Unit Sliding Mode Control for Disturbed Crowd Dynamics System Based on Integral Barrier Lyapunov Function

Abstract

This paper presents a new tracking controller for a crowd dynamics system. The crowd dynamics are described by a continuum model in the macro-scale. An appropriate control variable is chosen to solve the problem of the multi-directionality of crowd movement. In order to stabilize the state density of the disturbed crowd dynamics system at a given reference density, a unit sliding mode controller based on the integral barrier Lyapunov function is designed, and the reaching law approach is used to avoid chattering. By ensuring the boundedness of the integral barrier Lyapunov function in the closed-loop, the global constraints of the system state variables are obtained. The design of the controller and the stability analysis of the closed-loop system are all done in the distributed parameter system. A numerical example illustrates the utility of the proposed controller. INDEX TERMS Integral barrier Lyapunov function, unit sliding mode control, tracking control, disturbed crowd dynamics system, distributed parameter system.

A reinforcement learning‐based approach for near‐optimal sliding‐mode control of output‐constrained uncertain nonlinear systems

“…It is worth noting that, since the control inputs are limited by the actuator saturation constraints, instability can occur as a result of choosing large values for the sliding coefficients. In order to find the near-optimal values of 𝝀 subject to constraints (8), the barrier Lyapunov functions theorem is employed to define the cost function according to Definition 1.…”

“…In this section, the adaptive fuzzy SMC is designed for nonlinear system (1) subject to constraints (8). Section 3.1 introduces the auxiliary control input for transforming nonsquare system (1) into a fully-actuated MIMO nonlinear system.…”

“…For instance, sliding-mode control (SMC), a nonlinear control method valued for its properties of robustness versus relevant classes of uncertainties, 3,4 has been coupled with barrier functions to provide barrier function-based SMC approaches capable of controlling state constrained dynamical systems. [5][6][7][8] A barrier Lyapunov function tends to infinity as its arguments approach predefined limits, so that by ensuring the boundedness of the barrier Lyapunov function, some state constraints can be satisfied. Since upper bounds of uncertainties are in general not known or are difficult to obtain, BLF-based adaptive sliding-mode control schemes have been developed to control nonlinear systems subject to state constraints.…”

Fixed Settling Time Control for Self-Driving Car: Two-Timescales Approach

“…Furthermore, finite-time trajectory tracking control of an output-constrained quadrotor with sliding mode control is presented in [49]. Similar methodology is used in applications like hypersonic flight vehicles, robot manipulators, and distributed crowd dynamics [57], [58]. Extending these approaches, BLF can be used in conjunction with SMC to guarantee fixed time stability under the output constraint.…”

Finite-Time Trajectory Tracking Control of Output-Constrained Uncertain Quadrotor

“…There is no significant work on the application of SMC in conjunction with BLF on MUAVs. Though this methodology is developed in [31,32] and has been used on applications like robotic manipulators [31], fuel cell [32], distributed crowd dynamics [33], and hypersonic flight vehicles [34], etc.…”