arXiv subjects

Dalim Wahby

Publications and source records attributed to Dalim Wahby.

4 recordsLinked to original sources

arXiv2026

SOS-based Stability Verification for Saturated INDI Control of Hybrid-VTOL Aircraft Pitch Rate Dynamics

Incremental nonlinear dynamic inversion (INDI) is a prominent flight-control strategy valued for its robust disturbance rejection; however, its formal stability verification has traditionally been limited to linearized dynamical models. This paper presents a formal nonlinear stability certificate for a saturated INDI pitch-rate controller for a hybrid vertical take-off and landing (VTOL) aircraft by representing the INDI controller via an equivalent recurrent equilibrium network (REN). By casting the saturated INDI architecture as a REN, the closed-loop dynamics are exactly mapped to an augmented state-feedback system. This structural equivalence enables the use of sum of squares (SOS) programming to synthesize a locally valid Lyapunov function without relying on conservative bounding approximations. The resulting certificate yields an inner estimate of the region of attraction (RoA) that explicitly accounts for actuator saturation, formally verifying the controller's stability in operating regimes where standard linear margins lose their validity.

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arXiv2026

Region of Attraction Estimation for Linear Quadratic Regulator, Linear and Robust Model Predictive Control on a Two-Wheeled Inverted Pendulum

Nonlinear underactuated systems such as two-wheeled inverted pendulums (TWIPs) exhibit a limited region of attraction (RoA), which defines the set of initial conditions from which the closed-loop system converges to the equilibrium. The RoA of nonlinear and constrained systems is generally nonconvex and analytically intractable, requiring numerical or approximate estimation methods. This work investigates the estimation of the RoA for a TWIP stabilized under three model-based control strategies: saturated linear quadratic regulator (LQR), linear model predictive control (MPC), and constraint tightening MPC (CTMPC). We first derive a Lyapunov-based invariant set that provides a certified inner approximation of the RoA. Since this analytical bound is highly conservative, a Monte Carlo-based estimation procedure is then employed to obtain a more representative approximation of the RoA, capturing how the controllers behave beyond the analytically guaranteed region. The proposed methodology combines analytical guarantees with data-driven estimation, providing both a formally certified inner bound and an empirical characterization of the RoA, offering a practical way to evaluate controller performance without relying solely on conservative analytical bounds or purely empirical simulation.

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arXiv2025

Contributions to Semialgebraic-Set-Based Stability Verification of Dynamical Systems with Neural-Network-Based Controllers

Neural-network-based controllers (NNCs) can represent complex, highly nonlinear control laws, but verifying the closed-loop stability of dynamical systems using them remains challenging. This work presents contributions to a state-of-the-art stability verification procedure for NNC-controlled systems which relies on semialgebraic-set-based input-output modeling to pose the search for a Lyapunov function as an optimization problem. Specifically, this procedure's conservatism when analyzing NNCs using transcendental activation functions and the restriction to feedforward NNCs are addressed by a) introducing novel semialgebraic activation functions that preserve key properties of common transcendental activations and b) proving compatibility of NNCs from the broader class of recurrent equilibrium networks (RENs) with this procedure. Furthermore, the indirect optimization of a local region of attraction (RoA) estimate using a restricted set of candidate Lyapunov functions is greatly improved via c) the introduction of a richer parameterization of candidate Lyapunov functions than previously reported and d) the formulation of novel semidefinite programs (SDPs) that directly optimize the resulting RoA estimate. The value of these contributions is highlighted in two numerical examples.

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arXiv2025

Synthesis and SOS-based Stability Verification of a Neural-Network-Based Controller for a Two-wheeled Inverted Pendulum

This work newly establishes the feasibility and practical value of a sum of squares (SOS)-based stability verification procedure for applied control problems utilizing neural-network-based controllers (NNCs). It successfully verifies closed-loop stability properties of a NNC synthesized using a generalizable procedure to imitate a robust, tube-based model predictive controller (MPC) for a two-wheeled inverted pendulum demonstrator system. This is achieved by first developing a state estimator and control-oriented model for the two-wheeled inverted pendulum. Next, this control-oriented model is used to synthesize a baseline linear-quadratic regulator (LQR) and a robust, tube-based MPC, which is computationally too demanding for real-time execution on the demonstrator system's embedded hardware. The generalizable synthesis procedure generates an NNC imitating the robust, tube-based MPC. Via an SOS-based stability verification procedure, a certificate of local asymptotic stability and a relevant inner estimate of the region of attraction (RoA) are obtained for the closed-loop system incorporating this NNC. Finally, experimental results on the physical two-wheeled inverted pendulum demonstrate that the NNC both stabilizes the system, and improves the control performance compared to the baseline LQR in both regulation and reference-tracking tasks.

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