arXiv subjects

Jad Wehbeh

Publications and source records attributed to Jad Wehbeh.

4 recordsLinked to original sources

arXiv2026

Exact Continuous Reformulations of Logic Constraints in Nonlinear Optimization and Optimal Control Problems

Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability challenges and requires specialized solvers. This paper presents an exact reformulation of broad classes of logical constraints as binary-variable-free expressions whose differentiability properties coincide with those of the underlying predicates, enabling their direct integration into nonlinear programming models. Our approach rewrites arbitrary logical propositions into conjunctive normal form, converts them into equivalent max--min constraints, and applies a smoothing procedure that preserves the exact feasible set. The method is evaluated on two benchmark problems, a quadrotor trajectory optimization with obstacle avoidance and a hybrid two-tank system with temporal logic constraints, and is shown to obtain optimal solutions more consistently and efficiently than existing binary variable elimination techniques.

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arXiv2025

Optimistic vs Pessimistic Uncertainty Model Unfalsification

We present a novel, input-output data-driven approach to uncertainty model identification. As the true bounds and distributions of system uncertainties ultimately remain unknown, we depart from the goal of identifying the uncertainty model and instead look for minimal concrete statements that can be made based on an uncertain system model and available input-output data. We refer to this as unfalsifying an uncertainty model. Two different unfalsification approaches are taken. The optimistic approach determines the smallest uncertainties that could explain the given data, while the pessimistic approach finds the largest possible uncertainties suggested by the data. The pessimistic problem is revealed to be a semi-infinite program, which is solved using the local reduction algorithm. It is also shown that the optimistic and pessimistic approaches to uncertainty model unfalsification are mathematical duals. Finally, both approaches are tested using an uncertain linear model with data from a simulated nonlinear system.

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arXiv2024

Robust Output Feedback of Nonlinear Systems through the Efficient Solution of Min-Max Optimization Problems

We examine robust output feedback control of discrete-time nonlinear systems with bounded uncertainties affecting the dynamics and measurements. Specifically, we demonstrate how to construct semi-infinite programs that produce gains to minimize some desired performance cost over a finite prediction horizon for the worst-case realization of the system's uncertainties, while also ensuring that any specified nonlinear constraints are always satisfied. The solution process relies on an implicit description of the feasible state space through prior measurements and the system dynamics, and assumes that the system is always in the subset of the feasible space that is most detrimental to performance. In doing so, we can guarantee that the system's true state will meet all of the chosen performance criteria without resorting to any explicit state estimation. Under some smoothness assumptions, we also discuss solving these semi-infinite programs through local reduction techniques, which generate optimal scenario sets for the uncertainty realizations to approximate the continuous uncertainty space and speed up the computation of optima. When tested on a two-dimensional nonlinear quadrotor, the developed method achieves robust constraint satisfaction and tracking despite dealing with highly uncertain measurements and system dynamics.

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arXiv2024

Semi-Infinite Programs for Robust Control and Optimization: Efficient Solutions and Extensions to Existence Constraints

Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a previously proposed local reduction method to consider those with existence constraints on the uncountable variables. We also consider the possibility of non-unique trajectories that satisfy equality and inequality constraints. Crucially, we show that the problems of interest can be cast into a standard semi-infinite program and demonstrate how to generate optimal uncertainty scenario sets in order to obtain numerical solutions. We also include examples on model predictive control for obstacle avoidance with logical conditions, control with input saturation affected by uncertainty, and optimal parameter estimation to highlight the need for the proposed extension. Our method solves each of the examples considered, producing violation-free and locally optimal solutions.

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