Masashi Wakaiki

Masashi Wakaiki, Paulo Tabuada, Joao P. Hespanha

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.

Masashi Wakaiki, Kunihisa Okano, Joao P. Hespanha

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.

Masashi Wakaiki, Tadanao Zanma, Kang-Zhi Liu

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.

Masashi Wakaiki, Yutaka Yamamoto

We propose a stability analysis method for sampled-data switched linear systems with quantization. The available information to the controller is limited: the quantized state and switching signal at each sampling time. Switching between sampling times can produce the mismatch of the modes between the plant and the controller. Moreover, the coarseness of quantization makes the trajectory wander around, not approach, the origin. Hence the trajectory may leave the desired neighborhood if the mismatch leads to instability of the closed-loop system. For the stability of the switched systems, we develop a sufficient condition characterized by the total mismatch time. The relationship between the mismatch time and the dwell time of the switching signal is also discussed.

Masashi Wakaiki, Hideki Sano

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.

Masashi Wakaiki

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.

Masashi Wakaiki

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.

Masashi Wakaiki, Ahmet Cetinkaya, Hideaki Ishii

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.

Masashi Wakaiki, Yutaka Yamamoto

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.

Masashi Wakaiki, Yutaka Yamamoto

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.

Masashi Wakaiki, Yutaka Yamamoto

We propose a stability analysis method for sampled-data switched linear systems with finite-level static quantizers. In the closed-loop system, information on the active mode of the plant is transmitted to the controller only at each sampling time. This limitation of switching information leads to a mode mismatch between the plant and the controller, and the system may become unstable. A mode mismatch also makes it difficult to find an attractor set to which the state trajectory converges. A switching condition for stability is characterized by the total time when the modes of the plant and the controller are different. Under the condition, we derive an ultimate bound on the state trajectories by using a common Lyapunov function computed from a randomized algorithm. The switching condition can be reduced to a dwell-time condition.

Masashi Wakaiki, Yutaka Yamamoto

We propose an encoding and control strategy for the stabilization of switched systems with limited information, supposing the controller is given for each mode. Only the quantized output and the active mode of the plant at each sampling time are transmitted to the controller. Due to switching, the active mode of the plant may be different from that of the controller in the closed-loop system. Hence if switching occurs, the quantizer must recalculate a bounded set containing the estimation error for quantization at the next sampling time. We establish the global asymptotic stability under a slow-switching assumption on dwell time and average dwell time. To this end, we construct multiple discrete-time Lyapunov functions with respect to the estimated state and the size of the bounded set.