Deterministic Switches Research Articles

Stability Analysis of Stochastic Impulsive Switched Systems with Deterministic State-Dependent Impulses and Switches

This paper studies stability of stochastic impulsive switched systems with deterministic state-dependent impulses and switches. Here, “deterministic state-dependent” means that both switching and i...

Stochastic and deterministic switches in a bistable polariton micropillar under short optical pulses

Optical bistability of exciton polaritons in semiconductor microcavities is a promising platform for digital optical devices. Steady states of coherently driven polaritons can be toggled in tens of picoseconds by a short external pulse of appropriate amplitude and phase. We have analyzed the switching behavior of polaritons depending on the pulse amplitude, phase, and duration. The switches are found to change dramatically when the inverse pulse duration becomes comparable to the frequency detuning between the driving field and polariton resonance. If the detuning is large compared to the polariton linewidth, the system becomes extremely sensitive to initial conditions and thus can serve as a fast random-number generator.

Finite-time outer-synchronization for complex networks with Markov jump topology via hybrid control and its application to image encryption

This paper investigates the problem of finite-time outer-synchronization for discrete-time complex networks with Markov jump topology in the presence of communication delays and possible information losses and its application to image encryption. A hybrid control, which is subject to both stochastic jumps and deterministic switches, is proposed to realize finite-time and stochastic outer-synchronization for the concerned networks. By utilizing a stochastic Lyapunov functional combined with the average dwell-time method, sufficient conditions are found such that the synchronization error dynamical system is stochastically stable in finite-time. Two numerical examples are presented to illustrate the effectiveness of the proposed method. Finally, the complex network consists of four coupled Lorenz systems are utilized to generate chaotic sequences and a new chaotic image cryptosystem is constructed to transmit encrypted images based on the synchronized drive-response complex networks. Experiments are conducted by using numerical simulation, and the security is analyzed in terms of key space, key sensitivity, histogram distributions, correlation coefficients, information entropy and differential attack measures. The experimental results show that the proposed chaotic image cryptosystem has the advantages of high security against some classical attacks.

Emergence of free will and consciousness in humans: implications for doctor-patient interactions

Human brains have about 100 billion neurons each with about 1000 dendritic connections with other neurons giving a total of 100 000 billion deterministic dendritic switches. Various voting systems that...

Design of stabilizing strategies for discrete-time dual switching linear systems

Discrete-time dual switching linear systems are piecewise linear systems subject to both stochastic and deterministic commutations. Stochastic jumps, well-suited to account for unpredictable events like faults or abrupt changes in the parameters, are modeled by means of a Markov chain. The deterministic switches are dictated by a scheduling signal, used as a control variable in order to achieve stochastic stability and guaranteed input/output performance. We derive sufficient conditions for the existence of a state-feedback switching law attaining these goals. Further, the more challenging co-design problem is addressed, namely the joint synthesis of a linear state-feedback controller and a stabilizing switching strategy ensuring a prescribed performance. The results are illustrated by means of a numerical example concerning a networked control system under occasional communication failures.

Finite-Time Boundedness of Markov Jump System with Piecewise-Constant Transition Probabilities via Dynamic Output Feedback Control

This paper first investigates the problem of finite-time boundedness of Markovian jump system with piecewise-constant transition probabilities via dynamic output feedback control, which leads to both stochastic jumps and deterministic switches. Based on stochastic Lyapunov functional, the concept of finite-time boundedness, average dwell time, and the coupling relationship among time delays, several sufficient conditions are established for finite-time boundedness andH∞filtering finite-time boundedness. The system trajectory stays within a prescribed bound. Finally, an example is given to illustrate the efficiency of the proposed method.

Finite‐time H ∞ control with average dwell‐time constraint for time‐delay Markov jump systems governed by deterministic switches

This study considers the problem of finite-time H ∞ control for a class of discrete-time time-delay Markov jump linear systems governed by deterministic switches. By allowing the stochastic Lyapunov function to increase at every switching instant with a limited increase rate, new results on the stochastic finite-time boundness with given H ∞ disturbance attenuation level are derived. Moreover, the coupling relationship among time-delay, average dwell time and given finite-time horizon of the underlying system is obtained through an average dwell-time constraint. Finally, one example is given to demonstrate the validity of the obtained results.

Finite-time control for discrete-time Markovian jump systems with deterministic switching and time-delay

In this paper, the finite-time control problem is investigated for a class of discrete-time Markovian jump systems (MJLSs) with deterministic switching and time-delay. The considered systems are subject to a piecewise-constant transition probability (TP) matrix, which leads to both the deterministic switches and stochastic jumps. First, the stochastic finite-time boundedness (SFTB) and l2 gain analysis for the systems are studied by employing the average dwell time (ADT) approach. Note that a finite-time weighted l2 gain is obtained to measure the disturbance attenuation level. Then, the mode-dependent and variation-dependent controller is designed such that the resulting closed-loop systems are stochastically finite-time bounded and have a guaranteed disturbance attenuation level. Finally, a numerical example is given to verify the potential of the developed results.

Finite-time stabilization for Markov jump systems governed by deterministic switches

The problem of controller synthesis in a fixed time interval for discrete-time switching Markov jump systems is dealt with in this paper. Compared with the existing results, the new proposed stabilization conditions are obtained by permitting the stochastic Lyapunov energy function to rise at each switching instant, but the switching signal is constraint by an average dwell time. Finally, the validity of the obtained results is demonstrated with an example.

Almost Sure Stability of Markov Jump Linear Systems With Deterministic Switching

The technical note studies a class of linear systems whose piecewise-constant dynamic matrix is subject to both stochastic jumps, governed by a Markov chain, and deterministic switches. These systems will be dubbed switching dynamics Markov jump linear systems (SD-MJLS). Sufficient conditions for exponential almost sure stability (EAS-stability) are established under either hard or average constraints on the dwell-time between switching instants. The proof relies on easy-to-check norm contractivity conditions and the ergodic law of large numbers.

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Gossip Coverage Control for Robotic Networks: Dynamical Systems on the Space of Partitions

Future applications in environmental monitoring, delivery of services, and transportation of goods motivate the study of deployment and partitioning tasks for groups of autonomous mobile agents. These tasks may be achieved by recent coverage algorithms, based upon the classic methods by Lloyd. These algorithms, however, rely upon critical requirements on the communication network: information is exchanged synchronously among all agents and long-range communication is sometimes required. This work proposes novel coverage algorithms that require only gossip communication, i.e., asynchronous, pairwise, and possibly unreliable communication. Which robot pair communicates at any given time may be selected deterministically or randomly. A key innovative idea is describing coverage algorithms for robot deployment and environment partitioning as dynamical systems on a space of partitions. In other words, we study the evolution of the regions assigned to each agent rather than the evolution of the agents' positions. The proposed gossip algorithms are shown to converge to centroidal Voronoi partitions under mild technical conditions. Our treatment features a broad variety of results in topology, analysis, and geometry. First, we establish the compactness of a suitable space of partitions with respect to the symmetric difference metric. Second, with respect to this metric, we establish the continuity of various geometric maps, including the Voronoi diagram as a function of its generators, the location of a centroid as a function of a set, and the widely known multicenter function studied in facility location problems. Third, we prove two convergence theorems for dynamical systems on metric spaces described by deterministic and stochastic switches.

Electron logic devices and nanoinstrumentation based on laterally patterned interaction-free quantum measurement structures

Recent photonic experiments on non-invasive or interaction-free measurement are discussed within the interpretative deterministic framework put forward by Bohm. It is proposed that analogous mesoscopic electronic structures utilizing spin polarization could support the non-invasive effect. The incorporation of a full Zeno effect leads to the possibility of building deterministic quantum switches.