend on a (slowly) varying parametric uncertainty (“linear parameter‐varying”), for which the uncertainty can be converted to a bounded additive disturbance to a nominal linear system. Besides avoiding the reliance on a Robust Positive Invariant (RPI) set, LPV‐DRMPC allows to shift a significant portion of the computations offline. Rigorous proofs of recursive feasibility and robust exponential stability can be established, as shown in the article. The performance of LPV‐DRMPC is evaluated in a simulation study, based on a commonly used benchmark example. The study demonstrates that the proposed LPV‐DRMPC, using the origin as the terminal set and a slightly increased prediction horizon, is almost comparable to other, state‐of‐the‐art LPV‐MPC schemes, while offering a much simpler setup and a lower computational complexity.

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 the computational cost commonly used in standard nonlinear programming (NLP) systems. We illustrate the performance by numerical simulations.

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.

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.

The ballbot is a type of mobile robot that achieves dynamic stability by maintaining balance on a spherical ball. Its control poses significant challenges due to its nonlinear and unstable nature, as well as its five degrees of freedom and underactuated system dynamics with dynamic constraints. To the authors’ knowledge, there is a lack of a systematic approach in the literature that addresses these considerations, particularly when it comes to the parameter identification problem. This paper aims to provide a complete and straightforward approach for developing a model-based control of the ballbot, including hardware design and fabrication, detailed system modeling, advanced parameter identification, and control algorithm design. A planar dynamic model is adopted in this work to reduce system complexity and enable real-time control feasibility, serving as a tractable foundation for future extension to a fully coupled 3D dynamic model. The proposed approach is validated through several real-time experiments, demonstrating its robustness and validity. For instance, the identified model achieved a root mean square error (RMSE) of 0.0091 for the yz-plane and 0.0495 for the xy-plane, demonstrating accurate predictive performance, and the controller successfully maintained a tilt angle within ±1° under disturbances. The approach demonstrates a modular, low-complexity framework suitable for both research and educational platforms. Future work may explore extending this approach to more complex dynamic environments, advanced hardware, and nonlinear intelligent control strategies such as fuzzy logic and model predictive control.

Ensuring the safe operation of autonomous systems is a critical challenge that demands the development of sophisticated control strategies. This article proposes a safe control architecture (SCA) that employs a supervisor model predictive control (MPC) (supervisor) strategy to ensure the persistent satisfaction of state and input constraints. The supervisor continuously monitors the safety of potentially unsafe inputs generated by an operating controller (OC). If an input is predicted to lead the system to a future state where constraint violations are inevitable, it is deemed unsafe and thus blocked from the system. Instead, a backup input, generated by the supervisor in the previous time step, is applied to the system. However, uncertainties in system dynamics are unavoidable and can lead to incorrect decisions by the supervisor, which is based on MPC with a nominal model. This article proposes to enhance the robustness of the SCA by the integration of tube MPC. The resulting robust SCA (RSCA) has the capability to ensure safe operation of autonomous systems under model uncertainties, making it a practical solution for safety-critical autonomous systems, such as vehicles, drones, or medical robots. This article also proves the recursive feasibility and stability of the RSCA. The effectiveness of the approach is validated for an autonomous vehicle in IPG CarMaker, a high-fidelity simulation environment with realistic data on roads, vehicle dynamics, and obstacles.

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.

In this work, the right coprime factor for balancing and truncating unstable systems is extended to parameter-varying multidimensional systems employing recent works on coprime factor model reduction of one-dimensional uncertain systems. Since the balanced truncation method cannot be applied directly to unstable systems, state feedback gains should be computed and incorporated in order to stabilize the given system and to be able to apply the balanced truncation technique via defining the so-called stable coprime factor, as coprime factorization overcomes the stability condition required for model reduction. Parameter-dependent state feedback and parameter-dependent Gramians are considered in this work yielding less conservative techniques. In addition, the Gramians are defined as block diagonal matrices, which are partitioned according to the structure of the multidimensional systems. The application to a simulation example demonstrates the applicability and validity of the proposed reduction approach leading to small error bounds between the full and the reduced models.

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.

We derive novel methods that allow to synthesize LPV state-feedback controllers directly from a single sequence of data and guarantee stability and performance of the closed-loop system, without knowing the model of the plant. 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 synthesis problems that yield controllers that guarantee stability and performance in terms of infinite horizon quadratic cost, generalized $\mathcal{H}_2$-norm and $\mathcal{L}_2$-gain of the closed-loop system. The controllers are synthesized by solving an SDP with a finite set of LMI constraints. Competitive performance of the proposed data-driven synthesis methods is demonstrated w.r.t. model-based synthesis that have complete knowledge of the true system model in multiple simulation studies.