The optimal solution of a non-convex state-dependent LQR problem and its applications.

This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR) problem, in which the control penalty weighting matrix [Formula: see text] in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE) simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting [Formula: see text]. It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting [Formula: see text], in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions

The Values of Parameters in Simulation Case 01.

<p>*Diff. RE: .</p

Analysis of Chinese tilapia supply and demand without and with the COVID-19 epidemic impact

We analyzed the supply and demand for tilapia in China while assessing the future developmental trends. China has become the world’s largest producer, exporter, and consumer of tilapia. China entered a period of rapid aquaculture development in the 1990s, and the tilapia supply has increased yearly. Tilapia products are mainly supplied to the international market, especially the US. The global market for the Chinese tilapia has grown dramatically, but a downward trend occurred in 2019–2020. The Chinese domestic market demand is relatively stable, and even the COVID-19 epidemic did not significantly impact the supply and demand of tilapia. Internationally, it is expected that the demand for tilapia will decline considerably in the near future. However, this decline could be alleviated after the impact of the COVID-19 epidemic passes and increasing demand will resume. The increased supply of Chinese tilapia might slow down or even decrease due to market uncertainty, the increasing constraints on natural resources, and the Chinese government's requirements for high-quality aquaculture environments

Trajectories of <i> and </i>.

<p>Trajectories of <i> and </i>.</p

Three Goal Pursuit Behaviors: a) Control Energy Penalty R vs. Time; b) Control Energy Penalty R vs. Goal Discrepancy x; c) Feedback Gain K; d) Goal Discrepancy x; e) Control Effort u vs. Time; f) Control Effort u vs. Goal Discrepancy x.

<p>Three Goal Pursuit Behaviors: a) Control Energy Penalty R vs. Time; b) Control Energy Penalty R vs. Goal Discrepancy x; c) Feedback Gain K; d) Goal Discrepancy x; e) Control Effort u vs. Time; f) Control Effort u vs. Goal Discrepancy x.</p

The Values of Parameters in Simulation Case 02.

<p>The Values of Parameters in Simulation Case 02.</p

System Behavior of Simulation Case 01: a) Control Energy Penalty R vs. Goal Discrepancy x; b) Goal Discrepancy x.

<p>System Behavior of Simulation Case 01: a) Control Energy Penalty R vs. Goal Discrepancy x; b) Goal Discrepancy x.</p

Three Different Behaviors: GGB, SMB and CCB.

<p>Three Different Behaviors: GGB, SMB and CCB.</p