SDF‐based tracking control for state‐constrained nonholonomic systems with disturbances via relay switching control: Theory and experiment

Abstract

Summary This article investigates the tracking control problem for a kind of chained‐form nonholonomic systems in the presence of unknown time‐varying disturbances and full‐state constraints. First, a finite‐time tracking controller is constructed to drive the action of relay switching, which converts the whole control system into two design stages. In order to handle with the predefined asymmetric state constraints, the original tracking error system is turned into an unconstrained system on the basis of state‐dependent function (SDF) function transformations. In this framework, an adaptive tracking control strategy is proposed by means of backstepping and dynamic surface control. Correspondingly, another tracking control law is also constructed to assure the stability of the tracking error system before the action of switching. The theoretical analysis of stability indicates that the proposed tracking control scheme can guarantee that the output state tracking errors converge to zero and the desired state constraints are not violated. At the same time, all the closed‐loop system signals maintain bounded in entire control process. Finally, the validity of the presented tracking control algorithm is demonstrated by simulation and experiment results.

Tracking control of chained non‐holonomic systems with asymmetric function constraints and external disturbance

“…where (x a , y a ) is the position of the centre of mass on the plane, 𝜃 a is the forward angle of the robot, v a is the forward velocity, and 𝜔 a is the angular velocity of the robot, and 𝜀 is a small bias in orientation. The kinematic model with disturbance is likewise presented as follows in reference [32]:…”

“…Proof. The proof process refers to [32]. It can be seen from ( 15) that V0 ≤ 0, thus V 0 (t ) ≤ V 0 (0).…”

Finite‐time tracking control of disturbed non‐holonomic systems with input saturation and state constraints: Theory and experiment

“…By combining BLF and relay switching technology, the designed tracking controller guarantees that the tracking error states converge to a bounded set within a finite time. Different from the obtained results about nonholonomic systems with state constraints in [17,23], the article also considers input constraints. A constructively designed saturated state feedback is proposed and a new auxiliary design system is developed to reduce the risk of input saturation.…”

“…System state constraints and input saturation are ubiquitous due to restrictions and interference from various environments in the mechanical systems [14]. Up to now, the mainstream approaches for solving state constraint problems include model prediction [15,16], barrier Lyapunov function (BLF) [17][18][19][20] and state-dependent functions (SDF) [21][22][23]. The BLF is the most common method for dealing with state constraints, whose core idea is to construct suitable log-type BLF [17,18], integraltype BLF [24] or tan-type BLF [25] to ensure that limits are never violated.…”

Tracking controller of extended chained nonholonomic systems with matched disturbance and input saturation

“…Furthermore, [22] initially examined the finite-time trajectory tracking control of chained nonholonomic systems with full-state constraints, ensuring that the system state could achieve the desired tracking performance within a finite time. Meanwhile, [23,24] also concentrated on the tracking control of state-constrained nonholonomic systems through relay switching method. These control techniques offer beneficial tactics for handling nonholonomic systems subject to external disturbances, enhancing control efficiency, precision, and durability.…”