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We describe adaptive control algorithms whereby a chaotic dynamical system can be steered to a target state with desired characteristics. A specific implementation considered has the objective of directing the system to a state which is…
This paper proposes an algorithm capable of driving a system to follow a piecewise linear trajectory without prior knowledge of the system dynamics. Motivated by a critical failure scenario in which a system can experience an abrupt change…
In this work, inspired in the symbolic dynamic of chaotic systems and using machine learning techniques, a control strategy for complex systems is designed. Unlike the usual methodologies based on modeling, where the control signal is…
In this paper, a nonlinear system aiming at reducing the signal transmission rate in a networked control system is constructed by adding nonlinear constraints to a linear feedback control system. Its stability is investigated in detail. It…
In this article we consider the possibility of controlling the dynamics of nonlinear discrete systems. A new method of control is by mixing states of the system (or the functions of these states) calculated on previous steps. This approach…
A novel method for control of dynamical systems, proposed in the paper, ensures an output signal belonging to the given set at any time. The method is based on a special change of coordinates such that the initial problem with given…
The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force". In low-dimensional continuous systems, one method is that of reconstructing the tangent space, so that the…
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario…
Chaotic itinerancy is a frequently observed phenomenon in high-dimensional and nonlinear dynamical systems, and it is characterized by the random transitions among multiple quasi-attractors. Several studies have revealed that chaotic…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
Coupling of chaotic oscillators has evidenced conditions where synchronization is possible, therefore a nonlinear system can be driven to a particular state through input from a similar oscillator. Here we expand this concept of control of…
It is demonstrated that improved entrainment control of chaotic systems can maintain periodic goal dynamics near unstable periodic orbits without feedback. The method is based on the optimization of goal trajectories and leads to small…
Following a brief historical introduction of the notions of chaos in dynamical systems, we will present recent developments that attempt to profit from the rich structure and complexity of the chaotic dynamics. In particular, we will…
A novel model for dynamical traps in intermittent human control is proposed. It describes probabilistic, step-wise transitions between two modes of a subject's behavior - active and passive phases in controlling an object's dynamics - using…
We propose a novel and fully data driven control scheme which relies on machine learning (ML). Exploiting recently developed ML-based prediction capabilities of complex systems, we demonstrate that nonlinear systems can be forced to stay in…
In this paper we present a direct adaptive control method for a class of uncertain nonlinear systems with a time-varying structure. We view the nonlinear systems as composed of a finite number of ``pieces,'' which are interpolated by…
Non-deterministic chaos is a new dynamical paradigm where a non-deterministic system is influenced by random perturbations to produce the appearance of complexity. The non-determinism is envisioned to occur only at a single point in phase…
Controlling complex dynamical systems has been a topic of considerable interest in academic circles in recent decades. While existing works have primarily focused on closed-loop control schemes with infinite-time durations, this paper…
We present a novel, model-free, and data-driven methodology for controlling complex dynamical systems into previously unseen target states, including those with significantly different and complex dynamics. Leveraging a parameter-aware…
A chaos control algorithm is developed to actively stabilize unstable periodic orbits of higher-dimensional systems. The method assumes knowledge of the model equations and a small number of experimentally accessible parameters. General…