This paper addresses the problem of language opacity for a class of timed discrete-event systems whose transitions must occur within some known time interval after the system reaches a state. For this purpose, a new class of timed automata is proposed, time-interval automata (TIA), in which the time elapsed is associated with a unique clock, allowing each transition to be associated with a time interval of occurrence. We present new procedures to compute complement, projection, and intersection of time-interval regular languages using TIA, which, differently from existing approaches, do not require refinement by partition of the intervals when performed by using the automata that represent the considered languages. We extend the well-known language-based definition of opacity to time-interval language opacity and, to this end, we introduce new notions of language opacity: time independent(I)/dependent(D) strong(S)/weak(W) opacity(O): TISO, TIWO, TDSO and TDWO. We propose necessary and sufficient conditions for each one of the above notions of opacity and an algorithm for their verification.
Under scalar fields with unknown information, a cooperative formation source localization policy based on in-degree information is investigated for multiple double- integrator robots over directed networks in this paper. In the situation with unavailable field gradients, gradient estimators with adaptive strategies are developed as robotic navigation direction based on a partially unknown field approximator. For the unknown left eigenvector of the Laplacian matrix from directed networks, a predefined-time eigenvector observer is established to identify this eigenvector for prompting formation consensus. By building an auxiliary variable, we propose a velocity-based adaptive formation control scheme together with gradient estimators and eigenvector observers under weight-unbalanced directed networks, such that the formation center of robots approaches to the field source eventually. In the inexistence of eigenvector observers and velocity measurements, by virtue of some auxiliary variables and gradient estimators, we invent a velocity-free adaptive formation control scheme under general directed networks for helping robots locate the field source. At last, numerical simulations verify the effectiveness of the proposed schemes.
This paper studies the safety-constrained problem for a Markov decision process (MDP) in Borel state and action spaces. We show under natural conditions that it has an optimal strategy, which is not stationary but is in the special form that can be constructed by solving a linear program in the space of measures. This is done by reducing the original MDP problem to an unconstrained total cost problem for the original MDP model and a standard constrained total cost problem for an MDP model with a costless and absorbing state.
In this paper, we study the two-player linear-quadratic risk-sensitive zero-sum differential game for the singularly perturbed stochastic system driven by Brownian motion. The stochastic differential equation includes slow and fast dynamics determined by the singular perturbation variable $\varepsilon \in (0,1)$. We consider the $\log$-$\exp$ type risk-sensitive objective functional to capture the risk-averse behavior of the two players through the risk-averse index $\mu > 0$, where there are cross-coupling structures between controls of the players as well as the state dynamics. We first obtain the full-order Nash equilibrium (NE), represented by the (full-order) Riccati differential equation (RDE) in terms of $\varepsilon \in (0,1)$, by establishing the completion-of-squares method, where the change of probability measures as well as the ordered interchangeability property of multiple NE need to be applied. Then we obtain the approximation result of the (full-order) RDE by identifying the reduced-order (differential and algebraic) Riccati equations and boundary-layer systems, where we find the explicit approximation order of $O(\sqrt{\varepsilon })$ and $O(\varepsilon)$. This leads to the approximated RDE representation, which is applied to obtain the approximated NE as well as the approximated game value with order of $O(\sqrt{\varepsilon })$. Numerical simulation results of the full-order RDE and the reduced-order Riccati equations are presented to show the approximation performance with respect to $\varepsilon \in (0,1)$ as well as the risk-averse index $\mu > 0$.
This paper addresses the state estimation problem for networked systems incorporating intelligent reflecting surfaces (IRSs), a widely adopted technology for enhancing communication quality. A mathematical model is established to characterize the improvement of signal quality by IRSs, where the signal-to-noise ratio (SNR) is employed as the performance metric. The designable phase shifts of the IRS are explicitly formulated as tunable parameters. In consideration of the digital communication features, the influence of channel noises that induce data distortion is modeled as probabilistic bit flips, with the corresponding probability being dependent on the SNR. The consequent impact of data distortion on state estimation performance is subsequently analyzed. To improve estimation accuracy, an IRS-parameter-dependent estimator gain design is carried out within the linear minimal mean-square error estimation framework. An optimization problem is then formulated to devise the IRS parameters. To alleviate the computational complexity, a Differential-Evolution-based algorithm is developed. The effectiveness of the proposed method is finally validated through numerical simulations.
