Control of global variables for identical and non-identical Josephson junctions arrays

In the paper a way to solve an LQ-problem for a Josephson junction array with a common LRC-load is proposed. The cases of identical and non-identical Josephson junctions are considered. The solution ensures phase stabilization of Josephson current in every junction. The results are obtained using computer simulation in Jupyter Notebook and MATLAB.

Optimal control for controllable stochastic linear systems

This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of stochastic linear systems is studied. Then the optimal control is explicitly obtained by considering a parameterized unconstrained backward LQ problem and an optimal parameter selection problem. A notable feature of our results is that, instead of solving an equation involving derivatives with respect to the parameter, the optimal parameter is characterized by a matrix equation.

Feedback Game-Based Shared Control Scheme Design for Emergency Collision Avoidance: A Fuzzy-Linear Quadratic Regulator Approach

Driver-machine shared control scheme opens up a new frontier for the design of driver assistance system, especially for improving active safety in emergency scenario. However, the driver's stress response to steering assistance and strong tire nonlinearity are main challenges suffered by controller designing for collision avoidance. These unfavorable factors are particularly pronounced during emergency steering maneuvers and sharply degrade shared control performance. This paper proposes a fuzzy-linear quadratic regulator (LQR) game-based control scheme to simultaneously enhance vehicle stability while compensating driver's inappropriate steering reaction in emergency avoidance. A piecewise linear-based Takagi–Sugeno (T–S) fuzzy structure is presented to mimic driver's knowledge about vehicle lateral nonlinearity, and the control authority is shared between driver and emergency steering assistance (ESA) system through steer-by-wire (SBW) assembly. An identical piecewise internal model is chosen for ESA and the shared lane-keeping problem is modeled as a fuzzy linear quadratic (LQ) problem, where the symmetrical fuzzy structure further enhances vehicle's ability to handle extreme driving conditions. In particular, the feedback Stackelberg equilibrium solutions of the fuzzy-LQ problem are derived to describe the interactive steering behavior of both agents, which enables the ESA to compensate driver's irrational steering reaction. Hardware-in-the-loop (HIL) experiment demonstrates the ESA's capability in compensating driver's aggressive steering behavior, as well as the copiloting system's excellent tracking and stabilizing performance in emergency collision avoidance.