arXiv subjects

Masashi Wakaiki

Publications and source records attributed to Masashi Wakaiki.

At least 37 records · Page 2Linked to original sources

arXiv2022

Stability of Infinite-dimensional Sampled-data Systems with Unbounded Control Operators and Perturbations

We analyze the robustness of the exponential stability of infinite-dimensional sampled-data systems with unbounded control operators. The unbounded perturbations we consider are the so-called Desch-Schappacher perturbations, which arise, e.g., from the boundary perturbations of systems described by partial differential equations. As the main result, we show that the exponential stability of the sampled-data system is preserved under all Desch-Schappacher perturbations sufficiently small in a certain sense.

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arXiv2021

Cell Zooming with Masked Data for Off-Grid Small Cell Networks: Distributed Optimization Approach

Cell zooming has been becoming an essential enabler for off-grid small cell networks. Traditional models often utilize the numbers of active users in order to determine cell zooming strategies. However, such confidential measurement data must be concealed from others. We therefore propose a novel cell zooming method with masking noise. The proposed algorithm is designed based on distributed optimization, in which each SBS locally solves a divided optimization problem and learns how much a global constraint is satisfied or violated for temporal solutions. The important feature of this distributed control method is robustness against masking noise. We analyze the trade-off between confidentiality and optimization accuracy, using the notion of differential privacy. Numerical simulations show that the proposed distributed control method outperforms a standard centralized control method in the presence of masking noise.

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arXiv2021

Strong Stability of Sampled-data Riesz-spectral Systems

Suppose that a continuous-time linear infinite-dimensional system with a static state-feedback controller is strongly stable. We address the following question: If we convert the continuous-time controller to a sampled-data controller by applying an idealized sampler and a zero-order hold, will the resulting sampled-data system be strongly stable for all sufficiently small sampling periods? In this paper, we restrict our attention to the situation where the generator of the open-loop system is a Riesz-spectral operator and its point spectrum has a limit point at the origin. We present conditions under which the answer to the above question is affirmative. In the robustness analysis, we show that the sufficient condition for strong stability obtained in the Arendt-Batty-Lyubich-Vũ theorem is preserved between the original continuous-time system and the sampled-data system under fast sampling.

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arXiv2021

The Cayley transform of the generator of a polynomially stable $C_0$-semigroup

In this paper, we study the decay rate of the Cayley transform of the generator of a polynomially stable $C_0$-semigroup. To estimate the decay rate of the Cayley transform, for polynomial stability. Using this integral condition, we relate polynomial stability to Lyapunov equations. We also study robustness of polynomial stability for a certain class of structured perturbations.

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arXiv2019

Event-triggered Control of Infinite-dimensional Systems

This paper addresses the problem of event-triggered control for infinite-dimensional systems. We employ event-triggering mechanisms that compare the plant state and the error of the control input induced by the event-triggered implementation. Under the assumption that feedback operators are compact, a strictly positive lower bound on the inter-event times can be guaranteed. We show that if the threshold of the event-triggering mechanisms is sufficiently small, then the event-triggered control system with a bounded control operator and a compact feedback operator is exponentially stable. For infinite-dimensional systems with unbounded control operators, we employ two event-triggering mechanisms that are based on system decomposition and periodic event-triggering, respectively, and then analyze the exponential stability of the closed-loop system under each event-triggering mechanism.

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arXiv2019

Sampled-data Output Regulation of Unstable Well-posed Infinite-dimensional Systems with Constant Reference and Disturbance Signals

We study the sample-data control problem of output tracking and disturbance rejection for unstable well-posed linear infinite-dimensional systems with constant reference and disturbance signals. We obtain a sufficient condition for the existence of finite-dimensional sampled-data controllers that are solutions of this control problem. To this end, we study the problem of output tracking and disturbance rejection for infinite-dimensional discrete-time systems and propose a design method of finite-dimensional controllers by using a solution of the Nevanlinna-Pick interpolation problem with both interior and boundary conditions. We apply our results to systems with state and output delays.

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arXiv2019

Stability Analysis of Perturbed Infinite-dimensional Sampled-data Systems

This paper addresses the stability analysis of infinite-dimensional sampled-data systems under unbounded perturbations. We present two classes of unbounded perturbations preserving the exponential stability of sampled-data systems. To this end, we investigate the continuity of strongly continuous semigroups with respect to their generators, considering the uniform operator topology.

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arXiv2019

An LMI Approach to Stability Analysis of Coupled Parabolic Systems

We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by splitting space domains but take into account approximation errors during stability analysis. Using a quadratic Lyapunov function, we obtain sufficient conditions for exponential stability in terms of linear matrix inequalities.

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arXiv2018

Supervisory Control of Discrete-event Systems under Attacks

We consider a multi-adversary version of the supervisory control problem for discrete-event systems, in which an adversary corrupts the observations available to the supervisor. The supervisor's goal is to enforce a specific language in spite of the opponent's actions and without knowing which adversary it is playing against. This problem is motivated by applications to computer security in which a cyber defense system must make decisions based on reports from sensors that may have been tampered with by an attacker. We start by showing that the problem has a solution if and only if the desired language is controllable (in the Discrete event system classical sense) and observable in a (novel) sense that takes the adversaries into account. For the particular case of attacks that insert symbols into or remove symbols from the sequence of sensor outputs, we show that testing the existence of a supervisor and building the supervisor can be done using tools developed for the classical DES supervisory control problem, by considering a family of automata with modified output maps, but without expanding the size of the state space and without incurring on exponential complexity on the number of attacks considered., we construct observers that are robust against attacks and lead to an automaton representation of the supervisor. We also develop a test for observability under such replacement-removal attacks by using the so-called product automata.

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arXiv2018

Stabilization of Networked Control Systems under DoS Attacks and Output Quantization

This paper addresses quantized output feedback stabilization under Denial-of-Service (DoS) attacks. First, assuming that the duration and frequency of DoS attacks are averagely bounded and that an initial bound of the plant state is known, we propose an output encoding scheme that achieves exponential convergence with finite data rates. Next we show that a suitable state transformation allows us to remove the assumption on the DoS frequency. Finally, we discuss the derivation of state bounds under DoS attacks and obtain sufficient conditions on the bounds of DoS duration and frequency for achieving Lyapunov stability of the closed-loop system.

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arXiv2018

LQ-optimal Sample-data Control under Stochastic Delays: Gridding Approach for Stabilizability and Detectability

We solve a linear quadratic optimal control problem for sampled-data systems with stochastic delays. The delays are stochastically determined by the last few delays. The proposed optimal controller can be efficiently computed by iteratively solving a Riccati difference equation, provided that a discrete-time Markov jump system equivalent to the sampled-data system is stochastic stabilizable and detectable. Sufficient conditions for these notions are provided in the form of linear matrix inequalities, from which stabilizing controllers and state observers can be constructed.

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arXiv2018

Stability and $\ell^2$-gain Analysis of Adaptive Control Systems with Event-triggered Try-once-discard Protocols

This paper addresses the stability and $\ell^2$-gain analysis of adaptive control systems with event-triggered try-once-discard protocols. At every sampling time, an event trigger evaluates an error between the current value and the last released value of each measurement and determines whether to transmit the measurements and which measurements to transmit, based on the try-once-discard protocol and given lower and upper thresholds. For gain-scheduling controllers and switching controllers that are adaptive to the maximum error of the measurements, we obtain sufficient conditions for the practical stability and upper bounds on the $\ell^2$-gain of the closed-loop system.

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arXiv2017

Delayed Bet-Hedging Resilience Strategies Under Environmental Fluctuations

Many biological populations, such as bacterial colonies, have developed through evolution a protection mechanism, called bet-hedging, to increase their probability of survival under stressful environmental fluctutation. In this context, the concept of preadaptation refers to a common type of bet-hedging protection strategy in which a relatively small number of individuals in a population stochastically switch their phenotypes to a `dormant' metabolic state in which they increase their probability of survival against potential environmental shocks. Hence, if an environmental shock took place at some point in time, preadapted organisms would be better adapted to survive and proliferate once the shock is over. In many biological populations, the mechanisms of preadaptation and proliferation present delays whose influence in the fitness of the population are not well-understood. In this paper, we propose a rigorous mathematical framework to analyze the role of delays in both preadaptation and proliferation mechanisms in the survival of biological populations, with an emphasis on bacterial colonies. Our theoretical framework allows us to analytically quantify the average growth rate of a bet-hedging bacterial colony with stochastically delayed reactions with arbitrary precision. We verify the accuracy of the proposed method by numerical simulations and conclude that the growth rate of a bet-hedging population shows a non-trivial dependency on their preadaptation and proliferation delays. Contrary to the current belief, our results show that faster reactions do not, in general, increase the overall fitness of a biological population.

q-bio.PE↗

arXiv2017

Quantized output feedback stabilization by Luenberger observers

We study a stabilization problem for systems with quantized output feedback. The state estimate from a Luenberger observer is used for control inputs and quantization centers. First we consider the case when only the output is quantized and provide data-rate conditions for stabilization. We next generalize the results to the case where both of the plant input and output are quantized and where controllers send the quantized estimate of the plant output to encoders as quantization centers. Finally, we present the numerical comparison of the derived data-rate conditions with those in the earlier studies and a time response of an inverted pendulum.

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arXiv2017

Stabilization of systems with asynchronous sensors and controllers

We study the stabilization of networked control systems with asynchronous sensors and controllers. Offsets between the sensor and controller clocks are unknown and modeled as parametric uncertainty. First we consider multi-input linear systems and provide a sufficient condition for the existence of linear time-invariant controllers that are capable of stabilizing the closed-loop system for every clock offset in a given range of admissible values. For first-order systems, we next obtain the maximum length of the offset range for which the system can be stabilized by a single controller. Finally, this bound is compared with the offset bounds that would be allowed if we restricted our attention to static output feedback controllers.

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arXiv2016

Dynamic Analysis of Bet-Hedging Strategies as a Protection Mechanism against Environmental Fluctuations

In order to increase their robustness against environmental fluctuations, many biological populations have developed bet-hedging mechanisms in which the population `bets' against the presence of prolonged favorable environmental conditions by having a few individual behaving as if they sensed a threatening or stressful environment. As a result, the population (as a whole) increases its chances of surviving environmental fluctuations in the long term, while sacrificing short-term performance. In this paper, we propose a theoretical framework, based on Markov jump linear systems, to model and evaluate the performance of bet-hedging strategies in the presence of stochastic fluctuations. We illustrate our results using numerical simulations.

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arXiv2015

Stabilization of discrete-time piecewise affine systems with quantized signals

This paper studies quantized control for discrete-time piecewise affine systems. For given stabilizing feedback controllers, we propose an encoding strategy for local stability. If the quantized state is near the boundaries of quantization regions, then the controller can recompute a better quantization value. For the design of quantized feedback controllers, we also consider the stabilization of piecewise affine systems with bounded disturbances. In order to derive a less conservative design method with low computational cost, we investigate a region to which the state belong in the next step.

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arXiv2015

Stabilization of continuous-time switched linear systems with quantized output feedback

In this paper, we study the problem of stabilizing continuous-time switched linear systems with quantized output feedback. We assume that the observer and the control gain are given for each mode. Also, the plant mode is known to the controller and the quantizer. Extending the result in the non-switched case, we develop an update rule of the quantizer to achieve asymptotic stability of the closed-loop system under the average dwell-time assumption. To avoid quantizer saturation, we adjust the quantizer at every switching time.

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