Chaotic systems are a class of systems with high sensitivity to initial conditions. Stabilization of periodic solutions is an important problem in the study and exploitation of such systems. While this problem is widely addressed in the literature, existing methods assume the system model to be known or have known uncertainty bounds and known input gains. The main contribution of this paper is the development of an adaptive delayed feedback strategy to address chaos control in a more general class of high-order nonlinear systems with multiple degrees of freedom and with unknown parameters. The results are validated by a simulation example.

This work investigates platooning systems employing Adaptive Cruise Control (ACC) and Cooperative Adaptive Cruise Control (CACC) strategies, with the main focus being on controller parameter design for string stability under communication delays. ACC relies on onboard sensors, while CACC augments this capability with vehicle-to-vehicle (V2V) communication and both systems are used to synchronize vehicle speeds and maintain precise inter-vehicular spacing in platoons. Our goal is to find conditions on the controller’s proportional and derivative gains to balance individual vehicle stability and string stability. The latter is crucial to ensure that spacing errors do not amplify as vehicles traverse the platoon, a fundamental requirement for safe and efficient platooning. We provide a method for characterizing controller gains for string and individual stability based on the well-known $D$-decomposition in the time-delay systems literature. Numerical simulations validate the theoretical results.

We consider asymptotic behavior of integro-differential equations with periodic nonlinearities, featured by infinite sequences of equilibria. Such systems are also referred to as ``synchronization systems'' in view of numerous applications to dynamics of control circuits such as phase-locked, frequency-locked, and delay-locked loops. In these applications, one is typically interested in gradient-like behavior of a system, that is, the convergence of all solutions to equilibria and the absence of oscillations. In this talk, new frequency-domain conditions are obtained to ensure gradient-like behavior. Remarkably, the relaxation of these conditions to the subinterval of frequencies guarantees the absence of undesirable high-frequency oscillations in the system.

Nonlinear stiffness characteristics appear regularly in engineering applications including in systems with digital feedback. This paper proposes a novel method for bifurcation analysis of sampled systems with continuous nonlinearities and the presented approach is used to predict the characteristics of Hopf bifurcations in the digital force control of a mass and nonlinear spring system.

Time-delayed feedback (TDF) control methods have proven to be robust and versatile for nonlinear dynamical systems. Their abilities to take advantage of the system behaviour without the need of a calibrated model is particularly attractive. Most recently, the TDF control method has been expanded to switch between co-existing orbits. However, we observed that, in some cases, classical TDF control method stabilizes unintended orbits. In this work, we propose a modification of TDF control method to avoid these drawbacks and to guarantee the stabilization of only targeted orbits. We show that our modified control method stabilizes the targeted orbits whilst the classical TDF control fails to do so.

This paper addresses pole placement of a nonlinear system and experiment carried out using hammer test to demonstrate how the poles can be moved in the Laplace domain. Receptance method is developed for nonlinear systems that is extended formulation of the linear receptance method. The mathematical model considered in this manuscript to study the nonlinear equation is a duffing oscillator with cubic stiffness. First, mathematical equation of pole placement of a nonlinear system and the eigenvalue sensitivities to parametric perturbations are derived. Then eigenvalue sensitivities are minimized to enhance the performance robustness of dynamical system control. This approach is applicable to all the nonlinear systems that experience variations caused by manufacturing and material tolerances, damages, and environmental fluctuations. The nonlinear system's poles and eigenvalue sensitivities are assigned through linear feedback control and the Sherman-Morrison formula under varying levels of excitation and minimization of the calculated feedback gains. Given the amplitude-dependent response of the nonlinear system, an iterative method is employed to determine the optimal feedback gains. The proposed algorithm involves curve fitting perturbed frequency response functions (FRFs) using the rational fraction polynomial method, making it unnecessary to measure the ????,????,???? matrices.