This paper presents a model-based, cascaded control structure for a balancing manipulator actuated by pneumatic artificial muscles (PAMs). The balancer is designed to offer two operating modes: First, a balancing mode (BM) compensates for the total weight of the system so that the user feels only minimal resistance when moving the end-effector (EE) during load handling. Second, a position controller (PC) stabilizes the EE at a fixed reference position, even if the attached payload abruptly changes. The proposed cascaded control architecture consists of fast inner loops that control the pressures inside the PAMs, while an outer cascade allows for switching between BM and PC. A velocity-based backstepping approach is employed for the BM. For the position-control mode, a backstepping controller is implemented, which is extended with a cubic as well as an integral error term. An experimental validation on a test rig confirmed the effectiveness of both functions.
This paper develops a functional $\mathscr {H}_{\infty }$ filter for nonlinear descriptor systems subject to external disturbances. Conventional $\mathscr {H}_{\infty }$ filtering approaches for descriptor systems impose restrictive regularity assumptions and employ implicit descriptor-form filters, leading to practical implementation difficulties. Moreover, existing approaches mainly target full-or reduced-order state estimation, which is computationally inefficient when only a specific functional of the state is required. To address these limitations, the filter is formulated directly in an explicit state-space framework and can be initialized with arbitrary initial values. The filter order is chosen to be less than or equal to the dimension of the functional vector to be estimated, thereby reducing computational complexity. The considered nonlinearities are characterized using incremental quadratic constraints parameterized by appropriate multiplier matrices, which encompass Lipschitz, one-sided Lipschitz, monotone, and many other nonlinearities. Sufficient criteria for the existence of the proposed filter are established through a rank condition imposed on the system matrices together with a set of linear matrix inequalities (LMIs). Under these conditions, asymptotic stability of the estimation error dynamics is guaranteed, while the influence of external disturbances on the error is bounded within a prescribed $\mathcal {L}_{2}$-performance framework. Finally, numerical simulations demonstrate and validate the effectiveness of our theoretical results.
Safety and stability under model predictive control can be achieved by employing terminal ingredients, i.e., a terminal region, a terminal cost function, and a terminal controller. Thereby, the controlled system can be safely stabilized for relatively short prediction horizons, which, in general, reduces the online computational times. However, computing terminal ingredients for perturbed nonlinear systems with uncertain parameters is a challenging task, especially with increasing state dimension. In this paper, we encode this task as a set of reachable set containment problems and propose a tailored, computationally efficient successive convexification algorithm. This algorithm returns a volume-wise monotonically increasing sequence of terminal regions to obtain a large region of safe operation. To reduce the computational burden, we a) leverage scalable set-based reachability analysis, b) represent the terminal region as a zonotope, and c) choose the terminal cost as its Minkowski function. We demonstrate the computational efficiency and broad applicability of our approach using several examples from the literature with up to 18 dimensions.
This paper proposes a novel algorithm for estimating the region of attraction of equilibrium points for nonlinear discrete-time autonomous systems. The method iteratively expands an initial estimate of the region of attraction by constructing unions of sublevel sets of learned functions parametrized as neural networks. Unlike conventional techniques that rely on a single global Lyapunov function, the proposed approach provides a collection of local Lyapunov-like functions, enabling richer representations and potentially larger region of attraction estimates. These functions are trained using sampled state-space data, and their Lipschitz continuity ensures that desirable properties extend beyond the training samples. The devised strategy is tested via numerical simulations, demonstrating the effectiveness of the proposed approach.
Conventional energy-maximising controllers for wave energy converters (WECs) often exaggerate device motion, which can shorten device lifetime and increase operational costs (OpEx), by reducing maintenance intervals and system reliability. This paper proposes a novel health-aware WEC controller to achieve a suitable trade-off between captured energy and device lifetime, ultimately leading to a lower levelised cost of energy (LCoE). Using a reliability metric, the proposed controller incorporates power take-off degradation into the performance function of an economic model predictive controller (EMPC). The proposed performance function does not require additional (regularisation) terms to convexify the optimisation problem, as is often necessary for typical energy-maximising WEC EMPCs. Simulation results demonstrate the effectiveness of the proposed controller in achieving an optimal trade off between captured energy and device longevity. Furthermore, this study examines potential challenges in the implementation of health-aware control for WECs and outlines key directions for future research in the health-aware WEC control domain.
Policy synthesis in Markov decision processes uses a known reward function to compute a policy that maximizes it. However, onlookers may infer reward functions by observing agents, which can reveal sensitive information. Therefore, in this paper we introduce and compare two methods for privatizing reward functions in policy synthesis for multi-agent Markov decision processes, which generalize Markov decision processes. Reward functions are privatized using differential privacy, a statistical framework for protecting sensitive data. The methods we develop perturb (i) each agent's individual reward function or (ii) the joint reward function shared by all agents. We prove that both of these methods are differentially private and show approach (i) provides better performance. We then develop guidelines for selecting reward functions to achieve high performance while remaining private, and we quantify the increase in computation required to compute policies with privatized rewards. Numerical simulations are performed on several examples, and these examples show that even relatively strong differential privacy (epsilon =1.3) induces as little as a 5% decrease in performance and 0.016% increase in computation time.
This paper presents a novel algorithm for the dynamic inversion of nonlinear systems within the output tracking control framework, wherein the inverse serves as an open-loop nominal controller to facilitate feedback stabilization of the tracking error dynamics along a nominal trajectory. The desired dynamic response for the open-loop controlled system is treated as a pseudo identity from which the causal and stable inverse is defined. For non-minimum phase systems, the Fliess normal form is used to enable a practical pseudo-inverse design without the need for internal dynamics stabilization or reverse-time previewing. Unlike exact inversion, which can be unstable or anti-causal, the proposed pseudo-inverse is stable and implementable in real time. A nontrivial application example illustrates the algorithm.
Objective: This study aims to reduce expert annotation effort in detecting patient-ventilator asynchrony (PVA) by introducing a semi-supervised learning framework for time series classification. Methods and procedures: We propose a model-independent framework that integrates hierarchical clustering and dynamic time-warping (DTW) for efficient data selection and label projection. The framework includes five steps: data collection, selection, annotation, projection, and model training. It is validated using a fully labeled dataset from Fondazione I.R.C.C.S. Policlinico San Matteo and applied to an unlabeled dataset from Maasstad Hospital, where annotation consistency and label quality are analyzed. Results: The framework reduces annotation effort by over 75% while closely resembling classification performance. On the San Matteo dataset, the model trained with projected labels achieved performance close to that of a fully supervised model. The method effectively captured rare PVA types and improved macro-averaged F1 scores compared to random sampling. On the Maasstad dataset, despite annotation inconsistencies, the framework demonstrated moderate detection performance (75% micro-averaged $F_{1}$ score) using labels from a single clinical expert. Conclusion: Our semi-supervised framework enables scalable and efficient annotation of clinical time series data, maintaining model accuracy with minimal expert input. It is robust across datasets and adaptable to varying signal quality and annotation consistency.
This paper presents a new methodology for the design of PID controllers based on linear matrix inequalities (LMIs). The proposed method can be applied to arbitrary-order SISO time-delay systems. The core of the approach relies on an innovative state-space control architecture that enables the integration of arbitrary-order systems with PI/PID controllers combined with different measurement noise filters, or alternatively, with a pure PI controller. The methodology allows the consideration of multiple design objectives, including disturbance rejection, reference tracking, measurement noise attenuation, the imposition of an exponential decay rate, the guarantee of positive PID controller gains, and robustness margins in the frequency domain, by imposing upper bounds on the H(infinity )norm of the main sensitivity functions. Moreover, the approach explicitly accounts for parametric uncertainties. For validation, numerical examples were carried out ranging from low-order to higher-order models, combining different controller structures and multiple objectives simultaneously. The results were compared with recent and relevant methods from the literature, demonstrating the effectiveness and superiority of the proposed methodology.
We study stabilizing a scalar linear system over a “timing” channel, where information is communicated via the timestamps of transmitted symbols. Each symbol, sent from a sensor to a controller in a closed-loop system, is received after a random delay. The sensor encodes information in the waiting times between transmissions, and the controller decodes it using the inter-reception times of symbols. This setup resembles a telephone system: a transmitter signals a call with a “ring,” and the receiver becomes aware of the “ring” after a random connection delay. With no data payload exchanged, this setup provides an abstraction for performing event-triggering control with zero-payload rate. We show that for system stabilization (state converging to zero in probability), the timing capacity of the channel must be at least as large as the entropy rate of the system. For exponentially distributed symbol delays, we provide an “almost” tight sufficient condition using a coding strategy that refines the message estimate with each new symbol. Our results generalize previous zero-payload event-triggering control strategies, revealing a fundamental limit for using timing information in stabilization, independent of the transmission strategy.
Adversarial attacks are often modeled as pointwise perturbations of individual samples, which can miss structured distributional effects and may waste perturbation budget on examples that are already misclassified. We study a data-driven Wasserstein attack model in which the adversary shifts the empirical distribution under a label-preserving transport budget. Starting from this formulation, we derive a finite-dimensional transport surrogate and an equivalent lifting that makes the role of transport couplings explicit. We then introduce an entropic regularization, obtaining a difference-of-convex formulation that penalizes attacks which mainly amplify the loss of already misclassified samples. This leads to Partial Sinkhorn, an iterative algorithm that combines convex-concave linearization with Sinkhorn-type updates, such that any limit point of a convergent subsequence is a KKT stationary point of the penalized problem. Experiments on synthetic and MNIST tasks show that the proposed method generates stronger attacks than FGSM under comparable perturbation budgets, particularly in the low-distortion regime. The framework also highlights links between adversarial attack, optimal transport, and distributionally robust control.
The Koopman operator, which describes a dynamical system via a linear representation that can be approximately learned from data, allows application of linear control techniques to nonlinear systems. This work considers a nonlinear optimal control problem with final state constraints, which we alternatively represent by a linear problem on a lifted state space described by the Koopman operator. We show that the optimal cost-to-go to this linear problem has a piecewise linear form with respect to the lifted state. A robust formulation, in which we minimize the worst-case cost with respect to bounded errors in the initial state and Koopman dynamics, retains a piecewise affine structure. Due to the combinatorial nature of the problem, the number of possible input sequences grows exponentially in the horizon, and so we provide a heuristic pruning algorithm that reduces the search space to a much smaller subset. Our control approach is generally applicable, but its effectiveness depends on a domain-specific choice of lifting functions, termed observables. For a class of systems with dynamics described by some number of distinct “entities”, we define observables that describe “densities” of these entities, as well as products of densities that capture a richer class of interactions between entities.
In disaster scenarios, rescue plans must optimally allocate limited resources to maximize the number of feasible rescues. Full evacuation is often infeasible due to constraints such as limited fuel, time, or transportation capacity, making it crucial that allocations respect pre-established ethical priorities. These priorities are enforced through lexicographically ordered terminal sets. In this paper, we introduce the notion of blamelessness to network routing, which ensures routing plans yield terminal solutions in the highest feasible priority set. We model disaster response as a network routing problem, minimizing fuel usage while satisfying given ethical and physical constraints. First, we derive conditions on the cost function of a linear program (LP) to produce blameless but sub-optimal plans. Next, we formulate a two-stage LP that minimizes network routing cost subject to terminal priority set constraints. Finally, we show that a convex combination of blameless and optimal routing objectives always exists, allowing use of a single convex LP to produce plans that are resource-optimal subject to being blameless. Disaster rescue simulations are used to empirically study the sensitivity of blamelessness and network optimality to the convex-combination parameter. Routes must respect triage-based ethical priorities while minimizing network cost under a finite time horizon, limited route availability, and transportation capacity constraints.
In the aerospace control domain, Nonlinear Dynamic Inversion (NDI)-based control laws are widely spread. As a variation to Incremental Nonlinear Dynamic Inversion (INDI), the sensory Nonlinear Dynamic Inversion (sNDI) method was recently developed. Both methods rely on replacing model knowledge with sensor measurements. However, the methods differ in how the pseudo-controls are allocated: INDI allocates them incrementally, while sNDI allocates them globally, with corresponding advantages and disadvantages. While INDI requires a restoring mechanism in the control allocation due to path dependency issues in overactuated nonlinear systems, sNDI does not experience this problem. In addition to the comparison, the paper demonstrates that both methods lead to identical results if restoring is applied in the control allocation of INDI. Even though sNDI and INDI with restoring can lead to limit cycles for theoretical non-linear overactuated systems, the practical applicability of this approach to transition electrical vertical take-off and landing vehicles (eVTOL) is demonstrated in flight tests of the Variable Skew Quad Plane.
Existing closed-loop controllers for functional electrical stimulation are prone to exceeding subject-specific stimulation limits, thereby limiting performance and also accelerating stimulation-induced muscle fatigue. In view of these challenges, this paper develops a Lyapunov-based model predictive control method to control knee flexion and extension during input-delayed stimulation. The method incorporates a contractive constraint under an electromechanical delay (EMD) compensation control law that achieves system stability despite an unknown constant input delay, bounded control constraints, and imperfectly estimated model parameters. A Lyapunov stability analysis proves that the Lyapunov constraint renders the closed-loop error ultimately bounded, and gain conditions are provided to guarantee recursive feasibility. LMPC's performance is explored in simulation and experiments and compared against an analytical proportional derivative-dynamic surface controller (PD-DSC) and a proportional-derivative-delay compensation (PD-DC) controller. In simulation, LMPC improved tracking root-mean-square error by 75.57% and 71.71%, on average, compared to PD-DSC and PD-DC, respectively. We observed that incorporating a slackening term often improved LMPC's tracking performance, although strict enforcement of the Lyapunov constraint was superior when there was greater EMD estimation error. Additionally, unlike PD-DSC and PD-DC, LMPC was not destabilized when EMD was overestimated or underestimated, nor did it violate input constraints. In knee extension experiments, LMPC respected input constraints, which PD-DSC did not. The LMPC was also validated in overground walking experiments to test its ability to produce both knee flexion and extension in participants with and without spinal cord injury.
Affine formation control (AFC) is a subset of formation control methods that enables coordinated multiagent movement while preserving affine relationships, and has recently gained increasing popularity due to its utility across diverse applications. AFC is inherently distributed, where each agent's local controller relies on the relative displacements of neighboring agents. The unavailability of these measurements in practice, due to node or communication failures, leads to a change in the underlying graph topology and subsequently causes instability or sub-optimal performance. In this work, each edge in the graph is modeled using a state-space framework, allowing the corresponding edge-states to be estimated with or without up-to-date measurements. We then propose a Kalman-based estimation framework where we fuse both temporal information from agents' dynamics and spatial information, which is derived from the geometry of the affine formations. We give convergence guarantees and optimality analysis on the proposed algorithm, and numerical validations show the enhanced robustness of AFC against these topology changes in several practical scenarios.
We address the problem of safe adaptive control for a class of nonlinear systems with dynamical uncertainties, while satisfying control barrier function (CBF) type safety constraints with user-defined risk tolerances at all times. We develop a model reference adaptive control framework that provably guarantees safety in two stages. In the first stage, we design a safe reference model to generate reference trajectories that satisfy CBF-based safety conditions. However, asymptotically tracking a safe reference trajectory does not automatically guarantee safety at every time step. Therefore, in the second stage, we formulate a chance-constrained optimization problem for the nonlinear system with dynamical uncertainties to track the reference model, while provably guaranteeing CBF-based safety constraint satisfaction at each time step up to a user-defined risk bound. We then provide a risk-tunable sampling-based scenario design approach to tune parameterized controllers that solve this optimization problem. In addition, for the special case of linear dynamics, we provide conditions on the uncertainty samples for the existence of controller parameters that can guarantee safe tracking. We illustrate the performance of our framework on a quadcopter navigation problem with obstacle avoidance constraints.
The increasing use of machine learning in safety-critical domains amplifies the risk of adversarial threats, especially data poisoning attacks that corrupt training data to degrade performance or induce unsafe behavior. Most existing defenses lack formal guarantees or rely on restrictive assumptions about the model class, attack type, extent of poisoning, or point-wise certification, limiting their practical reliability. This paper introduces a principled formal robustness certification framework that models gradient-based training as a discrete-time dynamical system (dt-DS) and formulates poisoning robustness as a formal safety verification problem. By adapting the concept of barrier certificates (BCs) from control theory, we introduce sufficient conditions to certify a robust radius ensuring that the terminal model remains safe under worst-case ${\ell }_{p}$-norm based poisoning. To make this practical, we parameterize BCs as neural networks trained on finite sets of poisoned trajectories. We further derive probably approximately correct (PAC) bounds by solving a scenario convex program (SCP), which yields a confidence lower bound on the certified robustness radius generalizing beyond the training set. Importantly, our framework also extends to certification against test-time attacks, making it the first unified framework to provide formal guarantees in both training and test-time attack settings. Experiments on MNIST, SVHN, CIFAR-10, and CIFAR-100 show that our approach certifies non-trivial perturbation budgets while being model-agnostic and requiring no prior knowledge of the attack or contamination level.
This paper introduces a method for efficiently updating a nominal stabilizing static output feedback (SOF) controller in perturbed linear systems. As operating points and state-space matrices change in dynamic systems, accommodating updates to the SOF controller are necessary. Traditional methods address such changes by re-solving for the updated SOF gain, which is often (i) computationally expensive due to the NP-hard nature of the problem or (ii) infeasible due to the limitations of its semi definite programming relaxations. To overcome this, we leverage the concept of minimum destabilizing real perturbation (MDRP) to formulate a norm minimization problem that yields fast, reliable controller updates. This approach accommodates a variety of known perturbations, including abrupt changes, model inaccuracies, and equilibrium-dependent linearizations. We remark that the application of our proposed approach is limited to the class of SOF controllers in perturbed linear systems. We also introduce geometric metrics to quantify the proximity to instability and rigorously define stability-guaranteed regions. Extensive numerical simulations validate the efficiency and robustness of the proposed method. Moreover, such extensive numerical simulations corroborate that although we utilize a heuristic optimization method to compute the MDRP, it performs quite well in practice compared to an existing approximation method in the literature, namely the hybrid expansion-contraction (HEC) method. We demonstrate the results on the SOF control of multi-machine power networks with changing operating points, and demonstrate that the computed quick updates produce comparable solutions to the traditional SOF ones, while requiring orders of magnitude less computational time.
Model-based filtering is often carried out while subject to an imperfect model, as learning partially-observable stochastic systems remains a challenge. Recent work on Bayesian inference found that tempering the likelihood or full posterior of an imperfect model can improve predictive accuracy, as measured by expected negative log likelihood. In this paper, we develop the discrete-time tempered Bayes filter, improving performance of the belief-distribution estimate through both of the aforementioned, and one newly introduced, tempering modalities. The result admits a recursive implementation with a computational complexity no higher than that of the original Bayes filter. Our analysis reveals that — besides the well-known fact that likelihood tempering affects the balance between prior and likelihood — full-posterior tempering tunes the belief-distribution entropy level. We further find that a region of the tempering space can be understood as interpolating between the Bayes- and MAP filters, recovering these as special cases. Analytical results further establish conditions under which a tempered Bayes filter improves predictive performance. Specializing the results to the linear Gaussian case, we obtain the tempered Kalman filter. In this context, we interpret how the parameters affect the Kalman state estimate and covariance. Empirical results confirm that our method consistently improves predictive accuracy over the Bayes filter baseline.
