Structured state-space models (SSMs) have emerged as a powerful architecture in machine learning and control, featuring stacked layers where each consists of a linear time-invariant (LTI) discrete-time system followed by a nonlinearity. While SSMs offer computational efficiency and excel in long-sequence predictions, their widespread adoption in applications like system identification and optimal control is hindered by the challenge of ensuring their stability and robustness properties. We introduce L2RU, a novel parametrization of SSMs that guarantees input-output stability and robustness by enforcing a prescribed L-2 -bound for all parameter values. This design eliminates the need for complex constraints, allowing unconstrained optimization over L2RUs by using standard methods such as gradient descent. Leveraging tools from system theory and convex optimization, we derive a non-conservative parametrization of square discrete-time LTI systems with a specified L-2-bound, forming the foundation of the L2RU architecture. Additionally, we enhance its performance with a bespoke initialization strategy optimized for long input sequences. Through a system identification task, we validate L2RUs superior performance, showcasing its potential in learning and control applications.
In this paper, the reachability analysis for a class of nonlinear systems is addressed by resorting to a data-driven setting. The resulting approach combines into a unique framework linear time-invariant system behavior, data-driven modeling and reinforcement learning algorithms. This allows to determine inner and outer approximations of the exact predecessor and successor sets, whose accuracy is evaluated by means of statistical tests. Finally, the proposed approach is assessed by resorting to a benchmark example and providing numerical comparisons with a model-based competitor.
In this paper, we show how a separable structure between decision and uncertain variables in the constraints of non-convex robust scenario optimization problems can be exploited to bound the complexity associated with the solution. The resulting bounds are easily computable, and can be solved prior to determining the solution to the non-convex scenario program. Leveraging the scenario approach theory, these bounds can be used to find suitable certifications of the risk (a posteriori, once the scenarios are collected). Furthermore, this result can be exploited to determine the size of the scenario sample necessary to provide a user-chosen reliability level of the solution, for which we discuss both a one-shot and an iterative resolution approach.
The causal conditional (CC) directed information (DI) can test the Granger causality for stochastic processes. However, for point process networks, the CCDI has only been developed for a trivariate network. In this work, we develop the general multivariate CCDI under Kramer’s framework by developing the CC likelihood, which is characterized by marginal intensity functions. We establish several Granger causality equivalences, unifying and generalizing existing results. Further, for Hawkes networks, we develop an estimation method of CCDI requiring only one point process trajectory, by developing an analytical formula for the marginal intensity functions, and an ergodic theorem for the CCDI.
Recently, there has been a surge of interest in decentralized learning approaches to tackle complex collaborative tasks in multi-agent systems. One of the most promising approaches is multi-agent reinforcement learning (MARL). Yet, as the number of agents becomes larger, the sample complexity in MARL increases exponentially, making scalability a fundamental issue. Networked MARL algorithms can address this issue by leveraging a communication network for information exchange between the agents. For homogeneous network MARL, previous research established a regret upper-bound root MH(4)SAT. Recent approaches rely on global knowledge about the structure of the communication network, which poses a serious limitation when it is not known or changes depending on the task. In this paper, we overcome this limitation by proposing a novel networked MARL algorithm with an upper-confidence bound (UCB) exploration strategy, called provably efficient local-information networked (PrELIN) MARL, that does not require any global information but only relies on the local interactions between the agents. Furthermore, we derive the regret and sample complexity for our algorithm and show that the regret bound may still remain sublinear.
Autonomous vehicles envision a future where congestion games are played between cooperative rather than selfish players. We consider N cooperative players engaged in a congestion game on a graph G, where they all share the same source and destination nodes. The goal of the team of players is to minimize the sum of their trip times (costs). This model captures the interaction between a fleet of autonomous vehicles that constitutes all the traffic in a given area. We propose a communication-free distributed algorithm that enables players to learn the action profile (i.e., routing decisions) that minimizes the sum of their trip times. Our algorithm only requires each player to observe its own trip times for each edge it travels (i.e., bandit feedback). The delay functions of the edges, which map the loads to trip times, are unknown to all players and are assumed to be polynomials. We prove an expected regret bound for our algorithm that shows polynomial dependence on N and the size of G. We conduct numerical experiments that demonstrate the effectiveness of our algorithm.
This paper introduces a novel approach for controlling heterogeneous vehicle platoons with connected autonomous vehicles using digital controllers and macroscopic information sharing. The proposed method achieves practical and disturbance string stability despite asynchronous measurements, quantization effects, and redundant information exchange, while offering improved robustness against uncertainties and noise. Simulations illustrate the performances of the proposed controller.
This paper revisits the control problem of discrete-time linear systems subject to state and input delays, as well as norm-bounded parametric uncertainties. A robust recursive regulator based on an augmented system encompassing delays and uncertainties in a unified framework is proposed. A robust regularization approach with penalization is developed for a constrained optimization problem. Both delays are transformed in data under an umbrella of regularized least-squares problems. A recursive Riccati equation is obtained as a solution, providing standard conditions for proving convergence and stability a posteriori. Based on Gauss’s arguments, updated to account for uncertainties, this approach has been proposed as an alternative to Lyapunov-type solutions, where the stability of the feedback control system is defined a priori. We present two numerical examples where we consider an industrial electric heater model to illustrate the performance of the robust regulator. A comparative study is performed with three guaranteed cost approaches.
In this article we present a robustness theorem for controlled stochastic differential equations driven by approximations of Brownian motion, where the approximations are those that converge to the Brownian under the rough paths topology along sample paths. These approximations include the Wong-Zakai, Karhunen-Loeve, mollified Brownian and fractional Brownian processes, which can be interpreted to be more physical than the Brownian idealization of the driving noise process. We establish robustness using rough paths theory. To this end, in particular, we show that within the class of Lipschitz continuous control policies, an optimal solution for the Brownian idealized model is near optimal for a true system driven by a non-Brownian (but near-Brownian) noise.
Understanding the effect of inputs on system safety is one of the most important issues in the study of safety-critical systems. Integral input-to-state safety (iISSf) is a concept that can describe the dependence of safety on the integral of external inputs. This paper studies the characterization of iISSf properties from a barrier function perspective. We introduce iISSf barrier functions (iISSf-BFs) as a tool to verify iISSf, and establish that the existence of an iISSf-BF is a sufficient condition for iISSf. With iISSf control barrier functions (iISSf-CBFs) and quadratic programs (QPs), we construct a safety-critical controller to enforce iISSf with respect to a prescribed iISSf gain. Finally, under an additional assumption of integral input-to-state stability, we show that iISSfs-BFs are also necessary for iISSf.
This paper introduces a robust controller for multi-rotor systems that can effectively handle aggressive and high-magnitude disturbances, both in the orientation and position subsystems. Our control design uses only position and angular position vector information and comprises two primary algorithms: a state feedback controller and an extended high-gain observer. Moreover, the proposed controller provides asymptotic stability while satisfying user-imposed constraints on the position, velocity, and angular position error states. To achieve this goal, we introduce a barrier Lyapunov function, which guarantees that the tracking error trajectories of the system remain within the constraints. We evaluate the performance of our proposed control through numerical simulations and a comparison with a state-of-the-art popular controller. The results illustrate the effectiveness of our approach in coping with high-magnitude disturbances, especially in the positioning subsystem of the multi-rotor system.
This paper investigates the connections between two existing formal extensions of Koopman operator theory to general discrete-time control systems that are not necessarily control-affine. The frameworks, namely (i) Koopman operator via infinite input sequences and (ii) Koopman control family, encode the system behavior in fundamentally different ways and rely on different function spaces. In spite of this, we connect the frameworks by defining operations that allow to go from one function space to the other, and provide precise conditions that ensure the function spaces capture the same information. Moreover, we prove that under these conditions the formal approaches are equivalent in terms of encoding the state information and multi-step trajectories in function values.
There is an increasing interest in developing algorithmic fault detection and isolation (FDI) of aircraft air data sensors without relying on the existing hardware redundancy. This is a complex problem, as the available state equations have non-observable states in the event of a complete loss of all redundant sensors that measure a flight variable. Furthermore, FDI approaches commonly require surrogate models and the analytical relations they use are strongly subject to external disturbances. Trying to tackle these difficulties, we introduce the Neural Double Observer Scheme based on Long Short Term Memory units (LSTMs), a new estimation framework for FDI that allows for fault isolation in systems with intense coupling of physical equations. This framework is inspired by classic observer schemes for FDI and powered by LSTMs units. Evaluated on real flight data from an Airbus aircraft, it demonstrated promising performance compared to previously used model-driven methods.
Autonomous exploration of unknown environments is one of the fundamental capabilities of intelligent mobile robots, which affects their adaptability in complex environment navigation tasks. Traditional frontier-based exploration methods prioritize exploration coverage while neglecting path cost, whereas some novel machine learning-based approaches often require substantial training and tuning to maintain effectiveness. To address this issue, this paper integrates the frontier-based method with artificial potential fields to develop a new local navigation approach, enabling the robot to explore a local area while avoiding obstacles. Subsequently, the newly proposed global exploration strategy can effectively guide the robot to explore different local areas in an orderly manner by selecting the nearest area with exploration value, which is calculated based on the principle of minimum potential energy. Simulations and experiments demonstrate that in unstructured scenarios with irregular layouts, the proposed method ensures good exploration coverage while significantly reducing path cost compared to existing methods, thereby improving the efficiency of the robot in the exploration task.
This paper presents a novel reformulation of the queue-based Max-Pressure (MP) traffic signal control strategy using a decentralized framework that leverages only local intersection data to dynamically determine optimal phase durations, maximizing traffic throughput. We critically analyze the conventional store-and-forward modeling approach and highlight its limitations in representing phase-switching gaps at intersections. To overcome these issues, we propose an enhanced store-and-forward model coupled with an improved MP control formulation that explicitly accounts for phase-switching losses. Additionally, we introduce a dynamic constraint on phase durations, challenging the traditional assumption that minimal green times are inherently optimal and stable. Simulation results demonstrate that the negative impact of switching gaps escalates with increasing demand, underscoring the necessity of adaptive phase timing. Our refined control strategy contributes to a more robust, realistic, and efficient traffic signal management, enhancing overall network performance.
Distributed joint localization and target tracking is crucial for various applications. The major challenge lies in accurately estimating inter-robot and robot-target cross-correlations, particularly under intermittent or unreliable communication. Existing approaches suffer from several limitations, including the decoupled treatment of localization and target tracking, reliance on specific communication schemes, extensive measurement bookkeeping, overly conservative estimates, or restrictive measurement model assumptions. To address these issues, this paper proposes a recursive distributed framework in which each robot only maintains the latest estimate of its own pose and the tracked targets’ poses, eliminating the need for storing historical measurements and cross-correlations. Most importantly, our framework supports generic measurement models and allows flexible customization of update methods for different measurements, thus making full use of all available information. Furthermore, an event-triggered communication scheme is implemented, occurring only between robot pairs that share a relative measurement. Extensive Monte Carlo simulations validate the proposed method, demonstrating state-of-the-art accuracy performance among existing distributed methods.
Nonlinear iterative learning control (ILC) and nonlinear repetitive control (RC) approaches introduce additional design freedom compared to linear time-invariant (LTI) approaches. Since the actual performance improvements depend on the parameters used in the nonlinearity, the aim of this paper is to optimize these parameters during the learning process. With optimal parameters, the nonlinear algorithms can outperform their LTI counterparts, for example by achieving fast attenuation of repeating disturbances without amplifying non-repeating disturbances. In this paper, we present the algorithm for the automatic learning/tuning process and validate it using simulations of an industrial flatbed printer.
This paper deals with the identification of dynamical networks with partial excitation and measurement. Most of the work of the last few years on this topic has dealt with the design of valid Excitation and Measurement Patterns (EMP) (i.e. a selection of excited nodes and measured nodes that guarantee the generic identifiability of the network) while at the same time being sparse. Thus the objective was to identify the network with an EMP of small or even minimal cardinality, where the cardinality is the sum of the number of excited and measured nodes. In [5] a novel approach was taken, where the objective is no longer to design an EMP with small cardinality, but one that minimizes an experimental cost. A solution was proposed, but only for the case where all nodes are excited. In this paper, we extend the objective of designing a valid EMP with minimal experimental cost to the case where not all nodes are excited and not all nodes are measured. The resulting constrained optimization problem is considerably more complex. We propose two greedy algorithms with low computational cost and present a case study in which the optimal solution is obtained, though in general this can not be guaranteed. We also discuss the solution of the optimization for networks with particular topologies, for which customized algorithms can be conceived, and illustrate this idea for networks with a tree topology.
