High-Order Sliding Mode Control for Networked Control System with Dynamic Noncooperative Game Scheduling

Specific to the NCSs where sensor signals can be processed centrally, a collaborative design scheme of dynamic game scheduling and advanced control theory was proposed in the present study. Firstly, by using the Jordan standard state space equation of the research object, the three elements of state noncooperative game were built, and the existence and uniqueness of Nash equilibrium solution were verified. In addition, the iterative equation of the scheduling matrix was derived by complying with the designed utility function. Secondly, refer to the number of restricted states the order of sliding mode was determined. And based on it, the corresponding sliding surface was designed. Subsequently, the quadratic optimization theory was adopted to regulate the control value following the implementation of the scheduling strategy to ensure that the control quality was further enhanced in the limited network service. Lastly, a TrueTime simulation example is established to verify the effectiveness of the proposed scheme.

Dynamic Equilibrium of Market Making with Price Competition

In this paper, we discuss the dynamic equilibrium of market making with price competition and incomplete information. The arrival of market sell/buy orders follows a pure jump process with intensity depending on bid/ask spreads among market makers and having a looping countermonotonic structure. We solve the problem with the nonzero-sum stochastic differential game approach and characterize the equilibrium value function with a coupled system of Hamilton–Jacobi nonlinear ordinary differential equations. We prove, do not assume a priori, that the generalized Issac’s condition is satisfied, which ensures the existence and uniqueness of Nash equilibrium. We also perform some numerical tests that show our model produces tighter bid/ask spreads than those derived using a benchmark model without price competition, which indicates the market liquidity would be enhanced in the presence of price competition of market makers.

SYSTEMIC RISK: THE EFFECT OF MARKET CONFIDENCE

In a crisis, when faced with insolvency, banks can sell stock in a dilutive offering in the stock market and borrow money in order to raise funds. We propose a simple model to find the maximum amount of new funds the banks can raise in these ways. To do this, we incorporate market confidence of the bank together with market confidence of all the other banks in the system into the overnight borrowing rate. Additionally, for a given cash shortfall, we find the optimal mix of borrowing and stock selling strategy. We show the existence and uniqueness of Nash equilibrium point for all these problems. Finally, using this model we investigate if banks have become safer since the crisis. We calibrate this model with market data and conduct an empirical study to assess safety of the financial system before, during after the last financial crisis.

Real-Time Pricing-Based Scheduling Strategy in Smart Grids: A Hierarchical Game Approach

This paper proposes a scheduling strategy based on real-time pricing in smart grids. A hierarchical game is employed to analyze the decision-making process of generators and consumers. We prove the existence and uniqueness of Nash equilibrium and utilize a backward induction method to obtain the generation and consumption strategies. Then, we propose two dynamic algorithms for the generators and consumers to search for the equilibrium in a distributed fashion. Simulation results demonstrate that the proposed scheduling strategy can match supply with demand and shift load away from peak time.