Every electrical grid is, at its core, a promise: that when you flip the switch, the voltage will be right, the current will be shared fairly, and a sudden disturbance — a cloud passing over a solar array, a motor starting up — won't cascade into a blackout. Keeping that promise in a modern, decentralized grid is extraordinarily hard. It requires controlling dozens of interacting components whose behaviors depend on one another, in real time, often under conditions that weren't fully anticipated at design time. And increasingly, the engineers who build these systems don't have perfect mathematical models of the components they're connecting.
A new paper from researchers at the University of Notre Dame — Welikala, Song, Lin, and Antsaklis (2026) — proposes a solution that is both theoretically elegant and practically ambitious: a hierarchical control framework that can guarantee the robust stability of a networked system whether or not you know the equations governing its parts. The key insight is that you don't need to solve one giant, intractable optimization problem for the whole network. You can decompose it into layers — local, then global — each solvable with convex, efficient mathematics. And if you don't have a model, you can use data instead.
The Science
The setting is a class of networked systems: collections of linear subsystems — think individual power converters, generators, or building HVAC units — connected to each other and subject to external disturbances (unexpected load changes, measurement noise, weather). Each subsystem has inputs, outputs, and internal states, and the whole network has performance outputs: quantities you actually care about, like bus voltage or delivered current.
The theoretical backbone of the framework is dissipativity theory, a branch of control theory that treats stability the way physicists treat energy. A system is dissipative with respect to a supply function if it never internally generates more "energy" (defined abstractly) than it absorbs from external inputs. This is a generalization of classical stability: a dissipative system won't blow up, and — crucially — networks of dissipative subsystems are themselves dissipative under mild conditions. That compositionality is the key that unlocks the hierarchical design.
The design is structured in two levels. At the local level, each subsystem is individually given a controller that enforces a local dissipativity certificate — a mathematical guarantee that the subsystem, on its own, satisfies the supply-function bound. At the global level, these local certificates are assembled. The researchers then co-design two things simultaneously: distributed global controllers (coordination signals that flow between subsystems) and the interconnection topology itself — which subsystem connects to which, and how strongly. The topology co-design is particularly novel: rather than fixing the network architecture and then finding a controller, the framework treats the wiring as a design variable, optimizing it for cost while still meeting the global dissipativity requirement.
Both levels reduce to linear matrix inequalities (LMIs) — a class of convex optimization problem that can be solved reliably and efficiently with standard software. This is not a minor technical detail. Many control design problems are non-convex, meaning gradient-based solvers can get stuck in local minima, require careful initialization, and must be run many times before finding an acceptable answer. LMIs have no local minima. You solve them once, and you're done. The framework thus avoids what the authors call "non-convex, iterative design processes that are inefficient and centralized" (Welikala et al., 2026).
The second major contribution is the data-driven variant. In many real deployments, precise dynamical models of subsystems simply aren't available — either because the physics is too complex, because components change over time, or because the manufacturer doesn't provide them. The data-driven design replaces the system equations with raw input-state-output trajectory data collected from the subsystem, and derives dissipativity certificates directly from those measurements.
The hard part of data-driven control is that data is always noisy, and in the presence of unknown disturbances, you can't be certain whether a signal you measured reflects the true system dynamics or a fluke. Welikala et al. (2026) handle this by bounding the unknown disturbances with a quadratic matrix inequality (QMI) — a more flexible constraint than conventional approaches that use simple norm bounds or ellipsoidal sets. To convert this disturbance uncertainty into a tractable design condition, they invoke the matrix S-lemma, a result from robust optimization that allows you to eliminate the disturbance variable by absorbing its bound directly into the LMI constraint. The result: a data-driven design process that is almost as clean as the model-based one, still expressed as a sequence of LMIs, still compositional.
What They Found
The framework is validated on a DC microgrid — a small-scale direct-current power network of the kind increasingly used in data centers, electric vehicle charging stations, solar-plus-storage installations, and remote communities. The microgrid case study captures two canonical control objectives simultaneously: voltage regulation (keeping bus voltages close to a target setpoint despite disturbances) and current sharing (distributing load current proportionally among the generating units so no single converter is overloaded).
These two objectives are known to be in tension in DC microgrids. Tight voltage regulation typically requires aggressive local control that ignores the state of neighboring units, while fair current sharing requires information exchange across the network — the kind of coupling that can, if poorly designed, introduce oscillations or destabilize the system. The hierarchical framework handles this tension naturally: local controllers handle voltage regulation within each converter's own dynamics, while the global layer designs the communication topology and distributed controllers that enforce current sharing at the network level.
The model-based design successfully synthesizes local and global controllers, as well as an optimized interconnection topology, all by solving the relevant LMI sequences. The data-driven design replicates this performance using only trajectory data from the subsystems — no equations required. Both approaches produce closed-loop systems that are dissipative from disturbance inputs to performance outputs, meaning disturbances are attenuated rather than amplified as they propagate through the network.
A particular strength highlighted by the case study is scalability. Because the local design is entirely decentralized — each subsystem's controller is designed independently — the complexity of that step scales with the size of individual subsystems, not with the size of the network. The global step does involve all subsystems, but it exploits the local certificates as compressed summaries of each subsystem's behavior, keeping the problem tractable even as the number of nodes grows.
Why This Changes Things
Control theory has long wrestled with a fundamental tension: the most powerful stability guarantees require the most detailed models, but the systems we most need to control — power grids, traffic networks, biological networks — are precisely the ones where detailed models are hardest to obtain and least trustworthy.
Data-driven control has emerged over the past decade as a serious attempt to resolve this tension. Landmark results like Willems' Fundamental Lemma (2005) showed that, under certain conditions, all input-output behaviors of a linear system can be characterized by a single rich trajectory — no model identification needed. The approach in Welikala et al. (2026) builds on this tradition but extends it in two important directions: to networked systems (not just single subsystems), and to the setting of disturbance-affected data (not just clean measurements). The QMI disturbance bound is a meaningful advance here. Real data is always contaminated, and previous data-driven methods often assumed either noise-free measurements or simple norm-bounded disturbances. A quadratic matrix inequality can represent correlated, direction-dependent uncertainty — much closer to what engineers actually encounter.
The topology co-design aspect is equally forward-looking. As power grids decarbonize, they are becoming more modular: more solar arrays, more battery storage units, more small generators. The question of how to wire these together is increasingly live, not settled at the factory. A framework that treats topology as a design variable — optimized jointly with the control law — is directly relevant to the engineering of next-generation microgrids and distribution networks. The idea also has echoes in other domains: biological neural networks, where the connectivity pattern is part of what evolution is optimizing; supply chains, where logistics topology and inventory control policy are co-determined; and multi-robot systems, where communication links are a resource to be allocated.
The dissipativity lens brings another advantage that's easy to underappreciate: it generalizes multiple classical performance objectives. control (minimizing worst-case disturbance amplification), passivity (relevant to port-Hamiltonian systems and energy networks), and gain bounds are all special cases of dissipativity with different supply functions. Designing for dissipativity thus gives engineers a unified language that bridges these objectives. A system that is dissipative with respect to an $\mathcal{H}_\infty$-type supply function guarantees bounded disturbance rejection; one that is passive can be safely interconnected with other passive subsystems without special precautions. The hierarchical framework accommodates all of these by simply specifying the appropriate supply function at each layer.
The computational efficiency deserves emphasis in a world where control algorithms must run on embedded hardware with tight timing constraints. An LMI is solved offline, once, before deployment. What gets installed in the controller is just a fixed matrix — the outcome of the optimization — not a running solver. This makes the approach far more practical for field deployment than, say, model predictive control approaches that must re-solve an optimization at every timestep.
What's Next
The paper's scope is already broad, but several important extensions remain open. The framework currently assumes linear subsystems — a significant restriction. Many real power electronics components, motors, and communication systems are nonlinear, and extending dissipativity-based hierarchical design to nonlinear networked systems (using, for example, incremental dissipativity or contraction theory) would substantially widen applicability.
The data-driven design also assumes that the collected trajectory data is rich enough — in a technical sense called persistency of excitation — to capture all relevant system behaviors. In practice, engineers must actively design experiments to generate sufficiently informative data, and it's not always possible to excite a live power system freely without causing disturbances to real loads. Developing adaptive or sequential data collection strategies that satisfy persistency requirements with minimal disruption to normal operation is an important practical challenge.
Topology co-design introduces its own combinatorial complexity when the topology must be discrete — you can either run a cable between two nodes or you can't. The current framework handles topology as a continuous variable, which enables the LMI formulation but means the discrete physical realization requires a rounding step that may not always be straightforward. Future work could explore mixed-integer extensions or iterative rounding procedures with recovery guarantees.
Finally, the microgrid case study, while compelling, is relatively small in scale. Demonstrating the framework's performance on larger networks — or on hardware-in-the-loop testbeds where real power electronics introduce nonlinearities, delays, and digital quantization effects — would bridge the gap between theoretical guarantees and engineering confidence.
What Welikala et al. (2026) have built is a genuinely complete framework: two design paths (model-based and data-driven), two design layers (local and global), and two co-designed outputs (controllers and topology), all tied together by a single mathematical thread — dissipativity — and all reducible to convex optimization. The clean architecture of the result reflects the depth of the theoretical work behind it. For engineers building the decentralized power systems of the next decade, and for theorists looking for frameworks that scale, this is a paper worth studying closely.
The deeper message may be this: the age of centralized, model-dependent control is giving way to something more modular, more data-aware, and more compositional. The mathematics of dissipativity, developed in the 1970s by Jan Willems, turns out to be precisely the right language for this transition — not because it was designed for modern microgrids, but because it captures something fundamental about how energy-like quantities propagate and are absorbed in interconnected systems. Sometimes the most forward-looking tools are the ones that have been waiting quietly in the literature for the right problems to arrive.