Joao P. Hespanha

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.

Corentin Delacour, M Mahmudul Hasan Sajeeb, Joao P. Hespanha et al.

Sampling Boltzmann probability distributions plays a key role in machine learning and optimization, motivating the design of hardware accelerators such as Ising machines. While the Ising model can in principle encode arbitrary optimization problems, practical implementations are often hindered by soft constraints that either slow down mixing when too strong, or fail to enforce feasibility when too weak. We introduce a two-dimensional extension of the powerful parallel tempering algorithm (PT) that addresses this challenge by adding a second dimension of replicas interpolating the penalty strengths. This scheme ensures constraint satisfaction in the final replicas, analogous to low-energy states at low temperature. The resulting two-dimensional parallel tempering algorithm (2D-PT) improves mixing in heavily constrained replicas and eliminates the need to explicitly tune the penalty strength. In a representative example of graph sparsification with copy constraints, 2D-PT achieves near-ideal mixing, with Kullback-Leibler divergence decaying as O(1/t). When applied to sparsified Wishart instances, 2D-PT yields orders of magnitude speedup over conventional PT with the same number of replicas. The method applies broadly to constrained Ising problems and can be deployed on existing Ising machines.