We address the problem of improving the performance of pre-stabilized networked systems subject to plug-and-play (PnP) operations, namely additions or removals of subsystems. While distributed baseline controllers can preserve stability after a PnP transition, augmenting them with expressive neural policies can invalidate the formal stability guarantees. To overcome this issue, we build on recently proposed Performance Boosting controllers based on the Internal Model Control (IMC) principle, which reduce closed-loop stability to a finite ℓ2-gain requirement on an auxiliary operator. In the distributed setting, this operator is formed by interconnecting local neural operators that exchange information only between neighboring subsystems. We then derive free parametrizations of this interconnection, namely explicit maps from unconstrained trainable variables to interconnected neural operators satisfying a prescribed network gain bound for every parameter value. The obtained distributed neural controller can therefore be trained by unconstrained gradient-based optimization without stability constraints or projection steps, while retaining the prescribed gain bound at every training iterate. We develop two complementary parametrizations. A neighbor-based compositional parametrization uses local coupling bounds, so that after a PnP event only subsystems whose bounds change need to update their gain parameters. A network-norm parametrization instead uses a bound on the overall coupling matrix and can reduce conservatism, at the price of requiring network-wide information. A PnP DC-microgrid case study shows that the proposed neural layer improves voltage transients under topology changes and load variations while preserving nominal closed-loop stability.
Figures & tables
Figure 1: Example of a PnP update from G to G+ . At time tp subsystem Σ3 is removed, while Σ4 is plugged in and connected to Σ2 . The affected post-change set is A(G,G+)={2,4} .
Figure 2: Local IMC implementation at subsystem i . The residual e^[i] is reconstructed from the local model, while internal controller outputs from one-hop neighbors provide dynamic coordination. The complete neural interconnection realizes R∈RγRℓ2(G) .
Figure 3: Internal realization of R . The matrix Mve injects the external residual e^ , Mvz routes neighboring local-operator outputs z back to local-operator inputs v , and Muz reads the control input u from the local-operator outputs.
Figure 4: Feasible regions for the two-subsystem example with c=α[i](γ[i])2=0.25 : network gain certificate ( 23 ) (blue), neighbor-based parametrization (green), and network-norm parametrization (yellow).
Figure 5: DC microgrid case-study setup.
DGU
Rt
Lt
Ct
YL
IˉL
PL
Vref
Line resistances [Ω]
[ Ω ]
[mH]
[mF]
[S]
[A]
[W]
[V]
1
.20
1.8
2.2
.50
8.0
6.0
47.9
R12=.050
R16=.100
2
.30
2.0
1.9
.45
7.0
5.0
48.0
R13=.070
R26=.090
3
.10
2.2
1.7
.55
7.5
6.5
47.7
R24=.040
R36=.110
4
.50
3.0
2.5
.40
6.0
4.5
48.0
R34=.060
R46=.085
5
.40
1.2
2.0
.35
6.5
5.0
47.8
R45=.080
R56=.080
Table 1: Microgrid parameters. The last two columns list all line resistances appearing across the considered configurations; all line inductances are 1 mH.
Figure 6: Plug-in of DGU 6 at t=4s : PCC voltages under the proposed controller (blue) and the decentralized baseline [ 28 ] (red dashed).
Figure 7: Unplugging of DGU 3 at t=12s under the proposed controller (blue) and the decentralized baseline [ 28 ] (red dashed).
Figure 8: Load disturbance at PCC 6 at t=8s in the enlarged network under the proposed controller (blue) and the decentralized baseline [ 28 ] (red dashed).
The growing complexity of modern control tasks calls for controllers that can react online as objectives and disturbances change, while preserving closed-loop stability. Recent approaches for improving the performance of nonlinear systems while preserving closed-loop stability rely on time-invariant recurrent neural-network controllers, but offer no principled way to update the controller during operation. Most importantly, switching from one stabilizing policy to another can itself destabilize the closed-loop. We address this problem by introducing a stability-preserving update mechanism for nonlinear, neural-network-based controllers. Each controller is modeled as a causal operator with bounded ℓp-gain, and we derive gain-based conditions under which the controller may be updated online. These conditions yield two practical update schemes, time-scheduled and state-triggered, that guarantee the closed-loop remains ℓp-stable after any number of updates. Our analysis further shows that stability is decoupled from controller optimality, allowing approximate or early-stopped controller synthesis. We demonstrate the approach on nonlinear systems with time-varying objectives and disturbances, and show consistent performance improvements over static and naive online baselines while guaranteeing stability.
Institute of Mechanical Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland. · Department of Engineering Science, University of Oxford, United Kingdom
Transient stability control in smart grids requires rapid post-fault damping of generator frequency and rotor angle deviations to prevent cascading failures. This paper proposes FedPPO-PG, a Federated Multi-Agent Proximal Policy Optimization framework with Physics-Grounded neighborhoods, which reformulates transient stability control as a cooperative multi-agent reinforcement learning problem optimized directly against closed-loop stability objectives. Each generator hosts an independent local actor augmented with the frequency deviations of its two most strongly coupled electrical neighbors, identified from the post-fault Kron-reduced susceptance matrix. A guided policy initialization phase warm-starts all actors from the classical decentralized controller, while a centralized critic guides advantage estimation under the centralized training--decentralized execution (CTDE) paradigm. Evaluated on a simulation of the IEEE 39-bus benchmark system across five training and three unseen fault contingencies, FedPPO-PG achieves 100% stabilization in all 24 trials, reduces mean stability time by 72.4%, and cuts the control power by 7-14 times compared to the centralized baseline. Each actor executes independently with no central coordinator at deployment, and the per-actor inference latency satisfies the IEEE/IEC 60255-118-1-2018 real-time reporting requirements.
Omar Al-Refai, Ibrahim Shahbaz, Adam Ali Husseinat +1
iSTAR Lab, Texas A&M University College Station, TX, USA
Implicit neural controllers (INCs) are static feedback laws that are evaluated through an algebraic fixed point {equation}; they include as special cases neural network controllers. We propose a so-called implicit representation of neural networks as a key enabling device that exposes the controller as a trainable linear interconnection closed through a known static activation map, thereby making well-posedness and Lyapunov/IQC analysis mathematically easy to handle. For finite-dimensional LTI plants, we first develop a rigorous analysis theory for a given INC, including Perron--Frobenius and norm conditions for well posedness, LMI/IQC certificates for exponential stability, and LMIs for discounted infinite-horizon quadratic performance. We then formulate synthesis as a certification-compatible heuristic search: training is carried out under explicit well-posedness constraints, implicit-differentiation formulas provide gradients, and the resulting controller is accepted only after independent post-training LMIs or regional admissibility checks are feasible. Finally, we establish constrained-control separation results: for a specific scalar unstable plant with hard actuator bounds, an INC achieves a strictly smaller discounted infinite-horizon cost than any admissible finite-order dynamic linear controller. Additional results cover quadratic state-input costs, comparison with linear static output feedback, and computable upper/lower-bound certificates. Numerical examples illustrate the mechanism and the resulting certified performance.