We present a new algorithm for the design of maximum hands-off hybrid control sequences for discrete-time switched linear systems that satisfy pre-specified restrictions on the admissible actions and steer a given initial state of the switched system to the origin of the state-space in a pre-specified duration of time. The key apparatuses for our analysis are state-space abstraction and graph theory. A numerical example is presented to demonstrate our results.
This paper addresses the problem of finite-time bipartite consensus in probability for multi-agent systems (MASs) subject to hidden Markov switching topologies. Since it is impractical to obtain accurate mode information of switching topologies, the hidden Markov model (HMM) is adopted to deal with this issue. Asynchronous controllers, whose modes are determined by conditional probabilities, are designed to operate without requiring perfect synchronization with the topological switches. An extended switching matrix Wα representing cooperative-competitive interactions is employed, which avoids the need for gauge transformation. Within this unified framework, by constructing a mode-dependent quadratic Lyapunov function, sufficient conditions are derived for achieving finite-time bipartite consensus/stability in probability under structurally balanced/unbalanced topologies. Simulation results demonstrate the validity of the proposed approach.
Selective State Space Models (SSMs), notably Mamba, employ diagonal state transitions that limit both memory retention and bilinear computational capacity. We propose a factorized bilinear input modulation that augments the SSM with a state-input product. The bilinear form arising in Koopman control theory serves as a structural prior that identifies this missing term. After introducing a shared state across channels (Coupled SSM), the bilinear modulation admits two placements. Coupled Bilinear Input Modulation (seq-BIM) places the full bilinear product on the input side at the cost of sequential computation, and Parallel Bilinear Input Modulation (p-BIM) places the same bilinear product on the state transition while remaining parallel-scannable. Experiments on a multiple input-delay pendulum (memory retention) and NARMA-10 (bilinear computation) show that both bilinear variants improve memory retention and bilinear computation simultaneously over Standard and Coupled baselines. A pathway ablation shows that the bilinear signal acts mainly through the selectivity pathway for seq-BIM. The improvement is statistically robust, with the bilinear variants consistently outperforming the other variants on bilinear computation. Furthermore, only the bilinear variants benefit from increasing the SSM state dimension, while coupling alone shows no improvement, establishing the bilinear mechanism as uniquely capable of exploiting larger state spaces.
Voronoi partitions are widely used to model spatial dominance in multi-agent systems, but Euclidean distance can be a limited proxy when agents differ in initial velocity or dynamics (e.g., drag). This paper studies Cost-Induced Voronoi (CIV) regions, where spatial partitions are induced by transfer costs depending on the full agent state and dynamics. As a closed-form special case, we consider infinite-horizon Linear Quadratic Regulator costs for second-order agents with linear drag, yielding LQR-CIV regions. When a scalar utility is defined over a space, we can define agent utility as the integral over their CIV regions. To enable agents to maximize their spatial utility, we derive a closed-form boundary-integral expression for the utility gradient using the Reynolds Transport Theorem. This closed-form gradient bypasses the need for computationally expensive finite-difference approximations. In a soccer-inspired case study, we demonstrate that our analytical gradient reduces computational cost by a factor of 25 compared to finite-difference alternatives.
This letter studies safe output tracking of Boolean control networks with respect to a Boolean reference system. The objective is to construct a feedback matrix such that the system avoids forbidden states and achieves finite-time safe output tracking from admissible initial conditions. By deleting forbidden states and forming a reduced augmented system with the reference system, the problem is converted into a feasible-domain characterization problem. A matrix criterion is established for global safe output tracking. When the criterion is not satisfied, the same fixed-point computation yields the maximal feasible domain and a feedback matrix on this domain. An algorithm is provided for the domain computation and feedback design, and examples illustrate both non-global and global safe tracking cases.
We study the joint design of privacy and convergence rate for deterministic exact average consensus on strongly connected directed networks. Privacy is observability-based: an honest-but-curious agent must not recover another agent’s datum from its local trajectory. Using exact privacy distance as the deterministic metric, we pose two dual weight-design problems: fastest consensus under a privacy floor, and most private consensus under a convergence-rate ceiling. We prove finite-horizon stabilization of the metric and existence of solutions on compact rank-regular admissible subsets. A row-softmax parameterization enables offline weight design, while a reproducible grid yields empirically nondominated curves on odd cycles and an irregular eight-agent graph, with 6.0–10.5% faster convergence at a fixed exact margin and a 13.5–33.0% larger encoding amplitude at fixed rate, raising the statistical estimation-error floor under noise, while the noiseless normalized margin is a design-invariant graph constant. We further prove an exact-to-statistical lower bound and a formal separation from finite ε-DP, showing that non-recoverability and noise-based indistinguishability address complementary threat models.
Restoring the controllability of networked systems under structural constraints is an important control problem. However, establishing controllability without altering the network structure or introducing additional external controllers remains an open challenge. A temporal segmentation strategy is developed to transform a static network that is not strongly structurally controllable into a temporal network. By utilizing the characteristics of temporal network, strong structural controllability can be restored while preserving the original network edges and external controller configuration. Specifically, the proposed segmentation scheme constructs each snapshot as a serial buds cactus structure, thereby guaranteeing strong structural controllability of the resulting temporal network, independent of the snapshot durations. Based on this structural characterization, an efficient segmentation algorithm is further developed to construct the required snapshots. A numerical example is presented to demonstrate the effectiveness of the proposed method.
This paper introduces a variational control principle grounded in the minimization of free energy on Riemannian manifolds. Unlike classical approaches that treat stability, constraints, and adaptation as separate problems, the proposed framework integrates them into a single variational principle. Control laws, including adaptive parameter updates, are derived as natural gradient flows. This geometric structure inherently enforces hard constraints via barrier potentials, eliminating the need for discontinuous projection operators, while an entropy term provides regularization and robustness. Rigorous analysis establishes the passivity and input-to-state stability of the resulting closed-loop systems. The proposed framework seamlessly bridges the gap between adaptive control and direct state-feedback design. Numerical examples illustrate the method’s geometric anti-windup properties, robustness to disturbances, and the explicit role of entropic smoothing in improving numerical conditioning.
In this paper, we propose an energy-aware consensus control framework for multi-agent systems (MASs) with guaranteed battery safety via linear matrix inequalities (LMIs). Since battery-powered agents such as unmanned aerial vehicles (UAVs) have limited energy, conventional consensus strategies may induce aggressive control inputs, risking over-discharging and operational failures. To address this issue, we introduce state-of-charge (SOC)-dependent interaction weights that reduce the control burden on energy-depleted agents, resulting in a SOC-dependent Laplacian matrix. An observer-based control framework is then developed, where the observer and controller gains are synthesized using H∞ and polytopic LMI formulations, respectively. Based on these gains, sufficient conditions for battery safety are established, providing a computable safe operation horizon. The proposed framework is validated via a MAS formation control example.
This paper studies eigenstructure assignment of output-nulling friends for linear time-invariant systems. The internal and external assignment equations are reformulated as generalized Sylvester equations associated with the Rosenbrock polynomial matrix and the state-input polynomial matrix. The prescribed target matrices need not be in Jordan form. This permits the direct use of companion or block-companion, real Schur, or other convenient target coordinates. A complete parameterization is established based on the Sylvester mapping and the Smith form, separating all solutions into a polynomial right-nullspace part and a local torsion part. The latter is crucial for eigenstructure assignment at invariant zeros and for defective invariant-zero chains. Within the split-realization class, the framework parameterizes all output-nulling friends admitting a closed-loop invariant complement that carries the prescribed external structure. Fixed left-kernel bases convert the torsion constraints into unconstrained Smith-coordinate parameters. The contribution is exact, structural, and target-coordinate-covariant. When the target spectrum avoids the relevant rank-drop set, state-direction-space dimension formulas are extended to arbitrary target matrices.
Adversarial sensing is a security related problem in cyber physical systems (CPS), where a defender controlled target may be tracked by a non-cooperative adversary. The inverse filters, which are launched on the defender, have emerged as tools to infer the exposure of defender’s state to the adversary, which employs a standard filter (referred to as forward filter in this letter), such as Kalman filter, to recursively estimate the defender’s state. This letter proposes an inverse variational Kalman filter (IVKF), which extends the inverse Kalman filter to unknown and even time-varying adversarial measurement noise covariance (MNC) that plays an essential role in the forward (i.e., standard) filtering algorithms. The idea is to jointly estimate the inverse state and adversarial MNC, while the MNC cannot be straightforwardly estimated. Thus, the variational Bayesian (VB) framework is leveraged, and the stochastic natural gradient VB (SNGVB) inference is derived so as to solve the problem of non-conjugacy in computing the posterior of MNC. The performance of proposed IVKF is validated through simulations.
Two methods are presented to advance the modular paradigm of covering the periodic and synchronous sample-and-hold operator with a nominal model plus IQC-bounded error. First, we observe that error IQCs satisfied by one model induce error IQCs satisfied by other models. Second, new IQCs are obtained by Fourier analysis and treatment of the error path as an operator whose gain can be tractably bounded. These tools are used to obtain new static and dynamic error IQCs, including IQCs for a new rational model. Improvement is demonstrated on examples including L2 performance analysis of a structured uncertain sampled-data Lur’e system.
Quantum mean-field games (QMFGs) extend classical mean-field game theory to populations of indirectly observed quantum systems governed by Belavkin stochastic master equations. Prior QMFG literature provides theoretical foundations but, to our knowledge, no computed Hamilton–Jacobi–Bellman (HJB) optimal Nash equilibria. We present two contributions. First, we identify a structural failure mode of nanaïveve trajectory-sampled Bellman training on Belavkin SDEs: when the measurement diffusion direction is aligned with the value-function gradient, the Monte Carlo Bellman residual is dominated by innovation noise, and an asymptotic analysis shows the Bellman objective contains a singular alignment penalty that dominates the HJB residual as the timestep is refined, admitting spurious minimizers. We confirm the geometric prediction on two structurally distinct quantum benchmarks: under aligned noise the trained policy matches zero control, while in a near-orthogonal benchmark Bellman training recovers PDE-form (PINN) performance. Second, using PDE-form HJB learning inside a fictitious-play loop, we compute, to our knowledge, the first numerical Nash equilibrium for a multi-type Belavkin-filtered QMFG, exhibiting equilibria for priors p ∈ {0.25, 0.5, 0.75} and proving the symmetric Nash equilibrium at p = 1/2 by reflection symmetry.
This letter presents Shared-Partition Multi-Output Hinge Regression Trees (SP-HRT) for explicit MPC distillation. Unlike independent single-output trees, SP-HRT learns a vector-valued tree with a common state-space partition, ensuring consistent switching across coupled control channels. We provide a shared-partition approximation result and characterize the regionwise affine closed-loop dynamics of this policy. On an 8-state vehicle chassiscontrol task, SP-HRT yields a compact and fast learned explicit policy among the considered baselines. Paired with a predictive monitor for selective online-MPC fallback, SP-HRT recovers online-MPC-level feasibility at the nominal operating point while substantially reducing average deployment latency.
This paper proposes a novel approach to stabilize power transmission networks using phase theory. First, the power system model is linearized to enable the application of phase theory for analysis. Subsequently, a controller incorporating a lead compensator is designed based on phase theory to stabilize the system. Furthermore, the feedback stability of the interconnected system between the transmission network and the angle based feedback controller is verified. Finally, the efficacy of the method is validated via simulations conducted on a 17-generator-bus power system.
This paper studies a structural consequence of reciprocal delay asymmetry in first-order displacementb-ased formation control. Under an admissible delay margin, the prescribed displacement formation is preserved, while unequal reciprocal measurement delays destroy the nominal gradient structure of the closed-loop dynamics and activate the translational nullspace. As a result, the formation exhibits persistent rigid-body translation generated purely by endogenous interactions, without any external input or reference. We establish an explicit link between internal-force cancellation, centroid dynamics, and delay-induced discrepancy signals, and show that the locked collective velocity is determined by the transient accumulation of reciprocal delay asymmetry through the auxiliary layer. The admissible delay size is defined through the characteristic roots of the projected retarded system, so the locking mechanism is supported by a shapeconvergence and discrepancy-integrability guarantee in this delay-margin regime. The synchronized reciprocal-delay case and the zero/nonzero velocity cases are also characterized. Simulations on a baseline triangular formation, a larger sparse connected graph, and single-edge delay-asymmetry sweeps support the analysis and show that the locked translation is quantitatively modulated by the reciprocal delay pattern.
This work revisits the Differential Dynamic Programming (DDP) algorithm from a regularized dynamic programming perspective by incorporating entropy and KL regularization constraints in both soft- and hard-constrained formulations. We examine how these naturally produce momentum-accelerated DDP algorithms, leveraging curvature information to improve convergence speed, stabilize policy updates, and mitigate sensitivity to local minima and saddle points. Second, we provide a convergence analysis showing the algorithm reaches the maximum-entropy DDP solution, which can be made arbitrarily close to standard DDP with proper hyperparameter tuning. Benchmarks on nonlinear control problems demonstrate faster convergence and improved stability. Moreover, under soft constraints, these gains come without added computational cost.
We propose novel sufficiently smooth projection operators for adaptive control of a class of continuous-time nonlinear systems subject to uncertain parameters. We show: 1) stability of the set where both the plant state is in the target set and the estimate equals the uncertain parameter; 2) robust and uniform global asymptotic stability of the set above, whenever a solution-independent rank condition is satisfied on the target set; and 3) each bounded plant state approaches the target set. Compared with the existing strategies, we show that the proposed projection operators can be designed to increase computational efficiency, fasten adaptation for large estimation errors, or smooth control. We provide numerical simulations to illustrate the effectiveness and versatility of the proposed controller.
We prove global attractivity of the origin for a broad class of continuous-time nonlinear neutral systems that can contain several delays. Instead of restricting the sizes of pointwise delays, and instead of imposing global Lipschitz conditions on the nonlinear terms, we impose a gradient type condition. We cover systems whose uncertain nonlinearities can contain distributed delays. We also provide analogs for coupled difference and ODE systems. We use a new Lyapunov-based approach.
