Event-Based Robust Control Techniques for Wheel-Based Robots Under Cyber-Attack and Dynamic Quantizer

Abstract

Nowadays, mobile robots are becoming an increasingly significant part of daily human life. Humanoid robots, wheeled mobile robots, aerial vehicles, mobile manipulators, and more are examples of mobile robots. As opposed to other robots, they are capable of moving autonomously, with sufficient intelligence to make decisions in response to the perceptions they receive from their environment. In today’s world, cooperative tasks and the ability to control robots via networks make them a component of cyber-physical systems (CPSs). In this study, mobile robots that are acting as a part of CPSs are examined. Data-network burden, signal quantizers, cyber security, delayed transition, and robust performance are some of the challenges they face. A total of three sections are then devoted to addressing these issues in detail. As a first step, the governing equation for mobile robots is explained, and then their robust and resilient behavior of them is examined by establishing the event-triggered adaptive optimal terminal sliding mode control (AOTSMC) approach for nonlinear uncertain dynamic systems that are subjected to denial-of-service (DoS) cyber attacks. In this case, it is assumed that the conveyed signal is being corrupted randomly by an attacker. In this situation, it is essential to design the closed-loop controller parameters in such a way that the performance can be maintained under malicious attacks while the communication resources are preserved. Due to the unrealistic nature of delayed-free communication, the stability analysis is conducted for a general form of uncertain nonlinear delayed input dynamic systems. The quantization effect on the closed-loop control system is then analyzed in conjunction with robust behavior and event-based data transmission. A novel criterion is established to adjust dynamic quantizers’ parameters according to the variation of event-triggering error, enabling the quantizer to be more accurate and facilitating implementation procedures. Finally, simulation results validate the presented methodology.

Appendix

Proof of Proposition 1. The assumptions made in (9), (11) indicate that system states obey Lipchitz continuity and do not exhibit any finite-escape time behavior. Meanwhile, due to the slow-varying dynamic of $x(t_{k}^{i})$ in the $t\in [{{t}_{k}},{{t}_{k+1}})$, and having stabilizable dynamic outside the region $\left\| E(t) \right\| \le \lambda \left\| x(t) \right\|$, then one can obtain

$$\begin{aligned} {{k}_{2}}{{\left\| \dot{S}(t) \right\| }}-{{k}_{2}}\Vert {{\dot{S}}^{pq^{-1}-1}}(t)\Vert {{\left\| ({{{\dot{S}}}^{2-pq^{-1}}}(t)-{{{\dot{S}}}^{2-pq^{-1}}}(t_{k}^{i})) \right\| }}\ge 0 . \end{aligned}$$

(119)

Now, suppose that x(t) diverges the maximum rate of within the minimum inter-sampling time period.

Now, it is supposed that x(t) diverges with its maximum rate, that would occur during a period when no control inputs are being applied to the system, i.e., $t\in [0,D)$. Then, from (66), (92), and Assumption 13 one can obtain

$$\begin{aligned} \varLambda <{{k}_{2}}{{\alpha }_{1}}\left\{ \bar{\alpha }+{{\left\| \varDelta f(x)+d(x,t) \right\| }}+{{\left\| {{x}_{d}}(t) \right\| }}+{{\left\| {{{\dot{x}}}_{d}}(t) \right\| }} \right\} .\end{aligned}$$

(120)