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Turing's model has been widely used to explain how simple, uniform structures can give rise to complex, patterned structures during the development of organisms. However, it is very hard to establish rigorous theoretical results for the dynamic evolution behavior of Turing's model since it is described by nonlinear partial differential equations. We focus on controllability of Turing's model by linearization and spatial discretization. This linearized model is a networked system whose agents are second order linear systems and these agents interact with each other by Laplacian dynamics on a graph. A control signal can be added to agents of choice. Under mild conditions on the parameters of the linearized Turing's model, we prove the equivalence between controllability of the linearized Turing's model and controllability of a Laplace dynamic system with agents of first order dynamics. When the graph is a grid graph or a cylinder grid graph, we then give precisely the minimal number of control nodes and a corresponding control node set such that the Laplace dynamic systems on these graphs with agents of first order dynamics are controllable., Comment: 13 pages, 4 figures, submitted to automatica

This paper studies a system security problem in the context of observability based on a two-party non-cooperative asynchronous dynamic game. A system is assumed to be secure if it is not observable. Both the defender and the attacker have means to modify dimension of the unobservable subspace, which is set as the value function. Utilizing tools from geometric control, we construct the best response set under one-step or two-step optimality to minimize or maximize the value function. We find that the best response sets under one-step optimality are not single-valued maps, resulting in a variety of game outcomes. In the dynamic game considering two-step optimality, definition and existence conditions of lock and oscillation game modes are given. Finally, the best response under two-step optimality and the Stackelberg game equilibrium are compared.

In this paper, a fixed-time safe control problem is investigated for an uncertain high-order nonlinear pure-feedback system with state constraints. A new nonlinear transformation function is firstly proposed to handle both the constrained and unconstrained cases in a unified way. Further, a radial basis function neural network is constructed to approximate the unknown dynamics in the system and a fixed-time dynamic surface control (FDSC) technique is developed to facilitate the fixed-time control design for the uncertain high-order pure-feedback system. Combined with the proposed unified transformation function and the FDSC technique, an adaptive fixed-time control strategy is proposed to guarantee the fixed-time tracking. The proposed fixed-time control strategy can guarantee uniform control structure when addressing both constrained and unconstrained situations. Numerical examples are presented to demonstrate the proposed fixed-time tracking control strategy.

This paper studies a dynamical system that models the free recall dynamics of working memory. This model is a modular neural network with n modules, named hypercolumns, and each module consists of m minicolumns. Under mild conditions on the connection weights between minicolumns, we investigate the long-term evolution behavior of the model, namely the existence and stability of equilibriums and limit cycles. We also give a critical value in which Hopf bifurcation happens. Finally, we give a sufficient condition under which this model has a globally asymptotically stable equilibrium with synchronized minicolumn states in each hypercolumn, which implies that in this case recalling is impossible. Numerical simulations are provided to illustrate our theoretical results. A numerical example we give suggests that patterns can be stored in not only equilibriums and limit cycles, but also strange attractors (or chaos).

In unsupervised domain adaptive (UDA) semantic segmentation, the distillation based methods are currently dominant in performance. However, the distillation technique requires complicate multi-stage process and many training tricks. In this paper, we propose a simple yet effective method that can achieve competitive performance to the advanced distillation methods. Our core idea is to fully explore the target-domain information from the views of boundaries and features. First, we propose a novel mix-up strategy to generate high-quality target-domain boundaries with ground-truth labels. Different from the source-domain boundaries in previous works, we select the high-confidence target-domain areas and then paste them to the source-domain images. Such a strategy can generate the object boundaries in target domain (edge of target-domain object areas) with the correct labels. Consequently, the boundary information of target domain can be effectively captured by learning on the mixed-up samples. Second, we design a multi-level contrastive loss to improve the representation of target-domain data, including pixel-level and prototype-level contrastive learning. By combining two proposed methods, more discriminative features can be extracted and hard object boundaries can be better addressed for the target domain. The experimental results on two commonly adopted benchmarks (\textit{i.e.}, GTA5 $\rightarrow$ Cityscapes and SYNTHIA $\rightarrow$ Cityscapes) show that our method achieves competitive performance to complicated distillation methods. Notably, for the SYNTHIA$\rightarrow$ Cityscapes scenario, our method achieves the state-of-the-art performance with $57.8\%$ mIoU and $64.6\%$ mIoU on 16 classes and 13 classes. Code is available at https://github.com/ljjcoder/EHTDI.

The goal of Inverse Optimal Control (IOC) is to identify the underlying objective function based on observed optimal trajectories. It provides a powerful framework to model expert's behavior, and a data-driven way to design an objective function so that the induced optimal control is adapted to a contextual environment. In this paper, we design an IOC algorithm for linear-quadratic tracking problems with random time horizon, and prove the statistical consistency of the algorithm. More specifically, the proposed estimator is the solution to a convex optimization problem, which means that the estimator does not suffer from local minima. This enables the proven statistical consistency to actually be achieved in practice. The algorithm is also verified on simulated data as well as data from a real world experiment, both in the setting of identifying the objective function of human tracking locomotion. The statistical consistency is illustrated on the synthetic data set, and the experimental results on the real data shows that we can get a good prediction on human tracking locomotion based on estimating the objective function. It shows that the theory and the model have a good performance in real practice. Moreover, the identified model can be used as a control target in personalized rehabilitation robot controller design, since the identified objective function describes personal habit and preferences.

In this paper, the credit scoring problem is studied by incorporating networked information, where the advantages of such incorporation are investigated theoretically in two scenarios. Firstly, a Bayesian optimal filter is proposed to provide risk prediction for lenders assuming that published credit scores are estimated merely from structured financial data. Such prediction can then be used as a monitoring indicator for the risk management in lenders' future decisions. Secondly, a recursive Bayes estimator is further proposed to improve the precision of credit scoring by incorporating the dynamic interaction topology of clients. It is shown that under the proposed evolution framework, the designed estimator has a higher precision than any efficient estimator, and the mean square errors are strictly smaller than the Cram\'er-Rao lower bound for clients within a certain range of scores. Finally, simulation results for a special case illustrate the feasibility and effectiveness of the proposed algorithms., Comment: 19 pages, simulations and discussion added, motivation clarified, references updated

In this paper, the problem of finite horizon inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observation of optimal control sequences. We propose the first complete result of the necessary and sufficient condition for the existence of corresponding LQ cost functions. Under feasible cases, the analytic expression of the whole solution space is derived and the equivalence of weighting matrices in LQ problems is discussed. For infeasible problems, an infinite dimensional convex problem is formulated to obtain a best-fit approximate solution with minimal control residual. And the optimality condition is solved under a static quadratic programming framework to facilitate the computation. Finally, numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed methods., Comment: 16 pages, 2 figures

In this paper, we consider the inverse optimal control problem for the discrete-time linear quadratic regulator, over finite-time horizons. Given observations of the optimal trajectories, and optimal control inputs, to a linear time-invariant system, the goal is to infer the parameters that define the quadratic cost function. The well-posedness of the inverse optimal control problem is first justified. In the noiseless case, when these observations are exact, we analyze the identifiability of the problem and provide sufficient conditions for uniqueness of the solution. In the noisy case, when the observations are corrupted by additive zero-mean noise, we formulate the problem as an optimization problem and prove the statistical consistency of the problem later. The performance of the proposed method is illustrated through numerical examples.