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In this paper, we propose a method for estimating the algebraic Riccati equation (ARE) with respect to an unknown discrete-time system from the system state and input observation. The inverse optimal control (IOC) problem asks, ``What objective function is optimized by a given control system?'' The inverse linear quadratic regulator (ILQR) problem is an IOC problem that assumes a linear system and quadratic objective function. The ILQR problem can be solved by solving a linear matrix inequality that contains the ARE. However, the system model is required to obtain the ARE, and it is often unknown in fields in which the IOC problem occurs, for example, biological system analysis. Our method directly estimates the ARE from the observation data without identifying the system. This feature enables us to economize the observation data using prior information about the objective function. We provide a data condition that is sufficient for our method to estimate the ARE. We conducted a numerical experiment to demonstrate that our method can estimate the ARE with less data than system identification if the prior information is sufficient.

Chemical AI is chemically synthesized artificial intelligence that has the ability of learning in addition to information processing. A research project on chemical AI, called the Molecular Cybernetics Project, was launched in Japan in 2021 with the goal of creating a molecular machine that can learn a type of conditioned reflex through the process called classical conditioning. If the project succeeds in developing such a molecular machine, the next step would be to configure a network of such machines to realize more complex functions. With this motivation, this paper develops a method for learning a desired function in the network of nodes each of which can implement classical conditioning. First, we present a model of classical conditioning, which is called here a classical conditioning gate. We then propose a learning algorithm for the network of classical conditioning gates., Comment: submitted to New Generation Computing

This paper focuses on proposing a general control framework for large-scale Boolean networks (\texttt{BNs}). Only by the network structure, the concept of structural controllability for \texttt{BNs} is formalized. A necessary and sufficient criterion is derived for the structural controllability of \texttt{BNs}; it can be verified with $\Theta(n^2)$ time, where $n$ is the number of network nodes. An interesting conclusion is shown as that a \texttt{BN} is structurally controllable if and only if it is structurally fixed-time controllable. Afterwards, the minimum node control problem with respect to structural controllability is proved to be NP-hard for structural \texttt{BNs}. In virtue of the structurally controllable criterion, three difficult control issues can be efficiently addressed and accompanied with some advantages. In terms of the design of pinning controllers to generate a controllable \texttt{BN}, by utilizing the structurally controllable criterion, the selection procedure for the pinning node set is developed for the first time instead of just checking the controllability under the given pinning control form; the pinning controller is of distributed form, and the time complexity is $\Theta(n2^{3d^{\ast}}+2(n+m)^2)$, where $m$ and $d^\ast$ are respectively the number of generators and the maximum vertex in-degree. With regard to the control design for stabilization in probability of probabilistic \texttt{BNs} (\texttt{PBNs}), an important theorem is proved to reveal the equivalence between several types of stability. The existing difficulties on the stabilization in probability are then solved to some extent via the structurally controllable criterion.

The present paper proposes a novel broadcast control (BC) law for multi-agent coordination. A BC framework has been developed to achieve global coordination tasks with low communication volume. The BC law uses broadcast communication, which transmits an identical signal to all agents indiscriminately without any agent-to-agent communication. Unfortunately, all of the agents are required to take numerous random actions because the BC law is based on stochastic optimization. Such random actions degrade the control performance for coordination tasks and may invoke dangerous situations. In order to overcome these drawbacks, the present paper proposes the pseudo-perturbation-based broadcast control (PBC) law, which introduces multiple virtual random actions instead of the single physical action of the BC law. The following advantages of the PBC law are theoretically proven. The PBC law achieves coordination tasks asymptotically with probability 1. Compared with the BC law, unavailing actions are reduced and agents' states converge at least twice as fast. Increasing the number of multiple actions further improves the control performance because averaging multiple actions reduces unavailing randomness. Numerical simulations demonstrate that the PBC improves the control performance as compared with the BC law., Comment: 14 pages, 4 figures