Papers

Hamilton-Jacobi (HJ) reachability provides a principled framework for synthesizing safety certificates and robust controllers for safety-critical robotic systems. However, applying reachability analysis to high-dimensional nonlinear systems remains challenging: classical grid-based solvers suffer from the curse of dimensionality, continuous-time neural solvers require accurate spatial value gradients, and reinforcement-learning-based approaches often suffer from weak boundary anchoring and non-stationary adversarial policy optimization. We propose a discrete-time neural reachability framework for control-disturbance-affine systems that learns backward reachable tubes (BRTs) and backward reach-avoid tubes (BRATs) through Bellman-Isaacs value propagation. Our key idea is to combine equation-driven self-supervision with structured policy learning: rather than computing explicit PDE-gradients, we exploit the bang-bang structure of optimal safety interventions to construct approximate teacher actions from gradient-free value probes, converting adversarial actor learning into supervised policy learning. To stabilize long-horizon value propagation, we leverage the learned actor to train the value function backward from the terminal boundary using a windowed temporal curriculum, where each window is used as the boundary condition for the next window. Across benchmark problems up to 80 dimensions, our method learns accurate reachability value functions while improving stability over existing learning-based solvers. We further demonstrate observation-space scalability on F1-tenth racing with over 16,000-dimensional egocentric inputs. The learned safety filter generalizes zero-shot to unseen tracks and transfers to a physical RC car, achieving real-time robust collision avoidance.

Opinion dynamics have been studied for decades across disciplines, with much of the theoretical literature focusing on behaviors such as consensus, polarization, and clustering. Although classic models can exhibit more complex opinion patterns in simulations, quantifying such distributions is not fully understood. To address this question, in this paper, we study the behavior of nonlinear opinion dynamics over large-scale networks using graphons, which capture the underlying network structure. In the model, agents update their opinions according to a nonlinear rule that includes saturation effects in interactions. The network is represented by random graphs generated from a graphon, and a corresponding nonlinear dynamical model is introduced over the graphon. We show that the graphon dynamics approximate the finite-dimensional system, when the network size is large. Leveraging spectral approximation results for random graphs, we further show that the equilibria of the nonlinear model can also be approximated by those of the continuum limit. This result enables a quantitative characterization of the opinion distribution based on the underlying graphon structure. The theoretical results are illustrated by numerical simulation.

We present an optimal and convergent model-free policy gradient (PG) reinforcement learning (RL) framework for controlling nonlinear dynamical systems under hard safety constraints. We first construct a class of stochastic wrapper policies centered around a deterministic controller, thereby enabling exploration in unknown environments while preserving the underlying deterministic control structure. We then define a class of parameterized safe-by-construction control policies by truncating these stochastic policies onto hard safety constraints. We next establish, via measure-theoretic arguments, that the potentially nonconvex RL objective under the truncated policy class, as well as its policy gradients, are well-defined. We then develop a model-free PG algorithm based on stochastic gradient ascent that directly searches over these truncated policies and leverage gradient dominance to establish convergence and optimality guarantees. Finally, we validate this framework through simulations on a safe quadrotor navigation problem.

This paper addresses secure leader-follower formation of unknown nonlinear multi-agent systems under actuator constraints, external disturbances, and false-data-injection (FDI) attacks. The graph-coupled coordination-error dynamics are formulated as local zero-sum differential games, where a nonquadratic input utility yields saturation-compatible secure policies and actuator-channel FDI and disturbances act as adversarial inputs. To eliminate explicit dependence on the unknown nonlinear drift, an integral Bellman-Isaacs identity enables critic-only learning from finite trajectory data. A two-power state-cost structure and a deadline-parameterized critic update connect optimal learning with predefined-time stabilization. Unlike fixed-time methods whose settling-time bound is determined by preselected gains, the proposed framework assigns the overall deadline first and allocates it among data informativity, critic learning, the reinforcement window, and formation convergence. Practical predefined-time convergence of the critic and formation errors to bounded residual sets is established independently of initial conditions, while secure actuator constraints are satisfied by construction. Simulations validate the framework under FDI attacks, disturbances, input constraints, and different initial conditions.

This paper develops a resilient learning controller for unknown nonlinear systems operating under actuator limits, false-data-injection attacks, and external disturbances. The key idea is to learn a saturated secure policy directly from finite trajectory data while guaranteeing that both the learning error and the closed-loop state converge to compact neighborhoods within a uniform fixed time independent of initial conditions. An integral formulation removes the unknown drift from the implementable learning law, while stored informative data sustain learning after online excitation fades. To mitigate the closed-loop sensitivity to arbitrary critic initialization, pre-deployment data, which may also be reused from the replay stack, are lifted through a finite-dimensional Koopman representation to construct a stabilizing initial policy, whose inverse saturated-policy map provides a data-driven critic-weight warm start. The resulting controller preserves input constraints by construction and guarantees practical fixed-time robustness under persistent attacks and disturbances. The proposed learning and initialization architecture is further verified through a two-link robot stabilization example, where the results demonstrate rapid state recovery, bounded critic learning, reliable actuator-constraint satisfaction, and improved closed-loop behavior under informed critic initialization.

We consider the problem of objective inference in the context of receding-horizon linear-quadratic regulator (LQR). In this setting, we are given sequential state-action observations, where each observed action is the first control of a newly solved finite-horizon LQR problem. We characterize when the objective of that problem is uniquely identifiable from these observations and when additional observations provide no new information about the objective. We then analyze action prediction at unseen states and show that all objectives reproducing the observed actions yield identical actions throughout the affine hull of the observed states; outside this hull, we derive an upper bound on the prediction error. % and deriving a prediction-error bound outside this hull. Additionally, we show that, when only the linear objective terms are unknown, exact prediction holds at every state. Finally, numerical results show that, even under stochastic observation noise, re-optimizing an inferred objective enables accurate action prediction at unseen states across different planning horizons.

Existing operation formulations for AC/DC distribution grid often oversimplify the interplay of AC/DC interconnections and VSC characteristics. Moreover, current distributed algorithms depend on gradient-based methods, which achieve only linear convergence rates and struggle to scale efficiently for large systems. This paper proposes a convex ALADIN variant that exploits second-order derivatives of convex subproblems, achieving locally quadratic convergence for distributed nonlinear but convex optimization problems. Then, this convex ALADIN is applied to a separable AC/DC OPF model for AC/DC hybrid distribution grid, explicitly incorporating complicated AC/DC interconnections and multiple droop-controlled VSCs while retaining computational traceability. To bridge theory with practice, we implement the distributed convex second-order optimization framework using the PROcess Orchestration Framework, a co-simulation platform that automates workflow design, model integration, and distributed execution via a user-friendly graphical interface, eliminating manual coding. Numerical results illustrate effectiveness of the proposed model.

Diffusion-based generative models (DMs) have found applications in control problems, and in particular robotics, where the DMs enable exploration of possible control solutions. A critical shortcoming of these applications is that they have lacked optimality guarantees. This is a problem for their potential use in fuel-optimal spacecraft trajectories that are characterized with long time-horizons and bang-bang profiles. Alternatively, indirect optimal control methods ensure explicit satisfaction of necessary conditions, but are highly sensitive to the initial costate estimation needed to solve the resulting Hamiltonian boundary-value problems (HBVPs). To alleviate this sensitivity and enlarge the convergence domain of HBVPs, advanced indirect methods have been developed that use smoothing approaches and continuation. We propose a diffusion-based multiple shooting indirect control method that combines the exploration capability of DMs with indirect method to generate fuel-optimal spacecraft trajectories. We benchmark our method against an advanced indirect method on a fuel-optimal Earth-Mars low-thrust transfer problem, showing higher convergence robustness than the advanced indirect method that is based on random costate initialization. Code and visualizations are available at https://saeidtafazzol.github.io/Diffusion_Indirect_Control/.

Large language models (LLMs) are increasingly used in specialized university courses, but control-systems questions require coordinated terminology, notation, derivations, and stepwise explanations. Direct general-purpose responses may be inconsistently structured and hard to verify. Using exercises and reference solutions from a Linear Control Systems course, we built a supervised fine-tuning dataset of 360 system-user-assistant conversations. We applied LoRA to Qwen2.5-3B-Instruct and Qwen2.5-7B-Instruct. With identical data splits, inference settings, and evaluation protocols, we compared base and fine-tuned models and tested LoRA ranks r=4, 8, and 16. Evaluation used ROUGE, BERTScore, and structured-output features to measure reference-answer similarity and stability of the Solution-Method-Teaching Points format. LoRA improved both similarity and structured-output stability at both sizes. On the current test set, 7B-r16 achieved the highest ROUGE-L (0.4093) and BERTScore-F1 (0.8643), while r=8 offered a better balance between performance and parameter efficiency. Bootstrap resampling showed ROUGE-L gains of 0.0764 [0.0613, 0.0915] for 3B-r16 and 0.0874 [0.0687, 0.1042] for 7B-r16; both intervals exceeded zero, indicating stable textual-similarity improvements on the current test set. These results suggest LoRA can align open-source instruction-tuned models more closely with the language and pedagogical organization of course reference answers. However, the metrics mainly capture textual similarity and formatting consistency, not domain-specific reasoning or mathematical correctness, which require expert assessment and task-specific rubrics.

With the emergence of online social networks as a primary platform for advertising and advocacy, enhancing a user's influence has become of significant interest. In this paper, we investigate this problem under the Friedkin Johnsen opinion dynamics model, wherein stubborn agents influence the opinions of other agents in the network. Unlike most of the existing works, we leverage topological properties of the network to increase the influence of a desired stubborn agent. Specifically, we introduce the notion of edge modification, which mimics the mechanism of recommendations in social networks. First, we present a topology-based condition that identifies edge modifications that always increase the influence of a desired stubborn agent. It is shown that the impact of the chosen edge modifications remains robust to changes in parameters such as stubbornness and the interaction weights. Thereafter, we formulate a discrete optimisation problem to identify a set of edge modifications that maximise the agent's influence centrality. We present a computationally efficient approximate solution to the optimisation problem. Finally, we demonstrate the effectiveness of our approach on the Friedkin-Johnsen opinion dynamics over the Erdos Renyi random graph.

We study a finite-state partially observable restless multi-armed bandit (PO-RMAB) motivated by resource-constrained wildlife monitoring. The underlying condition of each location evolves independently, while only a limited number of locations can be actively monitored at each decision epoch. Activation reveals the current state, whereas passive operation provides no observation, yielding a collapsing-bandit belief dynamics. Our main contribution is a structural characterisation of optimal policies for the multidimensional belief-state problem. We establish sufficient conditions under which an activation advantage is monotone with respect to the belief state, and hence the optimal policy has the threshold type structure over the $(M-1)$-dimensional belief simplex. The key result is obtained by bounding the variation of the value function through a model-dependent Lipschitz constant. We further specialise the result to one-step birth-death dynamics and derive explicit bounds.

We study an inexact interior-point method for nonsmooth, possibly nonconvex optimization in a Hilbert space with inequality constraints ordered by a cone in a Banach lattice, with particular emphasis on infinite-dimensional state-constrained optimal control. The objective function is given by the sum of a smooth, possibly nonconvex term and a convex, possibly nonsmooth term with a computable proximal mapping. The constraints are formulated by means of an order cone in a Banach lattice. This setting covers finite-dimensional nonsmooth nonlinear problems with componentwise constraints as well as infinite-dimensional PDE-constrained optimization problems with pointwise state constraints. The method is based on barrier-regularized subproblems, which are solved inexactly by a proximal-gradient method. We consider logarithmic and power-type barriers and derive the differentiability and curvature estimates needed for the convergence and complexity analysis. Under suitable constraint qualifications and compactness assumptions, we establish approximate KKT conditions for the original problem and convergence of the inexact interior-point sequence. For logarithmic and power-type barriers, we derive complementarity estimates and outer iteration bounds; the corresponding power-barrier rates and total inner-outer complexity bounds are stated under explicit barrier-path and uniform smoothness assumptions. For convex problems, we obtain stronger convergence results. We apply the framework to state-constrained semilinear elliptic optimal control and sparse dictionary learning with nonlinear side constraints. Numerical experiments illustrate the proposed method.

Automatically recognising a fabric's construction (jersey, twill, satin) is a bottleneck in textile sourcing, where incoming swatches are still typed by hand. Benchmark accuracy suggests the problem is solved, yet rarely survives deployment. On the \numClasses{}-class FabricFlow benchmark we expose three gaps that headline accuracy hides. First, a duplication audit reveals train/test leakage that inflates accuracy; we rebuild leakage-free splits that report the true difficulty. Second, on the clean data the binding failure is acquisition-source shift between catalogues, not the peripheral shortcuts one might fear: on an archive-exclusive hold-out, standard training holds 58.0% Top-1 at a calibration error of 0.158, while a simple, architecture-agnostic central-texture recipe adds 13.5 Top-1 points and restores calibration. Third, because confusing one fabric family for another is costlier than a within-family slip, we optimise a taxonomic-severity cost: a confidence-gated routing policy auto-types confident swatches and refers only the uncertain minority to a human, sharply cutting onboarding cost. Throughout we report honest negatives: hierarchical classification, OCR fusion and zero-shot vision–language models all fail to help, yielding a concrete, calibrated, cost-aware recipe for deployable textile onboarding.

We establish the equivalence between the stochastic optimal control and path space formulations of the Schrödinger bridge problem (SBP) for the kinematic equation on a compact connected Lie group. Using the geometric concepts of horizontal lift and stochastic anti-development, we derive a Girsanov-type change-of-measure result, and show that the expected control energy equals the relative entropy of the controlled path law with respect to the reference Wiener measure. Thus, the SBP is equivalently a path space relative entropy minimization problem subject to prescribed endpoint marginals.Our result has three useful implications. From an analytic viewpoint, the shown equivalence helps prove the existence and uniqueness of the SB. From a probabilistic viewpoint, it helps interpret the SB as the most probable deviation of the uncontrolled stochastic dynamics consistent with the endpoint constraints. From a computational viewpoint, it allows using static Sinkhorn recursions to directly solve the relative entropy minimization problem and compute the optimal path measure. We illustrate the equivalence numerically on the torus $\mathbb{T}^2$. The code is publicly available at: https://github.com/gradslab/LargeDeviationSBP

Among various production methods, hydrogen generation via electrolysis powered by renewable energy plays a key role in achieving large-scale green hydrogen production. The triple active bridge isolated DC-DC conversion system exhibits significant application potential in hydrogen production due to its advantages, such as high energy density, wide step-down ratio, and high reliability. However, the output current ripple at the hydrogen production port critically affects the efficiency of the electrolyzer and the hydrogen production rate. Existing studies have limited optimization effects on current ripple and struggle to achieve dynamic optimization, leading to constrained ripple suppression under dynamic operating conditions. To address this issue, this paper proposes a low-ripple modulation strategy based on coordinated optimization of inner and outer phase-shift angles for multi-port power conversion systems in renewable energy hydrogen production. By establishing an accurate mathematical model, the optimal phase-shift angle combination under minimal current ripple conditions is derived. An improved differential evolution algorithm with adaptive parameter strategy is employed to achieve global optimization under dynamic conditions. Simulation and experimental results demonstrate that the proposed strategy effectively suppresses current ripple, providing an efficient and reliable solution for hydrogen production from fluctuating renewable energy sources.

This paper studies how a feedback law synthesized directly from data can be realized by spiking control while retaining a game-theoretic performance guarantee. We consider distributed $\varepsilon$-Nash equilibrium (NE) seeking in network games played by linear dynamical agents with unknown models and exogenous disturbances. The pseudo-gradient of the game is treated as a regulated error, and local internal models account for signals generated by known exosystems. Robust linear matrix inequalities are then used to compute stabilizing analogue feedback gains directly from noisy local input-state data, without identifying the agent dynamics. To implement these gains using only fixed-weight spikes, we develop two spiking realizations. The first realization uses non-interacting leaky integrate-and-fire units, while the second permits reset coupling among the neuronal units. In both cases, a continuous auxiliary coordinate exposes the impulsive closed loop as the stable analogue system driven by a bounded implementation error. This representation yields forward completeness, Zeno-freeness, and an ultimate bound on the pseudo-gradient, subject to explicit event-processing conditions for the connected architecture. The bound implies that, after a finite transient, the agents' outputs constitute an $\varepsilon$-NE for every $\varepsilon$ above a finite threshold. A spacecraft formation reconfiguration example illustrates the data-driven synthesis, the two spiking realizations, and their practical equilibrium behavior.

We study joint sensor placement and detector operating-point allocation for guarding a region against an adversarial crossing. Each sensor may adjust its detection threshold, while all sensors draw on a shared network-level false-alarm budget. For a Gaussian signal-excess model of a square-law detector, we give a necessary and sufficient condition for the negative-log miss hazard to be concave in a sensor's false-alarm probability. At fixed deployment, this yields a concave max-min allocation whose saddle point equalizes marginal barrier gain per unit alarm against a worst-case occupation measure. A perspective reformulation supplies linear cuts for the mixed-integer joint problem, and a separate certificate lower-bounds the continuum barrier strength independently of the graph used for path search. On a deep-water case study based on the canonical Munk profile, reallocating a fixed alarm budget raises the graph design objective by 14.9% at unchanged sensor count and alarm load, and the certificate establishes the barrier requirement on the interpolated continuum field, which the graph value alone cannot.

Control barrier functions (CBFs) enforce safety through conditions imposed pointwise in time without consideration of state evolution over a future horizon. Thus, CBF-based controls are typically myopic. Predicted-flow CBFs (P-CBFs) generalize CBFs from a function of the current state to a functional of the predicted flow under a parametrized control. P-CBFs can certify safety over the entire prediction horizon while simultaneously allowing for performance optimization over the horizon. However, prior work with P-CBFs only applies to control-affine systems, and suffers from a limitation where the prediction horizon can shrink or even vanish. This article addresses both of these shortcomings by introducing a planning control that smoothly transitions from a parametric plan to a backup control (if needed) and a time-shift parameter that determines if transition is needed. The evolution of the control-plan and time-shift parameters is determined from a single guaranteed-feasible convex optimization, which reduces to a quadratic program (QP) if the control limits are a convex polyhedron. The real-time executed control is determined from the instantaneous planning control and time shift. This method simultaneously addresses safety certification and performance optimization over the fixed prediction horizon. The approach is compared to nonlinear model predictive control in simulation of an autonomous car navigating a dense obstacle environment.

Control allocation for multirotors with bidirectional propellers is commonly formulated in signed-thrust variables, where the wrench map is linear. The signed-quadratic map from physical rotor speed to thrust, however, is not a local diffeomorphism at zero speed. This work derives two distinct consequences. Under nonredundant full actuation, a single-propeller reversal removes one instantaneous task direction; hence, no global continuously differentiable exact static allocator exists over the complete task space. Under redundant actuation, the physical task map may remain regular, yet a transverse pseudoinverse zero crossing requires an unbounded rotor-speed derivative. We define differential realizability as regularity of the physical lift of an actuator-output section, derive exact and first-order validity conditions, and distinguish structural rank loss from an allocator- induced rate singularity. A local nullspace deformation repairs isolated pseudoinverse reversals, while a global fixed-orthant construction establishes existence of regular sections at the cost of persistent task-preserving internal actuation.

We study the relation between positive semidefiniteness and entrywise nonnegativity for solutions of continuous-time Lyapunov equations. For a real Hurwitz matrix $A$, we show that the solution of $AP+PA^\top=-Q$ is positive semidefinite for every symmetric entrywise nonnegative $Q$ if and only if the solution of $A^\top X+XA=-R$ is entrywise nonnegative for every positive semidefinite $R$. This equivalence follows from the adjointness of the two solution operators and extends to all real unmixed matrices. We then prove that both properties hold for every real Hurwitz companion matrix, settling a conjecture previously established under the additional assumption of a real spectrum. The proof combines a controllability-Gramian normalization with a pairwise positivity theorem for the coefficients of the adjugate polynomial of a real accretive matrix. The latter is obtained from a coefficient-sign property of bivariate polynomials, an auxiliary determinant that does not vanish on the product of two open right half-planes, and a rank-one perturbation argument. Covariance and energy interpretations connect these results with dissipative realizations, damped second-order systems, and comparisons between input Gramians.

Training large AI models requires thousands of processors working in parallel. This synchronized load poses a challenge for traditional power delivery architectures, because IT power ramps much faster than grid hardware can compensate. This paper presents a hardware solution to this problem, introducing a novel power delivery architecture which automatically detects changes in load power and compensates using on-rack energy storage, giving time for the grid to respond to the varying load. The architecture is validated experimentally, powering a training load while limiting the grid-side power ramp rate such that it stays within pre-specified range. The prototype presented is rated to deliver up to 10 kW of buffered power in a 400 VDC system, with a bill of materials cost of $3,500 USD. The system design is described in detail. A key advantage of this architecture versus other approaches is that it reliably buffers power fluctuations without requiring any changes to system software, making it compatible with any training workload.

Recent developments in the US knowledge economy have created a significant growth in datacenter loads, with two major consequences for power generation. First, to compensate for growth in load, datacenters are encouraged to bring their own generating units. Second, in search of the remaining pools of dispatchable generation, utilities are increasingly turning to subtransmission and distribution level generating assets. Coupled with increasing loads and the resulting tighter grid conditions, both trends are likely to create a need to commit a large number of localized generating units under grid constraints. We propose an extension of Relax-and- Round Unit Commitment (RRUC) that is capable of committing generating units for larger problems faster than conventional methods, while staying within intertemporal and spatial MVA constraints. We demonstrate the performance of RRUC using synthetic congestible test systems ranging from 100 to 20,000 buses. RRUC consistently finds low cost solutions, independent of the problem size, and its run time increases sub-quadratically in the number of buses. RRUC can solve the 100 bus system in less than a second and the 20,000 bus system 7 minutes. In contrast, a leading state of the art solver cannot find a feasible solution to the 100 bus system in 15 minutes.

This paper develops an integrated framework for estimation, prognosis, and reliability assessment of stator inter-turn faults in induction motors. The fault is characterized by its severity, defined as the fraction of short-circuited turns, and its spatial orientation. A geometric fault model shows that the resulting output signature is affine in the fault severity and exhibits a fundamental spatial periodicity. Exploiting this structure, an augmented-state particle filter jointly estimates the nonlinear electromechanical state and the unknown fault severity while quantifying posterior uncertainty. The estimated degradation is then propagated using four prognostic models: linear trend, Holt exponential smoothing, Bayesian degradation, and particle-based forecasting. Their predictions are connected to threshold-crossing remaining useful life (RUL), first-passage reliability, degradation-dependent hazard reliability, and a Weibull lifetime benchmark, thereby providing both deterministic and probabilistic health assessments. Numerical results demonstrate accurate online fault estimation and output reconstruction, characterize the effects of degradation pattern and prediction horizon on prognosis, and show consistent reliability and threshold-crossing predictions. Moreover, estimation accuracy remains comparable across the distinct fault orientations induced by the spatial periodicity. The resulting framework provides a unified connection from physics-based inter-turn fault modeling to online diagnosis, degradation prognosis, and reliability assessment.

Relative navigation is a fundamental task in space proximity operations and autonomous rendezvous. The nonlinear relative orbital dynamics are equivariant and admit a semidirect product Lie group symmetry. This property is used to design an Equivariant Filter (EqF). The filter estimates the relative position and velocity between a chaser spacecraft and a target by lifting the filter dynamics to the group, while respecting the underlying geometry of the problem. Simulations demonstrate the filter's performance and effectiveness.

This work enhances global path planning via a pure-pursuit controller with multi-model kinematic switching that sustains plan fidelity across diverse terrains. The system includes a traversability graph for terrain analysis, a Heading-Aware A* algorithm for generating feasible paths, and a multi-model Pure Pursuit controller for dynamic tracking. A core innovation is adaptive kinematic modeling, enabling real-time switching between kinematic models based on terrain features and robot states. This adaptability optimizes path efficiency and energy use in challenging scenarios. We validate the approach in simulation on different platforms, namely the Artaban quadruped and the X3 quadrotor drone, showcasing improved performance, robustness, and adaptability over standard baselines.

We introduce an adaptive multi-parameter variant of ADMM and prove that it exhibits local superlinear convergence once the set of active constraints has been identified. In simulations, the proposed algorithm consistently outperforms OSQP, a standard ADMM solver, in terms of iteration count. We then implement an MPC solver based on our method and compare its runtime against a broader selection of state-of-the-art algorithms. Evaluations on challenging benchmark problems reveal that our approach delivers competitive performance both in terms of average and worst-case solve times, without being limited to coarse tolerances, as is typically the case for standard ADMM implementations and first-order methods.

Control barrier function safety filters enforce constraints by modifying a nominal input, but the resulting switching can destabilise the closed loop even when the nominal and filtered modes are individually stable. This paper presents a design framework for safe and globally exponentially stabilising controllers for linear systems with a single full-relative-degree affine constraint. We show that the filtered-mode spectrum is fixed by the barrier tuning and is independent of the plant, nominal controller, and quadratic-program weighting. This structure yields an explicit nominal controller for which the safety filter remains inactive everywhere. For a prescribed nominal controller, we prove that the nominal and filtered modes admit a strong common quadratic Lyapunov function if and only if the ratio of the nominal characteristic polynomial to the barrier polynomial is strongly strictly positive real. This equivalence characterises the existence of a common quadratic Lyapunov and provides a scalar frequency-domain test, along with an explicit interval of admissible gains. Building on these results, the extended analysis derives an explicit common storage function and reduces an existing LMI synthesis condition to a feasibility test in a single matrix variable. A flexible two-mass example explains a known instability mechanism and demonstrates how the proposed design restores safety and global exponential stability.

Robots are increasingly used in diverse application areas, where autonomous navigation plays a central role. As these systems become more widespread, improving their energy efficiency is critical to extending operational time and reducing environmental impact. The Robot Operating System (ROS) is a widely adopted middleware for robotics, offering a rich set of configurable packages. However, this flexibility can result in suboptimal software configurations in dynamic environments, negatively affecting both performance and energy consumption. This paper investigates the impact of ROS 2 package reconfigurations on the energy efficiency of mobile robot navigation. We conduct a controlled experiment in two warehouse-like scenarios (small and large) with varying obstacle layouts and Costmap 2D configurations (essential to the Nav2 stack). Through repeated trials, we measure energy usage, power profile, CPU load, memory consumption, and navigation performance. Results show that configurations must be carefully chosen for the specific robotic environment, and we were able to identify critical settings that lead to good and poor performance and energy consumption.

Optimal dispatch of battery energy storage systems requires balancing energy arbitrage against cycle-induced degradation, which is accurately quantified through rainflow cycle counting. However, rainflow's combinatorial, nondifferentiable algorithm is incompatible with both convex optimization and gradient-based neural network training. We present a self-supervised mixed-integer differentiable predictive control framework that trains neural policies directly on exact rainflow degradation through a novel differentiable rainflow layer combining exact gradients at state-of-charge extrema with dense proxy gradients on incremental changes, enabling stable end-to-end training while preserving true degradation physics. A mixed-integer differentiable architecture enforces power balance, dynamics, and mode exclusivity, with a safety filter guaranteeing constraint satisfaction. We evaluate the framework on 3,650 real battery-day scenarios (a 10-battery fleet over 365 days) spanning three utility regions (SDG&E California, Xcel Energy Colorado, APS Arizona) with diverse time-of-use pricing structures. A single-battery trained policy achieves a 0.35% performance gap on its training distribution with over 200x speedup, while fleet-wide training generalizes across all households and utility regions, achieving a 3.33% performance gap with 564x computational speedup (62 seconds vs. 9.7 hours) and 100% feasibility. The millisecond-scale inference reduces computation by over two orders of magnitude compared to mixed-integer solvers, enabling practical deployment at scale.

This work studies equilibrium-preserving non-stop trajectories of aerial carriers connected to rigid loads by variable-length cables. Internal-force motions vary the cable directions without changing the load wrench, while cable-length actuation shapes the radial realization of the carrier trajectories. We derive an explicit cable-length law for realizing prescribed carrier-position profiles along a fixed direction, with constant altitude as a relevant specialization. Under this constraint, a carrier stops exactly when its cable direction stops changing. This characterization reveals a distinction between unrestricted and level motion: variable cable lengths enable bounded non-stop motion with two carriers, whereas periodic level non-stop motion is obstructed for two carriers and constructively achieved for three or more under explicit geometric and feasibility conditions. Numerical simulations illustrate the constant-altitude construction.