This article presents a unified framework for dynamics modeling and control design using deep learning, focusing on incorporating prior side information on stabilizability. Control theory provides systematic techniques for designing feedback systems while ensuring fundamental properties such as stabilizability, which are crucial for practical control applications. However, conventional data-driven approaches often overlook or struggle to explicitly incorporate such control properties into learned models. To address this, we introduce a novel neural network (NN)-based approach that concurrently learns the system dynamics, a stabilizing feedback controller, and a Lyapunov function for the closed-loop system, thus explicitly guaranteeing stabilizability in the learned model. Our proposed deep learning framework is versatile and applicable across a wide range of control problems, including safety control, $L_{2}$ -gain control, passivation, and solutions to Hamilton-Jacobi inequalities. By embedding stabilizability as a core property within the learning process, our method allows for the development of learned models that are not only data-driven but also grounded in control-theoretic guarantees, greatly enhancing their utility in real-world control applications. This article includes examples that demonstrate the effectiveness of this approach, showcasing the stability and control performance improvements achieved in various control scenarios. The methods proposed in this article can be easily applied to modeling without control design. The code has been open-sourced and is available at https://github.com/kashctrl/Deep_Stabilizable_Models.

This paper introduces the risk-sensitive control as inference (RCaI) that extends CaI by using Rényi divergence variational inference. RCaI is shown to be equivalent to log-probability regularized risk-sensitive control, which is an extension of the maximum entropy (MaxEnt) control. We also prove that the risk-sensitive optimal policy can be obtained by solving a soft Bellman equation, which reveals several equivalences between RCaI, MaxEnt control, the optimal posterior for CaI, and linearly-solvable control. Moreover, based on RCaI, we derive the risk-sensitive reinforcement learning (RL) methods: the policy gradient and the soft actor-critic. As the risk-sensitivity parameter vanishes, we recover the risk-neutral CaI and RL, which means that RCaI is a unifying framework. Furthermore, we give another risk-sensitive generalization of the MaxEnt control using Rényi entropy regularization. We show that in both of our extensions, the optimal policies have the same structure even though the derivations are very different.

Self-organizing systems are focused on to realize novel network control systems that are highly scalable, adaptable, and robust. However, the uncertainty of information makes it difficult for self-organizing systems to work appropriately, thereby degrading their performance. It is necessary to improve the performance of self-organizing systems while retaining their advantages. Therefore, we apply the concept of flexible leadership of the collective decision-making in human groups to self-organizing control mechanisms. By incorporating this concept, agents dynamically and flexibly change their role (leader or follower) according to the confidence of their own information, which increases decision accuracy under information uncertainty. We propose a channel-selection mechanism based on collective decision-making in accordance with information confidence. Simulation experiments show that the proposed mechanism improves the performance of network systems while retaining the high adaptability.

Self-organization has the potential for high scalability, adaptability, flexibility, and robustness, which are vital features for realizing future networks. The convergence of self-organizing control, however, is slow in some practical applications in comparison with control by conventional deterministic systems using global information. It is therefore important to facilitate the convergence of self-organizing controls. Incontrolled self-organization, which introduces an external controller into self-organizing systems, the network is controlled to guide systems to a desired state. Although existing controlled self-organization schemes could achieve the same state, it is difficult for an external controller to collect information about the network and to provide control inputs to the network, especially when the network size is large. This is because the computational cost for designing the external controller and for calculating the control inputs increases rapidly as the number of nodes in the network becomes large. Therefore, we partition a network into several sub-networks and introduce two types of controllers, a central controller and several sub-controllers that control the network in a hierarchical manner. In this study, we propose a hierarchical optimal feedback mechanism for self-organizing systems and apply this mechanism to potential-based self-organizing routing. Simulation results show that the proposed mechanism improves the convergence speed of potential-field construction (i.e., route construction) up to 10.6-fold with low computational and communication costs.

Because of the rapid growth in the scale and complexity of information networks, self-organizing systems are increasingly being used to realize novel network control systems that are highly scalable, adaptable, and robust. However, the uncertainty of information (with regard to incompleteness, vagueness, and dynamics) in self-organizing systems makes it difficult for them to work appropriately in accordance with the network state. In this study, we apply a model of the collective decision-making of animal groups to enable self-organizing control mechanisms to adapt to information uncertainty. Specifically, we apply a mathematical model of collective decision-making that is known as the effective leadership model (ELM). In the ELM, informed individuals (those who are experienced or well-informed) take the role of leading the others. In contrast, uninformed individuals (those who perceive only local information) follow neighboring individuals. As a result of the collective behavior of informed/uninformed individuals, the animal group achieves consensus. We consider a self-organizing control mechanism using potential-based routing with an optimal control, and propose a mechanism for determining a data-packet forwarding scheme based on the ELM. Through evaluation by simulation, we show that, in a situation in which the perceived information is incomplete and dynamic, nodes can forward data packets in accordance with the network state by applying the ELM.

Due to the rapid growth in scale and complexity of information networks, self-organizing systems have been focused on for realizing new network control architectures that have high scalability, adaptability, and robustness. However, in self-organizing systems, the uncertainty (incompleteness, ambiguity, and dynamicity) of information observable for components in the system can lead to the slow adaptation to environmental changes and the lack of a global optimality, which complicates a practical use of self-organizing systems in industrial and business fields. In this study, we adopt the principle of collective decision making, in which a coordinated decision in a group is achieved through local interactions of components, in order to realize a network control mechanism adaptable to such information uncertainty. Specifically, we apply Effective Leadership model, which is a mathematical model of collective decision making, to a self-organizing control mechanism. In Effective Leadership model, there are two types of individuals, informed and non-informed ones, and collective decision is achieved through local interaction of them. Through simulation experiments, we reveal the advantages and characteristics of the network control mechanism based on Effective Leadership model.

Abstract This paper proposes a novel shadow removal technique for cooperative projection system based on spatiotemporal prediction. In our previous work, we proposed a distributed feedback algorithm, which is implementable in cooperative projection environments subject to data transfer constraints between components. A weakness of this scheme is that the compensation is conducted in each pixel independently. As a result, spatiotemporal information of the environmental change cannot be utilized even if it is available. In view of this, we specifically investigate the situation where some of the projectors are occluded by a moving object whose one‐frame‐ahead behaviour is predictable. In order to remove the resulting shadow, we propose a novel error propagating scheme that is still implementable in a distributed manner and enables us to incorporate the prediction information of the obstacle. It is demonstrated theoretically and experimentally that the proposed method significantly improves the shadow removal performance in comparison to the previous work.

Self-organization has potential for high scalability, adaptability, flexibility, and robustness, which are vital features for realizing future networks. Convergence of self-organizing control, however, is slow in some practical applications compared to control with conventional deterministic systems using global information. It is therefore important to facilitate convergence of self-organizing controls. In controlled self-organization, which introduces an external controller into self-organizing systems, the network is controlled to guide systems to a desired state. Although existing controlled self-organization schemes could achieve this feature, convergence speed for reaching an optimal or semioptimal solution is still a challenging task. We perform potential-based self-organizing routing and propose an optimal feedback method using a reduced-order model for faster convergence at low cost. Simulation results show that the proposed mechanism improves the convergence speed of potential-field construction (i.e., route construction) by at most 22.6 times with low computational and communication cost.

Self-organization has potential for high scalability, adaptability, flexibility, and robustness, which are vital features for realizing future networks. Convergence of self-organizing control, however, is comparatively slow in some practical applications. It is therefore important to enhance convergence of self-organizing controls without sacrificing the above advantages. Controlled self-organization is one key idea for that, which introduces an external controller into self-organizing systems to guide them to a desired state. We previously designed an external controller that provided the optimal input for fast convergence, however, it suffered from scalability issues. In this paper, we propose a hierarchical control system where a network is partitioned into some sub-networks, sub-controllers manage respective sub-networks, and the top-level deals with the global network stability. The proposed system achieves fast convergence speed with low computational and communication cost.

This paper proposes a novel radiometric compensation technique for cooperative projection system based-on distributed optimization. To achieve high scalability and robustness, we assume cooperative projection environments such that 1. each projector does not have information about other projectors as well as target images, 2. the camera does not have information about the projectors either, while having the target images, and 3. only a broadcast communication from the camera to the projectors is allowed to suppress the data transfer bandwidth. To this end, we first investigate a distributed optimization based feedback mechanism that is suitable for the required decentralized information processing environment. Next, we show that this mechanism works well for still image projection, however not necessary for moving images due to the lack of dynamic responsiveness. To overcome this issue, we propose to implement an additional feedforward mechanism. Such a 2 Degree Of Freedom (2-DOF) control structure is well-known in control engineering community as a typical method to enhance not only disturbance rejection but also reference tracking capability, simultaneously. We theoretically guarantee and experimentally demonstrate that this 2-DOF structure yields the moving image projection accuracy that is overwhelming the best achievable performance only by the distributed optimization mechanisms.

To tackle with problems emerging with rapid growth of information networks in scale and complexity, selforganization is one of promising design principles for future networks. Convergence of self-organizing controls, however, is pointed out to be comparatively slow in some practical applications. Therefore, it is important to reveal and enhance convergence of self-organizing controls. In controlled self-organization, which introduces an external observer/controller into self-organizing systems, systems are controlled in order to guide them to the desired state. Although previous controlled self-organization schemes could achieve this feature, convergence speed for reaching an optimal or a semi-optimal solution is still a challenging task. In this paper, we take potential-based self-organizing routing and provide an optimal feedback for faster convergence using the future state of the system. Simulation results show that the convergence speed of potentials is improved by 7.3 times with a proposed mechanism.

A lot of oscillatory phenomena exist in the natural world. In recent years, many of them have been found to play a crucial role in living organisms such as the circadian rhythms, neural networks, to list a few. This fact has prompted enormous theoretical research works on modeling/analysis of oscillatory phenomena. Among them, large scale arrays consisting of simple subsystems have drawn an intensive attention due to academic interest and also the similarity to actual cell models. In our work, we concentrate on the linearly coupled networks that have interesting applications such as Josephson junction networks. In general, the nonlinearity of the dynamics is indispensable for the occurrence of such phenomena. In this paper, we formulate the nonlinear individual subsystems within the framework of piecewise affine (PWA) systems, for which several practical analysis tools have been proposed. In summary, the overall dynamics is given as linearly coupled (a large number of) PWA systems. In this paper, we derive a sufficient condition under which the dynamics is Y-oscillatory. The Y-oscillation, originally introduced by Yakubovich, is a general notion of oscillatory phenomena that covers both periodic and aperiodic orbits. However, it is known that the analysis of PWA systems become more difficult to analyze as the number of modes increases, similarly to other switching systems. The main result is achieved by proving the well-posedness and ultimate boundedness. An important feature of the result is that, under the assumption that every subsystem has a property in common, the criteria can be rewritten in terms of connection topology and its complexity is considerably reduced so that it is applicable to large scale networks. For illustrative purpose, we analyze Fitzhugh-Nagumo equation that is a model for neural oscillator with the excitation property in mathematical physiology.

Discrete wavelet transform is usually executed by the so-called pyramid algorithm. It, however, requires a proper initialization, i.e., expansion coefficients with respect to the basis of one of the desired approximation subspaces. An interesting question here is how we can obtain such coefficients when only sampled values of signals are available. This letter provides a design method for a digital filter that (sub-)optimally gives such coefficients assuming certain a priori knowledge on the frequency characteristic of target functions. We then extend the result to the case of nonorthogonal wavelets. Examples show the effectiveness of the proposed method.