A Discrete-Time Event-Driven Near-Optimal Second-Order SMC for Multirobotic System Formation Prone to Network Uncertainties.

In this article, we propose a novel stochastic event-driven near-optimal sliding-mode controller design for addressing the consensus of a multiagent system in a network. The system is prone to external disturbances and network uncertainties, such as losses and delays of data packets. The randomness of network uncertainties introduces stochasticity in the system. The design starts with the formulation of control-affine dynamics based on a single integrator robot model, formation error, and sliding surface dynamics. An event-triggering condition is then derived for an update of control input for each agent. These input updates guarantee desired consensus in finite time with reaching time of each agent's sliding surface having an upper bound. The admissibility of event-driven near-optimal control updates is also ensured for each agent. The near-optimal control design for each agent has achieved through neural-network-based actor-critic architecture. The implementation of Pioneer P3-DX mobile robots illustrates threefold efficacy of the proposed design: 1) advantages of event-driven approach and higher order sliding mode controller; 2) robustness to network uncertainties; and 3) near-optimality in system performance.

Online Nash Solution in Networked Multirobot Formation Using Stochastic Near-Optimal Control Under Dynamic Events.

This article proposes an online stochastic dynamic event-based near-optimal controller for formation in the networked multirobot system. The system is prone to network uncertainties, such as packet loss and transmission delay, that introduce stochasticity in the system. The multirobot formation problem poses a nonzero-sum game scenario. The near-optimal control inputs/policies based on proposed event-based methodology attain a Nash equilibrium achieving the desired formation in the system. These policies are generated online only at events using actor-critic neural network architecture whose weights are updated too at the same instants. The approach ensures system stability by deriving the ultimate boundedness of estimation errors of actor-critic weights and the event-based closed-loop formation error. The efficacy of the proposed approach has been validated in real-time using three Pioneer P3-Dx mobile robots in a multirobot framework. The control update instants are minimized to as low as 20% and 18% for the two follower robots.

Uncertainty Compensator and Fault Estimator-Based Exponential Supertwisting Sliding-Mode Controller for a Mobile Robot.

This work proposes a novel event-triggered exponential supertwisting algorithm (ESTA) for path tracking of a mobile robot. The proposed work is divided into three parts. In the first part, a fractional-order sliding surface-based exponential supertwisting event-triggered controller has been proposed. Fractional-order sliding surface improves the transient response, and the exponential supertwisting reaching law reduces the reaching phase time and eliminates the chattering. The event-triggering condition is derived using the Lipschitz method for minimum actuator utilization, and the interexecution time between two events is derived. In the second part, a fault estimator is designed to estimate the actuator fault using the Lyapunov stability theory. Furthermore, it is shown that in the presence of matched and unmatched uncertainty, event-trigger-based controller performance degrades. Hence, in the third part, an integral sliding-mode controller (ISMC) has been clubbed with the event-trigger ESTA for filtering of the uncertainties. It is also shown that when fault estimator-based ESTA is clubbed with ISMC, then the robustness of the controller increases, and the tracking performance improves. This novel technique is robust toward uncertainty and fault, offers finite-time convergence, reduces chattering, and offers minimum resource utilization. Simulations and experimental studies are carried out to validate the advantages of the proposed controller over the existing methods.