Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2605.31270

Steering Fractional-Order Network Dynamics via Joint Parameter and State Control

Alessandro Varalda·Sergio Pequito
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper studies the control of discrete-time linear fractional-order networks, a flexible modeling framework for systems with long-range memory such as power grids, biological networks, and neuronal circuits. In contrast to the common view that fractional exponents (time-scales) are fixed parameters, we show that they can be systematically steered, together with the network coupling matrix, by appropriately designed input sequences. We first derive algebraic conditions under which the coupling matrix and the vector of fractional exponents of a given network can be reconfigured to desired values, and we characterize how truncating the infinite-memory term impacts the resulting dynamics. Building on these results, we construct an equivalent linear representation that isolates the contribution of memory, and we introduce a fractional reachability matrix that provides explicit conditions for jointly steering both network parameters and state in a finite number of steps. To address practical implementations, we further formulate an energy-constrained steering problem that incorporates actuator bounds and finite-memory approximations as a quadratic program. The framework is illustrated on low-dimensional toy examples, on larger networks with Erdos-Renyi, Barabasi-Albert, and Watts-Strogatz topologies, and on a brain network model inferred from electrocorticography recordings of an epilepsy patient, where we showcase transitions between pre-seizure and seizure configurations.

Explore related subjects

eess.SYcs.SY

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Alessandro Varalda, Sergio Pequito. 2026-05-29. Steering Fractional-Order Network Dynamics via Joint Parameter and State Control. https://arxiv.org/abs/2605.31270

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Constrained Feedback Control of Nonlinear Systems via Approximate HJB and Control Barrier Functions

This paper presents a two-stage framework for constrained feedback control of input-affine nonlinear systems. Offline, an approximate value function for the unconstrained problem is computed, for example using Hamilton--Jacobi--Bellman (HJB)-based policy iteration. Online, the proposed quadratic program (QP) minimizes the pre-Hamiltonian evaluated using the approximate value-function gradient subject to safety constraints enforced by control barrier functions (CBFs). This architecture decouples performance optimization from constraint enforcement, allowing constraints to be modified without recomputing the value function. As in CBF-QP architectures based on control Lyapunov functions (CLFs), safety is enforced as a hard constraint; however, the performance objective targets approximate optimality rather than a prescribed Lyapunov decay. Numerical results on a linear 2-state hovercraft and a nonlinear 9-state spacecraft attitude-control problem show agreement with the constrained open-loop optimal control problem (OCP) benchmark in the linear case, and performance close to the OCP benchmark, improving on CLF-based controllers, in the nonlinear case.

eess.SY↗
arXiv2026

Rao-Blackwellized Stein Gradient Descent for Joint State-Parameter Estimation

We present a filtering framework for online joint state estimation and parameter identification in nonlinear, time-varying systems. The algorithm uses a Rao-Blackwellization technique to infer joint state-parameter posteriors efficiently. In particular, conditional state distributions are computed analytically via Kalman filtering, while model parameters, including the measurement-noise covariance, are approximated using particle-based Stein Variational Gradient Descent (SVGD), enabling stable real-time inference. To handle parameters subject to physical constraints, we further introduce constrained variants that enforce them through an alternating direction method of multipliers (ADMM) splitting of the SVGD update, including nonlinear equality constraints that standard particle filters cannot readily handle. We derive a stability bound that relates the approximation error in the parameter posterior to the resulting error in the marginal state distribution. Performance of the proposed filters is validated on three case studies: a fed-batch bioreactor with Haldane kinetics and a damped pendulum, both under physical constraints, and a neural-network-augmented dynamic system. The examples cover parameter estimation under inequality and equality constraints and online neural-network training within a dynamical model.

eess.SY↗
arXiv2026

Firing Rate Neural Network Implementations of Model Predictive Control

Human and animal brains perform planning to enable complex movements and behaviors, a process that can be effectively described using model predictive control (MPC). How could the brain physically implement MPC? In this work, we translate model predictive controllers into firing rate neural networks, offering insights into the nonlinear neural dynamics that underpin planning. We propose a constructive method; no training is required. This is done first applying the projected gradient method to the dual problem to derive a baseline neural network implementation. We then use factorization and contraction analysis to systematically generate alternative network architectures; in other words, we systematically generate hypotheses for how planning is done in the brain via neural dynamics. Finally, we present numerical simulations to study different neural networks performing MPC to balance an inverted pendulum on a cart (i.e., balancing a stick on a hand), including one example in which imposing sparse connectivity (a property observed in brain networks) does not degrade control performance.

eess.SY↗