We study the problem posed by Martin et al. whether a flat control system, invariant by a symmetry group action, possesses always a flat output compatible with that action. For driftless systems with 3 states and 2 controls and any symmetry group we characterize all flat outputs compatible with its action. We show that 1-dimensional groups with no fixed points and strong symmetry groups always possess compatible flat outputs. We construct an action of a 4-dimensional group for which no compatible flat output exists thus providing a negative answer to the question of [7], [10].
Recently, the classical linear output regulation problem has been generalized from a single actuator to multiple actuators in a framework known as cooperative parallel operation of multiple actuators. The cooperative parallel operation problem aims to design a distributed control law that not only solves the output regulation problem of the overall closed-loop system but also ensures an equal distribution of the plant input among the actuators. In this paper, we further explore this framework for discrete-time linear systems, generalizing existing results on continuous-time systems. To tackle the problem in the discrete-time setting, we propose a novel distributed dynamic output feedback control law that is specific for the discrete-time case and we derive a new solvability condition that is unseen in the continuous-time counterpart. We illustrate that both output regulation of the closed-loop system and an equal distribution of the plant input among the actuators can be achieved by the discrete-time distributed control law. Finally, we construct a discrete-time model of a motor-driven system to validate the effectiveness of the proposed discrete-time distributed control law.
This manuscript proposes a data-driven min-max moving horizon estimation (MHE) method for state estimation of linear finite-dimensional time-varying systems with unknown parameters and bounded-and-unknown plant and measurement noises/disturbances. A set membership representation is leveraged to characterize the unknown system parameters using offline measured data. We show that the robust MHE formulation of the online state estimation problem can be relaxed to a convex semidefinite program problem subject to constraints of linear matrix inequalities. The proposed design is able to consider both the measurement and process noise and handle state constraints. The stability analysis of the state estimation error is further provided. Finally, a numerical example is provided to verify the effectiveness of the proposed method.
We develop a switched nonlinear predictor-feedback law that achieves semiglobal asymptotic stabilization of nonlinear systems with arbitrarily long input delay, under dynamic state/input quantization. Due to the mismatch between the (inapplicable) exact predictor state and the predictor state constructed in the presence of state quantization (or between the exact predictor-feedback law and its quantized version, in the case of input quantization), a semiglobal stabilization result is only achievable without imposing a global Lipschitzness assumption on the vector field and the nominal (for the delay-free case) feedback law (or assuming exponential stability of the delay/quantization-free system under the nominal controller). Nevertheless, the quantizer's range has to be sufficiently large, depending on the system data, the nominal feedback law, and an estimate of the size of initial conditions (to guarantee that the infinite-dimensional state of the system lies initially, and thus, it remains, within the quantizer's range). The nonlinear predictor-feedback laws developed employ quantized versions of exact predictor states in a nominal feedback law (or quantized versions of exact predictor-feedback laws), combined with a proper construction for the tunable parameter of the quantizer (the so-called “zoom” variable), which reduces, in a piecewise constant manner, the quantization error. The stability proofs rely on constructive derivation of solutions estimates, via a combination of input-to-state stability (ISS) arguments and backstepping transformations.
This paper introduces an adaptive extremum seeking scheme that modifies the dithering signal at run time to deal with non-convex cost functions. The adaptation law decreases the dithering when the local descent direction is easily deducible from the measurements, and increases it when the optimized cost function does not show a locally dominant trend. This adaptive scheme can provide advantages in practical applications where a conservatively large dithering would lead to unnecessarily high control energy. Stability guarantees are given in the form of semiglobal practical asymptotic stability of a compact attractor including the optimal point and whose size depends on the maximal dithering strength. The performance and possible advantages of the proposed scheme over existing algorithms are investigated through numerical simulations.
This paper studies time-varying aggregative games with time-varying coupled equality constraints for a multi-agent system over undirected and connected communication topologies. Since the cost function of each agent is time-varying, the generalized Nash equilibrium of the game is a trajectory over time instead of a fixed point. To solve the problem considered, a distributed finite-time convergence algorithm is proposed by combining the dynamic average consensus protocol and the primal-dual method. The proposed algorithm employs sign-based directional information to construct a finite-time coordination mechanism for aggregate estimation, multiplier agreement, and equality-constraint feasibility recovery. Further, based on the graph theory, finite-time stability theory, and Lyapunov analysis, it is shown that the closed-loop system admits a Filippov solution that tracks the time-varying generalized Nash equilibrium in finite time. Finally, a time-varying Nash-Cournot example is provided to illustrate the effectiveness of the theoretical results.
This note proposes a self-triggered trusted distributed model predictive control (DMPC) strategy for asynchronous coordination of heterogeneous multi-agent systems under bounded disturbances in a zero trust environment. The Dempster–Shafer theory is introduced to develop collaborative trusting computing that characterizes the global trust metric of interplay of inter-agents. Then by embedding this metric into the robust DMPC framework with tightened constraints, a trust-collaborative paradigm is designed to enable trust-aware decision-making via online optimization. Next, an analytical co-design criterion on distributed self triggered schedulers and adaptive prediction horizons is derived to characterize the intrinsic interaction between triggering instants and horizon lengths, which measures the convergence of coordination to preserve the coordination accuracy at terminal phase. This eliminates the need for online optimization of the triggering interval and substantially reduces communication and computational burdens associated with the DMPC implementation. Moreover, by adaptively regulating the reliance on neighbor information, recursive feasibility, robustness, and security properties are guaranteed under mild assumptions. The simulation results on robotic manipulators validate the advantages of the proposed scheme.
We analyze stability and recurrence of nonlinear stochastic discrete-time systems, also known as Markov control processes, under optimal control using discounted and undiscounted infinite-horizon cost functions. We make assumptions on cost-stabilizability as well as detectability with respect to the stage cost that apply to a range of stochastic systems. Furthermore, we assume regularity in the form of continuity of the model, stage cost and optimal value functions. Then, robust uniform semiglobal practical recurrence with respect to the discount factor is guaranteed. This property becomes global by strengthening the assumptions. In the case where policies with finite undiscounted infinite-horizon costs exist, the stronger property of uniform global asymptotic stability in probability holds under similar assumptions, as well as with discounting under extra conditions. Furthermore, since the continuity requirement of the optimal value function is not easily verified, we provide a novel sufficient condition in the form of strong continuity of the Markov kernel.
The collision avoidance control for multiple unicycle robots is necessary in practical applications. Robots need to avoid collisions with each other during collaborative operations, but nonholonomic constraints and motion limitations make distributed collision avoidance challenging. To solve this problem, we first propose a modified hand position (MHP), which transforms the unicycle model into a single integrator model. Subsequently, to generate non-conservative collision avoidance actions, we propose a non-Euclidean distance between two robots, which illustrates their spatial relationship. Then, a velocity command containing a velocity alignment term is designed for MHPs of robots. Formal analyses and proofs demonstrate that all robots can achieve collision avoidance with each other. If the two parameters in MHP are set to two specific values, all robots have bounded linear speeds, bounded linear accelerations and bounded angular speeds, provided that the velocity command is saturated by the maximum linear speed. To show the advantage of the proposed method, we discuss some other feasible designs of the distance and repulsive potential function between robots. Finally, the effectiveness of the proposed method is validated through numerical simulations and real experiments.
This paper investigates the construction of Lyapunov-Krasovskii functionals for discrete-time delay systems whose state trajectories evolve within symmetric cones. Using the scaling point representation on the Euclidean Jordan algebra associated with symmetric cones, we prove that the asymptotic stability of the system implies the existence of a Lyapunov-Krasovskii functional whose construction involves $\mathcal {K}$-nonnegative positive definite matrices ($\mathcal {K}$ represents a symmetric cone). For the case of single-delay systems, these positive definite matrices coincide with a cone-preserving solution of an algebraic Riccati inequality associated with the delay systems. Finally, the validity of the results is verified by considering a system defined on a second-order cone in numerical simulation.
This paper addresses the nonconvex distributed resource allocation problem for uncertain nonlinear multi-agent systems. The objective is to design distributed real-time gradient feedback protocols that steer the agents' outputs to the set of Karush-Kuhn-Tucker (KKT) points. Unlike conventional offline algorithms that require explicit analytical expressions of the gradients of local objective functions, the proposed protocols use only gradient values along agent trajectories. With the exchange of this local gradient information among neighbors, two classes of distributed real-time gradient feedback protocols are proposed. The first employs a constant feedback gain and guarantees convergence provided that the feedback gain is chosen below an explicit bound. The second adopts a vanishing time-varying feedback gain, requiring no prior knowledge of parameters associated with the agents, local objective functions, or communication graph, and enabling its fully distributed implementation. The results are further extended to jointly optimizing the agents' inputs and outputs when each open-loop system admits a desired input–output property. The effectiveness and advantages of the protocols are demonstrated through a numerical example on economic optimization of interconnected chemical reactors.
We present a data-driven moving horizon estimation (MHE) scheme for unknown linear systems represented by noisy data. A finite number of noisy data, not necessarily rich enough to identify a unique unknown linear model, is utilized for designing an MHE scheme with guaranteed robust global asymptotic stability. In order to bound the optimization problem, we introduce an artificial disturbance to the data-driven prediction model. By penalizing the artificial disturbance in the objective function, we guarantee that the estimated state and output sequences from the best data-driven prediction model are consistent with the finite and noisy data. The effectiveness of the proposed approach is verified through a numerical example.
This paper presents two approaches to enhance the accuracy and robustness of the conventional estimator from [1] for affine–state nonlinear systems affected by external perturbations and measurement noise. The proposed methods are: 1) integration of additional filtering mechanisms; and 2) modification of the conventional adaptive observer using the heavy–ball algorithm. The analysis shows the input-to-state stability property with a uniform exponential convergence rate under the regressor excitation assumption. These proposals offer the following improvements compared to [2]: a) disturbances and noise have a significantly weaker effect on parameter estimation, as the new filtering processes attenuate the propagation of high–frequency perturbations; and b) the convergence and robustness properties are no longer directly governed by the excitation signal, allowing for a more controlled convergence behavior. In addition, some simulations confirm superior accuracy compared to the conventional adaptive observers.
In this paper, a distributed constrained autonomous game (AG) is studied, where players have high-order dynamics. In contradistinction to previous related works, our constraints are inviolable. It is widely acknowledged that the continual satisfaction of constraints is a difficulty for AGs, because the actions of players are not decided by their control inputs directly owing to their dynamics. Hitherto, there are few results about AGs with inviolable constraints. Moreover, mainly attributing to inviolable constraints, existing methods fail to address our problem. Furthermore, the high-order dynamics also brings difficulties to our algorithm design and analysis, since the algorithms must be appropriate for all n-order systems. Here a distributed algorithm is developed, under which those high order players always adhere to their constraints. Besides, the algorithm is proved to be exponential convergent, better than existing methods for AGs with inequality/nonlinear/set constraints. Additionally, our method is employed to handle autonomous electricity market games. By using our method, turbine-generator systems, instead of human beings, take part in electricity market games autonomously.
Adaptive controllers include online update laws for adjusting their parameters using measured signals in real-time. While most adaptive laws are of first order nature, recent literature has introduced higher order adaptive tuners inspired from the concept of Nesterov acceleration. This work proposes a proportional-integral (PI) - higher order tuner (HOT) with a weighted integral component in the update law, offering a quantifiable set of benefits. With persistence of excitation (PE), it is proved that this tuner can lead to 1) exponential stability in the large (ESL), 2) accelerated convergence in terms of improved convergence rate with time. Robustness to disturbances as well as asymptotic stability with interval excitation are also established. Simulation studies are included that corroborate all theoretical derivations.
Networks with asymmetric topologies exhibit markedly different behaviors compared to their symmetric counterparts, which typically demonstrate superior performance across various metrics. However, a widely accepted method for accurately characterizing network asymmetry remains elusive—let alone one that allows its systematic reduction according to an optimal criterion. In this study, we introduce a novel approach for quantifying network asymmetry via the phase-rank of the associated Laplacian matrix, defined by the number of its nonzero phases. Building on this new measure, we formulate and solve an optimization problem aimed at reducing network asymmetry while minimizing approximation error. We also highlight how our proposed method fundamentally differs from existing network symmetrization techniques. Lastly, the effectiveness of the proposed method is demonstrated through a case study on consensus in dynamical networks.
This paper introduces a first-order dynamical system for constrained optimisation problems in which global exponential convergence is achieved through an adaptive penalty mechanism. By treating the penalty parameter as a dynamic state variable, the proposed framework enforces feasibility and improves convergence performance compared with fixed-penalty approaches. Building on this structure, we further propose a modified system that guarantees fixed-time convergence, ensuring convergence within a uniform finite time independent of initial conditions. Further more, the proposed systems achieve global exponential or fixed-time convergence without imposing strong convexity on the original objective function, a common assumption in the existing literature. The effectiveness and practical advantages of the fixed-time convergent dynamical systems are demonstrated through numerical simulations.
This paper is concerned with distributed nonconvex composite optimization, where each agent has a private smooth nonconvex cost function while sharing a common nonsmooth convex regularizer. We propose the first unified distributed algorithmic framework for this setting, which extends state-of-the-art methods to their proximal variants and generalizes existing unified approaches. Building on two key technical lemmas, we conduct a comprehensive convergence analysis and show that: (i)the proposed framework achieves linear convergence under the Proximal Polyak–Łojasiewicz condition; and (ii) it attains asymptotic convergence to stationary points at an $\mathcal {O}(1/T)$ rate for general nonconvex composite problems, matching the performance of centralized proximal methods. Numerical experiments further demonstrate the effectiveness of the proposed approach.
This technical note is concerned with the stabilization of continuous-time switched linear systems under aperiodic sampled-data control. An extended looped-functional framework is developed by introducing a novel piecewise Lyapunov functional that explicitly incorporates sampled switching information. Based on this construction, sufficient asymptotic stability conditions are derived in terms of Metzler-matrix inequalities, enabling the joint design of state-dependent switching laws and state-feedback controllers. Unlike existing approaches, the proposed method can ensure stability even when all subsystems are unstable or uncontrollable, including the limiting case where no control input is available and switching acts as the sole stabilizing mechanism. The resulting sampled switching strategy inherently enforces a minimum dwell time determined by the sampling interval, avoids chattering, and allows direct computation of admissible aperiodic sampling bounds. The framework is also applicable to systems with parametric uncertainties. Numerical examples illustrate the reduced conservatism and effectiveness of the proposed approach.
This paper investigates the distributed estimation problem for discrete-time uncertain linear time invariant systems under the joint observability condition. The problem is highly challenging and remained unresolved until it was recently addressed by an adaptive approach. This papersolvesthisproblemusinganonadaptive approach that introduces new features. An observability transformation is first introduced to decompose the uncertain system, thereby facilitating the parameter and state reconstruction by the two nonlinear mappings. Then, a novel class of distributed nonadaptive observers is pro posed, composed of a nonlinear distributed Luenberger type observer dynamics and two nonlinear mappings. By Lyapunov stability analysis and nonlinear mappings recon struction, we show that the parameter and state estimation are achieved asymptotically for discrete-time jointly observable uncertain linear systems. The proposed nonadaptive scheme enriches design tools for robust control, and circumvents the convergence and stability issues inherent in adaptive approaches as well. Besides, the observer is fully distributed, requiring only local measurements and neighbor-to-neighbor communication, which ensures computational efficiency and scalability.
