Resilient H∞ State Estimation for Discrete-Time Stochastic Delayed Memristive Neural Networks: A Dynamic Event-Triggered Mechanism.

In this article, a resilient H∞ approach is put forward to deal with the state estimation problem for a type of discrete-time delayed memristive neural networks (MNNs) subject to stochastic disturbances (SDs) and dynamic event-triggered mechanism (ETM). The dynamic ETM is utilized to mitigate unnecessary resource consumption occurring in the sensor-to-estimator communication channel. To guarantee resilience against possible realization errors, the estimator gain is permitted to undergo some norm-bounded parameter drifts. For the delayed MNNs, our aim is to devise an event-based resilient H∞ estimator that not only resists gain variations and SDs but also ensures the exponential mean-square stability of the resulting estimation error system with a guaranteed disturbance attenuation level. By resorting to the stochastic analysis technique, sufficient conditions are acquired for the expected estimator and, subsequently, estimator gains are obtained via figuring out a convex optimization problem. The validity of the H∞ estimator is finally shown via a numerical example.

Agent's Optimal Compensation Under Inflation Risk by Using Dynamic Contract Model.

This paper studies the problem of principal-agent with moral hazard in continuous time. The firm's cash flow is described by geometric Brownian motion (hereafter GBM). The agent affects the drift of the firm's cash flow by her hidden effort. Meanwhile, the firm rewards the agent with corresponding compensation and equity which depend on the output. The model extends dynamic optimal contract theory to an inflation environment. Firstly, the authors obtain the dynamic equation of the firm's real cash flow under inflation by using the Itô formula. Then, the authors use the martingale representation theorem to obtain agent's continuation value process. Moreover, the authors derive the Hamilton-Jacobi-Bellman (HJB) equation of investor's value process, from which the authors derive the investors' scaled value function by solving the second-order ordinary differential equation. Comparing with He[1], the authors find that inflation risk affects the agent's optimal compensation depending on the firm's position in the market.

H∞ and l2-l∞ state estimation for delayed memristive neural networks on finite horizon: The Round-Robin protocol.

In this paper, a protocol-based finite-horizon H∞ and l2-l∞ estimation approach is put forward to solve the state estimation problem for discrete-time memristive neural networks (MNNs) subject to time-varying delays and energy-bounded disturbances. The Round-Robin protocol is utilized to mitigate unnecessary network congestion occurring in the sensor-to-estimator communication channel. For the delayed MNNs, our aim is to devise an estimator that not only ensures a prescribed disturbance attenuation level over a finite time-horizon, but also keeps the peak value of the estimation error within a given range. By resorting to the Lyapunov-Krasovskii functional method, the delay-dependent criteria are formulated that guarantee the existence of the desired estimator. Subsequently, the estimator gains are obtained via figuring out a bank of convex optimization problems. The validity of our estimator is finally shown via a numerical example.

Delay-distribution-dependent state estimation for neural networks under stochastic communication protocol with uncertain transition probabilities.

In this paper, the protocol-based remote state estimation problem is considered for a kind of delayed artificial neural networks. The random time-varying delays fall into certain intervals with known probability distributions. For the sake of reducing the data collisions in communication channel from the sensors to the estimator, the stochastic communication protocol (SCP) is employed to decide which sensor is allowed to transmit its data to the remote estimator through the channel at each fixed instant. The scheduling principle of the SCP is governed by a Markov chain whose transition probability is allowed to be uncertain so as to reflect the possible imprecision when implementing the SCP. Through a combination of Lyapunov-Krasovskii functional method and the stochastic analysis technique, a sufficient criterion is obtained for the existence of the desired remote state estimator ensuring that the corresponding augmented estimation error dynamics is asymptotically stable with a prescribed H∞ performance index. Furthermore, the estimator parameter is acquired by solving a convex optimization problem. Finally, the validity of the established theoretical results is demonstrated via a numerical simulation example.