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Data-Driven Communication Topology and Distributed Controller Synthesis: Control-Aware and Co-Design
Michael C. A. Nestor, Jiaxin Wang, Fei Teng
TL;DR
Distributed control topology can constrain performance or make structured stabilization infeasible, while prior data-driven topology design often separates topology and controller decisions. This paper develops data-driven co-design and sequential control-aware MISDP approaches; in the tested examples, control-aware design produced competitive topologies with lower computation times than co-design.
Problem
Topology choices can limit closed-loop performance or make structured stabilization infeasible, while control-agnostic design does not incorporate the eventual controller synthesis constraints and objectives.
Source: §1 · pp. 1–2Method
The paper formulates data-driven co-design of links and a structured H2 controller, plus sequential control-aware topology design using control-design relaxations and feasibility-preserving constraints, as MISDPs.
Source: §1 · p. 2, §5.2 · p. 6Results
In the tested examples, control-aware design produced competitive topologies with lower computation times than co-design; for the IEEE 14-bus example, it averaged around one hour while co-design did not terminate within 24 hours.
Source: §7 · p. 10, §6.3 · p. 10Takeaways & Limitations
Both approaches account for link costs and noisy data, allow communication topologies that differ from the physical interconnection, and certify a compatible stabilizing controller under stated assumptions.
Source: §1 · p. 2The extended-state control-design approach requires pℓ = n, a condition the paper describes as restrictive because generally pℓ ≥ n.
Source: §4.1 · p. 5
Abstract
from arXiv · showhide
In distributed control schemes, the communication topology that defines information sharing between agents must be designed prior to online control execution. Previous data-driven works typically decouple the topology and controller design problems. This paper investigates data-driven approaches to topology design that guarantee the existence of a stabilizing controller, whilst trading off the level of required communication against control performance. We formulate a data-driven co-design scheme that directly co-optimizes the topology and controller over the link costs and closed-loop control cost. When the topology designer does not have access to the agents' control objectives, we propose a control-aware approach that couples the two design problems within a sequential scheme. In both cases, the topology is optimized within a mixed-integer semidefinite program (MISDP). Simulations including the IEEE 14-bus power system test case demonstrate the effectiveness of both co-design and control-aware schemes. Numerical examples show lower computation time for the control-aware case than for co-design.
1 Introduction
The paper treats communication topology as a design variable coupled to distributed controller design, since topology can constrain closed-loop performance or make structured stabilization infeasible. It proposes joint data-driven co-design and sequential control-aware design to balance link costs and control performance while preserving controller feasibility.
1 Introduction
- Co-design selects communication links and controller gains together, while control-aware design selects links using a performance proxy and constraints intended to preserve subsequent controller feasibility.The control-aware scheme is sequential and does not explicitly optimize the controller over closed-loop control cost.Source: §1 · pp. 1–2
- Topology design can produce stabilizing but poorly performing controllers, and may not preserve feasibility under the relaxations or constraints used in the eventual controller synthesis.The paper calls approaches that design structure without incorporating control objectives or synthesis constraints control-agnostic.Source: §1 · p. 2
- Existing co-design approaches may be computationally challenging for large systems and may be unavailable when agents do not share their cost parameters with the topology designer.Earlier data-driven topology methods focus on matching the communication topology to an identified physical network graph.Source: §1 · p. 2
- Both proposed data-driven approaches account for link costs and noisy data, allow topologies that differ from the physical interconnection, and certify a compatible stabilizing controller under stated assumptions.The methods are formulated as mixed-integer semidefinite programs.Source: §1 · p. 2
2 Preliminaries
The preliminaries define a network of interconnected linear subsystems and distinguish physical interconnections from designed communication links. The data-driven setup permits unknown system matrices, noisy output measurements, and synthesis based on recorded input-output data, subject to stated assumptions.
2 Preliminaries
- The system comprises interconnected subsystems, each with a control agent; the physical graph records state influence, while the designed cyber graph records which agents receive other agents’ input-output streams.A Boolean variable δ_ij indicates whether a link from agent j to agent i exists.Source: §2 · p. 2
- Each possible communication link has a nonnegative cost that can represent bandwidth, energy, or infrastructure expenditure needed to maintain the network’s desired quality of service.Source: §2 · p. 2
- Subsystem dynamics include state evolution, local control input, process disturbance, and noisy output measurements; the state-space matrices may be unknown.The stated assumptions include known system lag, observability and controllability, and pℓ = n.Source: §2 · p. 3
- The data-driven approach uses recorded input-output samples to address unknown dynamics, with an extended-state representation and a linear fractional transformation of known and unknown dynamics.Source: §2 · p. 3
3 Problem Formulation
The formulation couples communication-link selection with distributed controller synthesis, either jointly trading communication and control costs or sequentially designing a topology with compatible synthesis constraints.
3.1 Co-Design of Topology and Controller
- Co-design minimizes communication-link costs together with control cost while jointly optimizing the controller, Lyapunov matrix, and topology.A communication budget can instead constrain link costs while control performance is optimized.Source: §3.1 · p. 3
- The communication cost adds the cost c_ij whenever agent j sends a link to agent i.The total link cost is combined with the control cost in the co-design objective.Source: §3.1 · p. 3
- Stability, performance, and structure constraints ensure closed-loop stability, bound control performance, and match controller information use to the selected topology.A controller block is zero when its corresponding communication link is absent.Source: §3.1 · p. 4
- Joint stability and structure conditions are non-convex, so their relaxations affect feasibility; design-dependent SFMs generalize the structural-feasibility analysis.Unstable design-dependent SFMs indicate infeasibility of the chosen sufficient synthesis conditions for a topology, while absence of classic unstable SFMs is necessary but not sufficient for synthesis feasibility.Source: §3.1 · p. 4
3.2 Sequential Topology and Controller Design
- The sequential control-aware scheme designs topology first and uses compatible constraints in both stages so every feasible topology admits a feasible subsequent controller synthesis.The topology-design problem may include an optional performance constraint.Source: §3.2 · p. 4
- The sequential topology stage seeks a stabilizing topology and controller using a proxy control-cost objective, which can differ from the controller designer’s true objective.Choosing the true control cost recovers the co-design objective; a different proxy can represent unavailable objectives or reduce computation burden.Source: §3.2 · p. 4
4 Stability and Structure Constraints
The section develops data-driven stability and sufficient structure constraints for topology and controller synthesis, using prior knowledge and data to bound uncertainty.
4 Stability and Structure Constraints
- The uncertainty set combines a priori system knowledge with a data-inferred set, under assumptions that bound disturbance and uncertainty through known sets.The multiplier descriptions use known convex cones of symmetric matrices with LMI representations.Source: §4 · pp. 4–5
4.1 Data-Driven Stability Constraint (Cstab, (7b))
- The extended stability parameterization uses KG = L and G + G^T − X ≻ 0 to decouple controller parameterization from the Lyapunov matrix and enlarge the feasible set.The standard parameterization KX = L uses X = P^-1 ≻ 0.Source: §4.1 · p. 5
- Feasibility of the proposed stability LMI yields a controller and Lyapunov matrix that guarantee input-to-state stability of the extended-state dynamics with respect to the disturbance.The recovered controller is K = LG^-1.Source: §4.1 · p. 5
- The extended-state approach requires pℓ = n, which the authors note is restrictive because pℓ ≥ n generally.Source: §4.1 · p. 5
4.2 Structure Constraint Formulation (Cstr, (7c))
- Exact convex expression of controller structure is unavailable generally, so sufficient L and G conditions impose sparsity at the cost of conservatism.The chosen conditions are taken as the structural constraint Cstr.Source: §4.2 · p. 5
5 Data-Driven Topology Design Schemes
The schemes jointly or sequentially design communication topology and control while accounting for communication costs and control performance. Under stated assumptions, their synthesis constraints provide stabilizing controllers compatible with the selected topology.
5.1 Co-Design of Topology and H2 Controller
- Co-design bounds the closed-loop H2 norm from disturbance to performance signal using trace(Γ), and minimizes that bound to represent control performance.The bound applies under the stated assumptions when the performance constraint is feasible.Source: §5.1 · p. 6, §5.1.1 · p. 6
5.1.1 Implementation of the Co-Design Problem (7)
- The co-design MISDP returns a topology and compatible stabilizing controller that minimize communication costs plus a certified upper bound on squared closed-loop H2 performance.The guarantee holds under Assumptions 1, 4, and 5.Source: §5.1.1 · p. 6
5.2 Control-Aware Communication Topology Design
- The control-aware scheme addresses settings where topology and controller designers are separate or control costs are not shared, using structural and stability constraints for controller synthesis.A feasible structure-design solution yields a structured controller that stabilizes the dynamics under the stated assumptions.Source: §5.2 · p. 6, §5.2.1 · p. 7
5.2.1 Data-Driven Dynamic Coupling Estimation
- The control-aware method estimates subsystem coupling from data using a normalized predictor-sensitivity metric as a proxy for communication value, not as a bound on closed-loop performance.The metric is motivated by subspace predictive control and robust regression.Source: §5.2.1 · pp. 6–7
- Its MISDP trades link costs against estimated coupling strength while enforcing feasibility; an optional worst-case performance constraint can move the design toward full co-design.Removing the coupling discount instead minimizes communication cost under the stated synthesis constraints.Source: §5.2.1 · pp. 7–8
6 Numerical Examples
Across the 4-subsystem chain’s bidirectional topology comparison, co-design achieved the lowest synthesis bounds and realized closed-loop cost, while control-aware design achieved the lowest or near-lowest values. In the IEEE 14-bus example, control-aware design took around one hour on average, whereas co-design exceeded a 24-hour timeout.
6 Numerical Examples
- The examples use excited-system input-output data to design topologies, then synthesize structured H2 controllers under stability, structure, and performance constraints.The comparison varies communication costs across examples.Source: §6 · p. 8
6.1 4-Subsystem Chain Example
- In the 4-subsystem experiments, relative to the exhaustive bidirectional comparison set, co-design attained the lowest synthesis bounds and realized closed-loop cost, while control-aware design attained the lowest or near-lowest values of both.Source: §6.1 · p. 8, Figure 2 · p. 9
- As disturbance bounds increased, the minimum feasible link count rose from zero to one and then two before robust stabilization became infeasible; control-aware performance also degraded from 3 to 6 links.The non-monotonicity is consistent with sufficient structural conditions changing constraints on L and G when links are added.Source: §6.1 · p. 8, Figure 2 · p. 9
6.2 Decentralized Fixed Mode Example
- Data-driven co-design closely matched the model-based co-design benchmark, while control-aware design was conservative for the 4-link topology.Table 1 reports the control-cost upper bound, trace (Γ), for this example.Source: §6.2 · p. 9, Table 1 · p. 9
6.3 IEEE 14-Bus Example
- On the IEEE 14-bus test case, control-aware design took around one hour on average, while co-design did not terminate within 24 hours.Control cost and its synthesis upper bound were closely correlated, and both cost and topology sparsity increased with communication cost.Source: §6.3 · p. 10, Figure 5 · p. 10
7 Conclusion
The paper presents data-driven control-aware and co-design approaches for communication topology design. In the tested examples, control-aware design produced competitive topologies with lower computation times than co-design, while the requirement pℓ = n limits applicability.
7 Conclusion
- The control-aware MISDP couples control-structure characterization with convex synthesis methods and uses an open-loop coupling-strength proxy for performance.The data-driven co-design MISDP minimizes a certified upper bound on squared closed-loop H2 norm together with communication costs.Source: §7 · p. 10
- In the tested examples, control-aware design produced competitive topologies with lower computation times than co-design.Source: §7 · p. 10
- The necessary condition pℓ = n limits real-world applicability; future work could relax it and consider topology design in distributed synthesis.Source: §7 · p. 10