Væringjar II · Independent Research · Kyiv, Ukraine

Control of an irreversibly damaged plant.

Residual-resource assessment, feasible-function selection and control reformulation after structural failure.

Research identity

LEAD

Dmytro Humennyi (Дмитро Гуменний), Ph.D.

Væringjar II is his independent research programme. Scientific direction, methodology and research roadmap are defined by the research lead.

FUNDING

Independently funded

The programme is funded by Dmytro Humennyi. It is not presented as an institutional or corporate-funded research programme.

ACADEMIC CONTEXT

KPI · KNUCA

Academic work at Igor Sikorsky KPI and KNUCA provides research context. Selected subproblems are developed through supervised PhD and MSc research work.

Premise

The post-failure object is not the nominal object.

Let the nominal controlled plant be \(\mathcal P_0\). A critical damage operator \(\mathcal D\) transforms it into the damaged plant \(\mathcal P_d\). During the mission, restoration of \(\mathcal P_d\) to \(\mathcal P_0\) is not assumed to be available.

\[ \mathcal P_0 \xrightarrow{\;\mathcal D\;} \mathcal P_d, \qquad \mathcal P_d\not\equiv\mathcal P_0. \] The task is not recovery of the object. The task is control of the damaged object that actually remains.

This distinction separates post-failure control from repair, simple failover and nominal-state recovery.

Residual state

Damage creates a new resource vector.

Surviving resources can be fully operational, degraded, constrained or unavailable. The state is therefore represented beyond a binary healthy/failed model.

\[ \boldsymbol{\rho}(t) = \begin{bmatrix} \rho_1(t) & \rho_2(t) & \cdots & \rho_n(t) \end{bmatrix}^{\!\top}, \qquad \boldsymbol{\rho}(t)\in[0,1]^n. \] \(\rho_i(t)\) expresses residual operability of physical or logical resource \(i\) after damage.

The vector can include sensing, actuation, compute, communication, energy and other resources that determine the residual control authority of the system.

Core reasoning chain

Residual resources → feasible functions → new control problem.

RResource stateWhat remains available, and at what level of operability?

FFunction setWhich functions can still be realized using those resources?

MMission priorityWhich remaining functions matter most in the current situation?

CConfigurationWhich feasible structure should the system adopt?

UControl strategyHow should the changed plant now be controlled?

Survivability objective

Preserve valuable functionality, not the original configuration.

\[ S\!\left(c,\boldsymbol{\rho}\right) = \sum_{j=1}^{m} w_j\, f_j\!\left(\boldsymbol{\rho}\right)\, \delta_j(c), \qquad w_j\ge 0. \] Survivability combines mission relevance, resource-dependent feasibility and function activation in configuration \(c\).

\[ f_j(\boldsymbol{\rho}) = \prod_{i\in\mathcal R_j}\rho_i \prod_{k\in\mathcal O_j}\max\!\left(\rho_k,\rho_{j,\mathrm{backup}}\right). \] Required and redundant resource sets make the resource-to-function dependency explicit for function \(F_j\).

The optimization objective is not to reconstruct the nominal configuration. It is to select a feasible post-failure configuration that preserves the most valuable achievable functionality under current constraints.

\[ c^\star(\boldsymbol{\rho}) \in \operatorname*{arg\,max}_{c\in\mathcal C_{\mathrm{feas}}(\boldsymbol{\rho})} S\!\left(c,\boldsymbol{\rho}\right). \] The selected configuration is conditional on the actual residual-resource state and the feasible configuration set.

\[ \Phi(c,t)=\sum_{j=1}^{m}w_j\,\varphi_j(c,t), \qquad \Phi(c,t)\ge \Phi_{\min}\!\left(q(t)\right). \] Configuration selection is constrained by a minimum mission-functionality requirement, not by survivability score alone.

Scope boundary

What this research is — and is not.

≠

Not physical recovery

The damaged plant may be irrecoverable during the mission.

≠

Not only redundancy

A predefined backup may not exist, or may not restore the original capability.

≠

Not only safe-state transition

Safe stop remains a terminal option when no acceptable continued-control strategy exists.

Post-failure control

Assess what remains controllable and reformulate control around it.

Research goal

Develop a control methodology for cyber-physical systems with very high survivability.

The target is not preservation of the nominal configuration. The methodology seeks the best verified behaviour that can still be achieved on residual resources after failure or irreversible damage.

Implementation →