Research on Optimal Allocation of Water Resources Based on Large-Scale System Decomposition and Coordination Model

The construction of water resources optimal allocation model is the premise and foundation of solving and evaluating the optimal allocation model of water resources. The allocation of water resources includes not only the simple allocation of water resources, but also the protection of water resources and the analysis of the relationship between water supply and demand. Aiming at the problem of water shortage in the receiving area of water diversion from Hanjiang River to Weihe River, the large-scale system decomposition and coordination algorithm is used to optimally allocate the water use departments of each district of the water diversion area from Han to Wei River in Shaanxi Province, and establish the water diversion project from Han to Wei River. Optimal allocation model of water resources in the water receiving area. The results show that: in the 2030 planning level, the water supply of key cities, Xixian new district, medium/small cities, and industrial parks were 153.57, 368.16, 632.04, and 208.68 million m3, respectively, and the corresponding water shortage rate was 2.8%, 5.6%, 8.4%, 11.2%. The water supply sequence has a lower water shortage rate than the previous one, and the water shortage rate of the domestic water sector in key cities is only 1.2%. From the water shortage situation of various water departments in 2030, it can basically meet the water shortage of water receiving objects and effectively improve the water shortage in water receiving areas.

Direct and indirect transactions and requirements

The indirect transactions between sectors of an economic system has been a long-standing open problem. There have been numerous attempts to conceptually define and mathematically formulate this notion in various other scientific fields in literature as well. The existing direct and indirect effects formulations, however, can neither determine the direct and indirect transactions separately nor quantify these transactions between two individual sectors of interest in a multisectoral economic system. The novel concepts of the direct, indirect and transfer (total) transactions between any two sectors and associated demand distributions are introduced, and the corresponding requirements coefficients and matrices are systematically formulated relative to both final demands and gross outputs based on the system decomposition theory in the present manuscript. It is demonstrated theoretically and through illustrative examples that the proposed transactions and coefficients accurately define and correctly quantify the corresponding direct, indirect, and total interactions and relationships. The proposed requirements matrices for the US economy using aggregated input-output tables for multiple years are then presented and briefly analyzed.

Analytical synthesis of the pitch-invariant control of the helicopter longitudinal motion with invariance of a pitch angle

The control for the linearized model of the longitudinal motion fourth order for a single-rotor helicopter is analytically synthesized which ensures the invariance of the pitch angle in the presence of disturbances in the control channels, as well as the required the poles placement of the closed-loop system, given from the region of their stability. The results of the numerical synthesis control for the longitudinal motion of a single-rotor helicopter by using analytically synthesized laws of invariant control, which confirm the reliability of the analytical expressions are shown. Keywords invariance; disturbances in the control channels; MIMO-system; decomposition; pole placement; analytical synthesis; longitudinal motion of a single-rotor helicopter; poles of a dynamical system

Bridging the gap between safety and real-time performance in receding-horizon trajectory design for mobile robots

To operate with limited sensor horizons in unpredictable environments, autonomous robots use a receding-horizon strategy to plan trajectories, wherein they execute a short plan while creating the next plan. However, creating safe, dynamically feasible trajectories in real time is challenging, and planners must ensure persistent feasibility, meaning a new trajectory is always available before the previous one has finished executing. Existing approaches make a tradeoff between model complexity and planning speed, which can require sacrificing guarantees of safety and dynamic feasibility. This work presents the Reachability-based Trajectory Design (RTD) method for trajectory planning. RTD begins with an offline forward reachable set (FRS) computation of a robot’s motion when tracking parameterized trajectories; the FRS provably bounds tracking error. At runtime, the FRS is used to map obstacles to parameterized trajectories, allowing RTD to select a safe trajectory at every planning iteration. RTD prescribes an obstacle representation to ensure that obstacle constraints can be created and evaluated in real time while maintaining safety. Persistent feasibility is achieved by prescribing a minimum sensor horizon and a minimum duration for the planned trajectories. A system decomposition approach is used to improve the tractability of computing the FRS, allowing RTD to create more complex plans at runtime. RTD is compared in simulation with rapidly-exploring random trees and nonlinear model-predictive control. RTD is also demonstrated in randomly crafted environments on two hardware platforms: a differential-drive Segway and a car-like Rover. The proposed method is safe and persistently feasible across thousands of simulations and dozens of real-world hardware demos.

Multi-attribute optimization-based system decomposition considering several value chain stakeholder perspectives

The final architecture of a complex system reflect preferences of several value chain stakeholders on system attributes, also called “ilities”. Owing to differences in their individual roles and responsibilities, different stakeholders prefer different approaches to architect and decompose a system to optimize their attributes of interest. However, owing to increasing complexity of modern engineering systems, optimizing multiple attributes of complex systems has become challenging; moreover, very few researches have been published in this regard. Thus, to address this gap in available literature, this paper presents a multi-attribute optimization framework for complex system decomposition. The proposed framework primarily optimizes two attributes—system robustness (to the perspective of the stakeholder), and modularity—while system maintainability is considered an optimization constraint. Feasibility of the proposed framework has been demonstrated through a case study, wherein system attributes of three different mechanical clock models having different architectures were optimized.