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**Knotek Š- Hengster-Movric K - Šebek M: Distributed adaptive consensus protocol with decaying gains. International Journal of Robust and Nonlinear Control, 2020.**

Abstract—This article brings a distributed adaptive protocol for consensus and synchronization in multiagent systems on directed communication networks. Agents are modeled as general linear time-invariant systems. The proposed protocol introduces a novel adaptation scheme allowing control coupling gains to decay to their reference values. This approach improves upon existing adaptive consensus protocols which may result in overly large or even unbounded coupling gains. The protocol design in this article does not rely on any centralized information; hence it is distributed. Nevertheless, the price to pay for this is the need to estimate those reference values. Convergence of the overall network dynamics is guaranteed for correctly estimated references; otherwise, the trajectory of the system is only uniformly ultimately bounded. Two estimation algorithms are proposed: one based on the interval-halving method and the other based on a distributed estimation of Laplacian eigenvalues. Numerical simulations validate the proposed approach.

**Knotek Š- Hengster-Movric K - Šebek M: Distributed Estimation on Sensor Networks With Measurement Uncertainties. IEEE Transactions on Control Systems Technology, 2021.**

Abstract— This article brings distributed estimation for large-scale systems. The plant is considered affected by process disturbance, and measurements are corrupted by measurement noise. The proposed approach fuses measurements of differing reliability so that all nodes reach consensus on the plant's state estimate. This architecture is flexible to the addition of new nodes and, to a certain extent, robust to node or communication link failures. In spite of limited observability by each of the nodes, data fusion over the network allows each node to obtain the full estimate of the plant's state. Structured Lyapunov functions are used to prove the convergence of the estimator. Estimation error covariances are analyzed in detail. The proposed distributed observer design is validated by numerical simulations.

Keywords: Observers, Robustness, Kalman filters, Sensor fusion, Large-scale systems, Lyapunov methods

**Zhang X- Hengster-Movric K- Šebek M - Desmet W - Faria C: Distributed Observer and Controller Design for Spatially Interconnected Systems. IEEE Transactions on Control Systems Technology, 2017.**

Abstract— This paper tackles networked distributed observer and controller design problem over directed graph topology for spatially interconnected systems. Traditional centralized design methods suffer from a lack of adaptability to graph variations incurred by network reconfiguration, communication failures, and redundant sensors integration. In this paper, to handle the foregoing limitations imposed by centralized design, state observers are designed in a distributed manner facilitated by pinning control precepts. On the one hand, this novel approach adds fault tolerance with respect to communication link failures. On the other hand, the proposed approach brings flexibility of integrating additional sensors into the network. In addition, this approach affords a reduction of computational cost. A sufficient condition to guarantee stability of the closed-loop system is derived. The controllers, though in the end implemented in a distributed way, are designed in a centralized framework, where linear-quadratic-regulator theory is adopted to handle the fact that separation principle fails to hold in the networked observer and controller design. Numerical simulation results of a piezoelectric actuated smart flexible system are presented, and the effectiveness of the proposed design is thereby verified.

Keywords: Consensus, distributed control, flexible structures, large-scale systems, networked control, pinning control, vibration damping.

**Dong ZZ - Faria C - Hromčík M - Pluymers B - Šebek M - Desmet W: Equivalent force modeling of macro fiber composite actuators integrated into nonhomogeneous composite plates for dynamic applications. Smart Materials & Structures, 26(9), 2017.**

Abstract—Smart structures with integrated macro fiber composite (MFC) piezoelectric transducers have been increasingly investigated in engineering. A simple but elaborate system model of such smart structure not only can predict system dynamics, but also can reduce challenges in application. Therefore, the equivalent force (EF) modeling approach is presented to model the plate-type structures with integrated piezoelectric actuators in a semi-analytical fashion: analytical EF is applied to finite element (FE) structural models. The EF is derived from the bending effort balance between the equivalent loads, and the equivalent loads are developed by introducing the spatial distribution into a generalized Hamilton's principle. The proposed approach is validated by cantilever aluminum beams with integrated MFC actuators and it is consistent with existing alternative approaches from literature. Then, it is validated on a non-homogeneous composite plate for dynamic applications: a laminated composite plate with integrated MFC actuators was manufactured and both an impact test and MFC drive test were elaborately carried out. The modal validation shows the high fidelity of the EF model and the predicted velocity frequency responds functions (FRFs) agree well with experimental measurement. Being applicable to both numerical and analytical modeling approaches, the EF is actually assigned to the out-plane displacement on the structure and distributed along the edges of the actuators. Therefore, it is convenient to use in EF models. The rotational degrees of freedom could also be eliminated in the EF models without losing structure complexity, since they neither link to the electromechanical coupling nor have a significant kinetic contribution to the system. .

Keywords: macro fiber composite actuators, laminated composite plate, equivalent force, dynamic applications.

**Pčolka M - Žáčeková E - Čelikovský S - Šebek M: Towards a Smart Car: Hybrid Nonlinear Predictive Controller with Adaptive Horizon. IEEE Transactions on Control Systems Technology. 2017.**

Abstract—This paper focuses on the development of an optimization algorithm for car motion predictive control that addresses both hybrid car dynamics and hybrid minimization criterion. Instead of solving computationally demanding nonlinear mixed-integer programming task or approximating the hybrid dynamics/criterion, the Hamiltonian-switching hybrid nonlinear predictive control algorithm developed in this paper incorporates the information about hybridity directly into the optimization routine. To decrease the time complexity, several adaptive prediction horizon approaches are proposed, and for some of them, it is shown that they preserve maneuverability-related properties of the car. All developed alternatives are verified on an example of a motion control of a racing car and compared with the approximation-based nonlinear predictive control and a commercial product. Moreover, a sensitivity analysis examining robustness of the algorithm is included as well. .

Keywords: Autonomous vehicles, hybrid systems, nonlinear model predictive control (MPC), optimization, vehicle control.

**Martinec D - Herman I - Šebek M: A Travelling wave approach to a multi-agent system with a path-graph topology. Systems Control Letters 99, 90–98, 2017.**

Abstract—The paper presents a novel approach for the analysis and control of a multi-agent system with nonidentical agents and a path-graph topology. With the help of irrational wave transfer functions, the approach describes the interaction among the agents from the ‘local’ perspective and identifies travelling waves in the system. It is shown that different dynamics of the agents create a virtual boundary that causes a partial reflection of the travelling waves. Undesired effects due to the reflection of the waves, such as amplification/attenuation, long transients or string instability, can be compensated by the feedback controllers introduced in this paper. We show that the controllers achieve asymptotic and even string stability of the system.

Keywords: Multi-agent system; Travelling waves; Wave transfer function; Path graph; Irrational transfer function.

**Herman I - Martinec D - Hurák Z- Šebek M: Scaling in bidirectional platoons with dynamic controllers and proportional asymmetry. IEEE Transactions on Automatic Control, 62 (4), 2034-2040, 2017**

Abstract—We consider platoons composed of identical vehicles with an asymmetric nearest-neighbor interaction. We restrict ourselves to intervehicular coupling realized with dynamic arbitrary-order onboard controllers such that the coupling to the immediately preceding vehicle is proportional to the coupling to the immediately following vehicle. Each vehicle is modeled using a transfer function and we impose no restriction on the order of the vehicle. The only requirement on the controller and vehicle model is that the platoon is stable for any number of vehicles. The platoon is described by a transfer function in a convenient product form. We investigate how the H-infinity norm and the steady-state gain of the platoon scale with the number of vehicles. We conclude that if the openloop transfer function of the vehicle contains two or more integrators and the second smallest eigenvalue of the graph Laplacian is uniformly bounded from below, the norm scales exponentially with the growing distance in the graph. If there is just one integrator in the open loop, we give a condition under which the norm of the transfer function is bounded by its steady-state gain—the platoon is string-stable. Moreover, we argue that in this case it is always possible to design a controller for the extreme asymmetry—the predecessor following strategy.

Index Terms—Asymmetric control, scaling, string stability, transfer functions, vehicle platoon.

**Martinec D - Herman I - Šebek M: On the necessity of symmetric positional coupling for string stability. IEEE Transactions on Control of Network Systems PP, no. 99, 1-10, 2016**

Abstract - We consider a distributed system with identical agents, constant-spacing policy and asymmetric bidirectional control, where the asymmetry is due to different controllers, which we describe by transfer functions. By applying the wave transfer function approach, it is shown that, if there are two integrators in the dynamics of agents, then the positional coupling must be symmetric, otherwise the system is string unstable. The main advantage of the transfer function approach is that it allows us to analyse the bidirectional control with an arbitrary complex asymmetry in the controllers, for instance, the control with symmetric positional but asymmetric velocity couplings.

Keywords - Stability criteria; Transfer functions; Couplings; Topology; Asymptotic stability; Bidirectional control.

**Herman I - Martinec D - Hurák Z - Šebek M: Nonzero bound on Fiedler eigenvalue causes exponential growth of H-infinity norm of vehicular platoon. IEEE Transactions on Automatic Control, 60 (8), 2248 - 2253, 2015.**

Abstract—We consider platoons composed of identical vehicles and controlled in a distributed way, that is, each vehicle has its own onboard controller. The regulation errors in spacing to the immediately preceeding and following vehicles are weighted differently by the onboard controller, which thus implements an asymmetric bidirectional control scheme. The weights can vary along the platoon. We prove that such platoons have a nonzero uniform bound on the second smallest eigenvalue of the graph Laplacian matrix-the Fiedler eigenvalue. Furthermore, it is shown that existence of this bound always signals undesirable scaling properties of the platoon. Namely, the H-infinity norm of the transfer function of the platoon grows exponentially with the number of vehicles regardless of the controllers used. Hence the benefits of a uniform gap in the spectrum of a Laplacian with an asymetric distributed controller are paid for by poor scaling as the number of vehicles grows.

Keywords - Asymmetric control, eigenvalues uniformly bounded from zero, exponential scaling, Fiedler eigenvalue, harmonic instability, vehicular platoons.

**Hengster-Movric K - Lewis FL - Šebek M: Distributed Static Output-feedback Control for State Synchronization in Networks of Identical LTI Systems. Automatica, 53, 282–290, 2015.**

Abstract—This paper studies state synchronization of multi-agent systems with disturbances using distributed static output-feedback (OPFB) control. The bounded L_2 gain synchronization problem using distributed static OPFB is defined and solved. The availability of only output measurements restricts the local controls design, while the communication graph topology restricts global information flow among the agents. It is shown here that these two types of restriction can be dealt with in a symmetric manner and lead to two similar conditions guaranteeing the existence of bounded L_2gain static OPFB. One condition is on the output measurement matrix on a local scale, and the other on the graph Laplacian matrix on a global scale. Under additional conditions a distributed two-player zero-sum game using static OPFB is also solved and leads to distributed Nash equilibrium on the communication graph. As a special case the static OPFB globally optimal control is given. A new class of digraphs satisfying the above condition on the graph Laplacian is studied. The synchronizing region for distributed static OPFB control is exposed and found to be conical, different than the infinite right-half plane synchronizing region for distributed state feedback.

Keywords - Multi-agent systems; Distributed control; Synchronization; Synchronizing region; Static output-feedback-control; Cooperative two-player zero-sum game; Optimal control.