arXiv subjects

John P. Swensen

Publications and source records attributed to John P. Swensen.

3 recordsLinked to original sources

arXiv2026

A Block-Alternating Iterative Approach for a Class of Non-Convex Optimization Problems

Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs. To address this challenge, this paper proposes a novel block-alternating iterative method that decomposes the original problem into variable-specific subproblems, which are solved iteratively. Under the assumption that the problem is convex with respect to each decision variable, the proposed approach reformulates the original problem into a sequence of convex subproblems. Theoretical results are established regarding the convergence and optimality of the method. In addition, a numerical example and a real-world control engineering application are presented to demonstrate its effectiveness. Finally, this paper introduces a ready-to-use Python platform that implements the proposed method, together with existing algorithms, to facilitate comparison and adoption.

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arXiv2025

Provably-Stable Neural Network-Based Control of Nonlinear Systems

In recent years, Neural Networks (NNs) have been employed to control nonlinear systems due to their potential capability in dealing with situations that might be difficult for conventional nonlinear control schemes. However, to the best of our knowledge, the current literature on NN-based control lacks theoretical guarantees for stability and tracking performance. This precludes the application of NN-based control schemes to systems where stringent stability and performance guarantees are required. To address this gap, this paper proposes a systematic and comprehensive methodology to design provably-stable NN-based control schemes for affine nonlinear systems. Rigorous analysis is provided to show that the proposed approach guarantees stability of the closed-loop system with the NN in the loop. Also, it is shown that the resulting NN-based control scheme ensures that system states asymptotically converge to a neighborhood around the desired equilibrium point, with a tunable proximity threshold. The proposed methodology is validated and evaluated via simulation studies on an inverted pendulum and experimental studies on a Parrot Bebop 2 drone.

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arXiv2025

A Guaranteed-Stable Neural Network Approach for Optimal Control of Nonlinear Systems

A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online optimization, it can be computationally expensive, and thus unrealistic for systems with limited computing resources. One potential solution to this issue is to incorporate a Neural Network (NN) into the control loop to emulate the behavior of the optimal control scheme. Ensuring stability and reference tracking in the resulting NN-based closed-loop system requires modifications to the primary optimization problem. These modifications often introduce non-convexity and nonlinearity with respect to the decision variables, which may surpass the capabilities of existing solvers and complicate the generation of the training dataset. To address this issue, this paper develops a Neural Optimization Machine (NOM) to solve the resulting optimization problems. The central concept of a NOM is to transform the optimization challenges into the problem of training a NN. Rigorous proofs demonstrate that when a NN trained on data generated by the NOM is used in the control loop, all signals remain bounded and the system states asymptotically converge to a neighborhood around the desired equilibrium point, with a tunable proximity threshold. Simulation and experimental studies are provided to illustrate the effectiveness of the proposed methodology.

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