The growing deployment of networked multi-vehicle systems for autonomous mobility and logistics underscores the need for robust and resilient control under adversarial and uncertain conditions. Vehicular platooning offers benefits in traffic efficiency, energy savings, and safety; yet, conventional equilibrium-based control schemes remain vulnerable to cyber-physical attacks such as jamming, spoofing, and denial-of-service (DoS), threatening reliable coordination. In this paper, we propose a socially optimal linear-quadratic (LQ) control framework that embeds collective performance objectives directly into the quadratic cost formulation. This approach targets operating configurations that reflect platoon-level social optimality, which may differ from the closed-loop equilibrium. This results in an extended LQ tracking formulation that steers the platoon toward the equilibrium closest, in a quadratic sense, to the socially optimal configuration. To counter adversarial conditions, we integrate resilience mechanisms against cyber-physical attacks—including false data injection (FDI), spoofing, and jamming—addressing attacks directed at the supervisory unit and individual vehicles. Simulation results demonstrate the effectiveness, robustness, and practical implementability of the proposed approach in both nominal and adversarial scenarios.

This research focuses on improving the transistor-based fractional exponentiation circuit (also known as 444 circuit). It aims to address the issue of insufficient stability and verifies the adaptability of the chaotic system through hardware experiments. Starting from three feedback capacitors as the improvement point, mathematical modeling analysis and circuit simulation verification effectively improve the system’s bandwidth and dynamic response characteristics. The optimized circuit is embedded in the VB5 system, constructing a series of chaotic systems with nonlinear feedback. The chaotic phase trajectories obtained from experimental observations are highly consistent with the theoretical predictions, providing key empirical evidence for the improvement of the stability of the 444 circuit. This research achievement opens up a low-cost technical implementation path for the realization of complex nonlinear feedback, such as fractional exponent operation in chaotic circuits.

Convergence of nonlinear circuits towards equilibrium points (EPs) is one of the most basic properties both from a theoretic and a practical viewpoint. It is especially relevant for nonlinear circuits modeling neural networks, since a convergent network with multiple stable EPs is tailor made to implement content addressable memories (CAMs) storing multiple patterns as stable EPs or to solve combinatorial optimization problems in real time. Convergence has been widely investigated in the last few decades. By far, the available convergence results can be applied to circuits without memristors, while the study of convergence in presence of memristors is only in its infancy. In this paper, a class of nonlinear circuits containing memristors, capacitors, passive or active resistors and independent sources, is considered. Active resistors are crucial, since they permit to obtain circuits with multiple stable EPs. A number of basic results on convergence are obtained via the flux-charge analysis method (FCAM) and a fundamental reciprocity principle for the considered class of circuits. The conditions for convergence are robust, i.e., they hold also for perturbations of the circuit parameters and memristor nonlinearities involved. The results are illustrated via selected examples where use is made of the celebrated HP memristor model.

The paper considers a wide class of nonlinear circuits with an ideal memristor, capacitors, inductors and current or voltage sources. A fundamental dynamical property is that each memristor circuit in this class admits a first integral (invariant of motion or preserved quantity), i.e., a function which is constant along the solutions. The first main result is that we can put the state equations of each circuit in a universal form, known as linear-gradient form, given by a state-dependent skew-symmetric matrix times the gradient of the first integral. This is a simple and general form which is both of theoretic and practical interest. First of all, it makes manifest the existence of a first integral. Moreover, it admits an elegant discrete-time (DT) analogue. Indeed, the linear-gradient form, combined with geometric discretization methods and the concept of discrete gradients, yields a DT version of each memristor circuit that exactly preserves the first integral for any discretization time step. This is relevant, since the existence of a first integral is a fragile property that is in general destroyed by typical discretization schemes used in the literature no matter how small the step size is. On one hand, the proposed discretization scheme can be used for constructing numerical algorithms that better approximate the solutions of memristor circuits for small step sizes. On the other hand, for larger step sizes the obtained DT memristor circuits can be of interest by themselves since they are able to easily generate complex dynamics potentially useful for engineering applications (computational chaos). Furthermore, the paper shows that, thanks to the decomposition of the state space in invariant manifolds, the derived DT circuits exhibit extreme multistability, i.e., the coexistence of infinitely many different attractors for fixed set of circuit parameters, memristor nonlinearity and step size.

Nonvolatile memristive devices display nonlinear characteristics suitable for implementing circuits exhibiting oscillations or more complex dynamic behaviors, including chaos. However, the results presented in related works are mostly limited to simulations and employing ideal memristor models whose resistance is governed by a charge-flux relation that is not connected to real devices, thus hindering the realization of such nonlinear oscillators. In this work, we present the framework for the physical implementation of a tunable memristor Chua’s circuit, which is based on a nonvolatile memristive device that provides the nonlinear conductance required by the circuit and the possibility to tune it for the purpose of selecting among different oscillation patterns. We first establish design guidelines to guarantee complex oscillations in the tunable memristor Chua’s circuit. Further, we physically implement the circuit after characterizing and modeling the tunable current-voltage characteristic of a real device. Our circuit successfully generates different oscillation patterns just by programming the nonvolatile memristive device to different states. The devised design guidelines and device modeling were used to extend the experimental work and draw further requirements for device properties for a successful circuit implementation.

Controlling multistability, i.e., designing control laws for switching among different attractors, is an emerging issue in the area of memristor circuits. The paper considers the Chua’s memristor circuit which is known to display infinitely many attractors, each one contained in an invariant manifold of the circuit state space. The problem of switching among these attractors via pulse-programmed feedforward control laws, which are implementable via a unique current/voltage source, is investigated. In particular, it is shown that if the shape of the voltage source in series to the inductor is suitably designed, then it is possible to switch in finite time from one attractor to another.

Random mechanisms including mutations are an internal part of evolutionary algorithms, which are based on the fundamental ideas of Darwin’s theory of evolution as well as Mendel’s theory of genetic heritage. In this paper, we debate whether pseudo-random processes are needed for evolutionary algorithms or whether deterministic chaos, which is not a random process, can be suitably used instead. Specifically, we compare the performance of 10 evolutionary algorithms driven by chaotic dynamics and pseudo-random number generators using chaotic processes as a comparative study. In this study, the logistic equation is employed for generating periodical sequences of different lengths, which are used in evolutionary algorithms instead of randomness. We suggest that, instead of pseudo-random number generators, a specific class of deterministic processes (based on deterministic chaos) can be used to improve the performance of evolutionary algorithms. Finally, based on our findings, we propose new research questions.

This article introduces a new class of memristor neural networks (NNs) for solving, in real-time, quadratic programming (QP) and linear programming (LP) problems. The networks, which are called memristor programming NNs (MPNNs), use a set of filamentary-type memristors with sharp memristance transitions for constraint satisfaction and an additional set of memristors with smooth memristance transitions for memorizing the result of a computation. The nonlinear dynamics and global optimization capabilities of MPNNs for QP and LP problems are thoroughly investigated via a recently introduced technique called the flux-charge analysis method. One main feature of MPNNs is that the processing is performed in the flux-charge domain rather than in the conventional voltage-current domain. This enables exploiting the unconventional features of memristors to obtain advantages over the traditional NNs for QP and LP problems operating in the voltage-current domain. One advantage is that operating in the flux-charge domain allows for reduced power consumption, since in an MPNN, voltages, currents, and, hence, power vanish when the quick analog transient is over. Moreover, an MPNN works in accordance with the fundamental principle of in-memory computing, that is, the nonlinearity of the memristor is used in the dynamic computation, but the same memristor is also used to memorize in a nonvolatile way the result of a computation.

Memristors are more and more seen as the basic elements for the development of new unconventional computational schemes. One of the appealing property of memristor circuits is multistability, i.e., the coexistence in the state space of a rich variety of different attractors. This paper considers the problem of controlling multistability for a circuit with a charge-controlled memristor which displays infinite stable equilibrium points and limit cycles. Specifically, it is shown how voltage and current sources can be pulse programmed in order to steer the circuit dynamics from one stable equilibrium point to a different stable equilibrium point within a given finite time interval.

Circuits containing memelements (memory elements) are suitable for the design of new unconventional computational schemes. The coexistence of a rich variety of different attractors is one of the appealing property of these circuits, which has stimulated the so-called “multistability control” problem. This paper considers the multistability control problem for a circuit with a charge-controlled memristor. It is shown how pulse control inputs can be generated via an external current generator in order to drive the system dynamics from an attractor to another one in a given finite time interval.