Interconnection and Damping Assignment Passivity-Based Control using Sparse Neural ODEs

• URL: http://arxiv.org/abs/2512.06935v2
• Date: Mon, 05 Jan 2026 15:21:27 GMT
• Title: Interconnection and Damping Assignment Passivity-Based Control using Sparse Neural ODEs
• Abstract summary: Passivity-Based Control (IDA-PBC) is a nonlinear control technique that assigns a port-Hamiltonian (pH) structure to a controlled system using a state-feedback law.<n>The main limitation of IDA-PBC stems from the complexity of analytically solving a set of partial differential equations (PDEs)<n>We propose a novel numerical approach for designing IDA-PBC controllers without solving the matching PDEs exactly.
• Score: 0.359986669039879
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) is a nonlinear control technique that assigns a port-Hamiltonian (pH) structure to a controlled system using a state-feedback law. While IDA-PBC has been extensively studied and applied to many systems, its practical implementation often remains confined to academic examples and, almost exclusively, to stabilization tasks. The main limitation of IDA-PBC stems from the complexity of analytically solving a set of partial differential equations (PDEs), referred to as the matching conditions, which enforce the pH structure of the closed-loop system. However, this is extremely challenging, especially for complex physical systems and tasks. In this work, we propose a novel numerical approach for designing IDA-PBC controllers without solving the matching PDEs exactly. We cast the IDA-PBC problem as the learning of a neural ordinary differential equation. In particular, we rely on sparse dictionary learning to parametrize the desired closed-loop system as a sparse linear combination of nonlinear state-dependent functions. Optimization of the controller parameters is achieved by solving a multi-objective optimization problem whose cost function is composed of a generic task-dependent cost and a matching condition-dependent cost. Our numerical results show that the proposed method enables (i) IDA-PBC to be applicable to complex tasks beyond stabilization, such as the discovery of periodic oscillatory behaviors, (ii) the derivation of closed-form expressions of the controlled system, including residual terms in case of approximate matching, and (iii) stability analysis of the learned controller.

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