In this article, a novel Lyapunov-based event-trigger mechanism is proposed to reduce the computation cost of model predictive control (MPC) algorithm for discrete-time nonlinear input-affine safety-critical systems. Unlike conventional approaches that require continuous error monitoring, the proposed mechanism leverages the predictive capability of MPC to determine triggering instants directly based on the evolution of the closed-loop Lyapunov function. Safety and stability are enforced by incorporating control barrier functions (CBFs) and control Lyapunov functions (CLFs) as constraints within the MPC optimization. Furthermore, the recursive feasibility of the proposed event-triggered MPC algorithm is rigorously analyzed, with special attention to the potential infeasibility caused by hard CBF constraints. Input-to-state practical stability (ISpS) of the resulting closed-loop system is also established. Simulation results demonstrate that the proposed event-triggered CBF-CLF-MPC algorithm effectively eliminates unnecessary controller updates, reducing computational consumption while maintaining tracking performance comparable to that of a conventional time-triggered MPC algorithm.

This paper presents an adaptive fuzzy tracking control protocol for a category of uncertain nonlinear multi-agent systems (MASs) subject to deception attacks and multiple constraints (time-varying asymmetry constraints on tracking error and system states). Fuzzy logic systems (FLSs) are employed to approximate the unknown nonlinear dynamics in MASs. Since deception attacks over the sensor network make the actual states of the MASs unavailable, this paper employs the compromised states for feedback control. Based on the relationship between the compromised states and actual states, the problem of satisfying the original state constraints boils down to the new constraints on compromised states. The use of a nonlinear mapping together with the dynamic surface control (DSC) strategy can ensure that the multiple constraints are solved with the constraint boundaries of system output being freely selected by the user, the feasibility requirement on the virtual controller is removed, and the computational explosion is mitigated. Under this control protocol, the tracking performance of MASs subject to deception attacks is achieved, while all constraints are not violated. Ultimately, simulation results verify the effectiveness and advantage of the developed control method.

In soft deformable terrain environments, the robot slips due to dynamic changes in wheel-ground contact, which poses a great challenge to the design of the driving torque of its motion control system. To solve the trajectory tracking control problem of wheeled mobile robots in soft deformation terrain, an event triggering mechanism based on wheel-ground mechanical parameters was designed, in which wheel-terrain mechanics has an important influence on the driving torque and is included in the control system design process. Aiming at the wheeled mobile robot in the working environment of soft ground, considering the rolling resistance of the wheel during its driving process, a dynamic model based on wheel-ground interaction is established. Estimation of unmodelled dynamic and rolling resistance terms for wheeled mobile robots in soft deformable terrain environments by adaptive neural networks. Based on the static event triggering strategy based on constant threshold, a hybrid threshold dynamic event triggering strategy based on rolling resistance is proposed. By proving that there is a positive lower bound on the inter-event time, which means that Zeno behavior is avoided. Meanwhile, the lower bound of inter-event time will change with the designed dynamic threshold. Finally, the good control performance of the proposed algorithm under different ground environments is verified by simulation. Note to Practitioners—With the advancement of detection tasks, the working environment of wheeled mobile robots has become increasingly complex. In the motion control of a wheeled mobile robot in a soft deformable terrain working environment, the influence of the robot ’s wheel-to-ground contact is crucial to the successful realization of the task. The existing wheeled mobile robot control methods for soft deformable terrain working environment usually ignores the influence between wheels and ground, which cannot meet the application requirements of this complex scene. Aiming at the problem of tracking control of wheeled mobile robots in soft deformable terrain working environment, this paper, the traction force change caused by wheel-ground contact mechanics is taken as the main factor of event-triggered mechanism, and the force feedback event-triggered tracking control method is designed. Theoretical algorithms and simulation results show that a trade-off between robot tracking performance and communication resources in different ground environments is realized.

In this paper, an adaptive neural network control algorithm based on event-triggered reinforcement learning is proposed for a four-wheel independent steering and four-wheel independent driving (4WS4WD) mobile robot. A kinematic model is established based on the kinematic relationship between the robot wheels and the body under the consideration of the effect of slip-turn perturbation. The dynamics model is established using the Lagrangian dynamics equations. An improved performance metric function is designed and approximated using the Critic neural network and the Actor neural network to approximate the unknown long-term performance metric function and controller respectively. A threshold band event triggering is proposed for reducing the consumption of communication and computational resources. It is rigorously demonstrated using Lyapunov analysis that both the neural network error and the system error are up to the final consistent bound. As well as proved that the proposed event-triggered mechanism can eliminate the Zeno phenomenon. Finally, comparative experiments demonstrated the effectiveness of the proposed algorithm.

In the soft deformable terrain environment, the running state of the wheeled mobile robot is easily affected by the complex wheel-ground interaction, which limits its running state variables and input torque. In this paper, the tracking control of wheeled mobile robot under soft deformable terrain is studied, and a dynamic event trigger mechanism is proposed. Based on the proposed trigger strategy, an adaptive event trigger optimal tracking control algorithm for wheeled mobile robot system with nonlinear constraints is designed. By analyzing the nonlinear constraint problem faced by the dynamic model of wheeled mobile robot considering skidding and slipping, the dynamic model of wheeled mobile robot in soft deformable terrain environment with force-speed mixed constraints is constructed. Combining the force-speed constraint and the state error event-triggered idea, a dynamic event-triggered mechanism containing constraint information is designed, and Zeno behavior is avoided. An adaptive event-triggered optimal controller is constructed by combining adaptive dynamic programming algorithm and policy iteration algorithm. To make the wheeled mobile robot complete the tracking control. Finally, it is verified by simulation.

Multimode motion capability in self-reconfigurable wheeled mobile robots (SRWMRs) can be achieved by designing various control modes and the corresponding switching strategies adapted to different motion objectives. While SRWMR is capable of strong traction and moving at a fast speed by utilizing robot creeping (RC) and wheel rolling (WR) modes, respectively, the autonomous RC mode control is challenging due to the parameter definition of mode-switching control (MSC). Therefore, to obtain the main control parameters in an SRWMR, an ROSTDyn Vortex platform is developed to analyze the traction, slippage, and sinkage variation of the modes on varied soil terrains. To autonomously activate the RC mode while the robot is in WR mode, an MSC method is proposed by utilizing fuzzy logic algorithms, taking into account the slip ratio of wheels and their change in rate. Furthermore, for RC mode, to enhance the motion efficiency by adaptively changing the wheelbase length on different types of soil terrains, the control indices on energy consumption and forward movement are presented with the consideration of the defined slip ratio indices. According to the results of simulation experiments, including climbing slopes and escaping from the wheel sinking on the designed soil terrains with varied sloping degrees and stiffness, the autonomous RC control was effectively achieved by the proposed MSC, leading to body traction enhancement. In addition, a 31% reduction in energy consumption was achieved by RC mode with adjustable parameters, compared to the regular RC control.

Based on actor-critic neural networks (NNs), an optimal controller is proposed for solving the constrained control problem of an affine nonlinear discrete-time system with disturbances. The actor NNs provide the control signals and the critic NNs work as the performance indicators of the controller. By converting the original state constraints into new input constraints and state constraints, the penalty functions are introduced into the cost function, and then the constrained optimal control problem is transformed into an unconstrained one. Further, the relationship between the optimal control input and worst-case disturbance is obtained using the Game theory. With Lyapunov stability theory, the control signals are ensured to be uniformly ultimately bounded (UUB). Finally, the effectiveness of the control algorithms is tested through a numeral simulation using a third-order dynamic system.

In this article, the problem of full state constraints for a class of uncertain nonlinear switched systems with time-varying delays under average dwell time is studied, and an adaptive event-triggered mechanism is proposed. The Lyapunov–Krasovskii function (LKF) is employed to solve the trouble caused by time-varying delays, neural networks are selected to approximate the uncertain terms in the system, and the state constraint problem is solved by constructing tan barrier Lyapunov function (Tan-BLF). What’s more, the constraint boundaries considered in this article can be expressed as functions that rely on time and historical information of the system. In addition, the mismatch behavior between subsystem and its controller is also considered. Finally, numerical simulation results verify the availability of the control strategy.

An optimal tracking control system using neural adaptive techniques is introduced for nonlinear systems subjected to time delay and inequality constraints, which is partially uncertain. The nonlinear inequality constraints and partial uncertain time delay of the state are considered in the discrete-time nonlinear system. By transforming the inequality constraint information into augmented system state variables, and using the precompensator method, an augmentation system that contains constraints and transformed controller information is obtained. The Lyapunov–Krasovskii functionals (LKFs) can be used to deal with the partial uncertain state time delay. Subsequently, the optimal controller, the long-term cost function, the uncertain resistance, and system dynamics can be approximated by the action, critic, the disturbance, and the state estimation NNs, and suitable adaptive laws are obtained. Furthermore, the uniform ultimate boundedness (UUB) of the signals in the closed-loop control system can be obtained by the designed near-optimal controller. The inequality constraints are satisfied and the challenge arising from partial uncertain time delay has been successfully addressed, while a numerical simulation verification example is presented.

This article proposes an adaptive finite-time tracking control based on fuzzy-logic systems (FLSs) for an uncertain nonstrict nonlinear multi-input-multi-output (MIMO) full-state-constrained system with the coupled uncertain dead-zone input. By using three kinds of FLSs: the uncertain system, the uncertain dead zone, and the uncertain input transfer inverse matrix are approximated using the system function FLS, dead-zone FLS, and input transfer inverse matrix FLS, respectively. After defining the barrier Lyapunov function, the fuzzy-based adaptive tracking controllers are designed, and the fuzzy weights are updated through the proposed adaptive laws. Then, based on the extended finite-time convergence theorem, with the design parameters chosen properly, the target uncertain nonlinear system is guaranteed to be semiglobal practical finite-time stable (SGPFS); and the full-state constraints are not violated while avoiding the effects of the dead zones. Furthermore, a simulation is presented to verify the validity of the proposed algorithm.

Considering the uncertain nonstrict nonlinear system with dead-zone input, an adaptive neural network (NN)-based finite-time online optimal tracking control algorithm is proposed. By using the tracking errors and the Lipschitz linearized desired tracking function as the new state vector, an extended system is present. Then, a novel Hamilton-Jacobi-Bellman (HJB) function is defined to associate with the nonquadratic performance function. Further, the upper limit of integration is selected as the finite-time convergence time, in which the dead-zone input is considered. In addition, the Bellman error function can be obtained from the Hamiltonian function. Then, the adaptations of the critic and action NN are updated by using the gradient descent method on the Bellman error function. The semiglobal practical finite-time stability (SGPFS) is guaranteed, and the tracking errors convergence to a compact set by zero in a finite time.

An adaptive neural network (NN)-based finite-time tracking control method is presented for the nonstrict nonaffined nonlinear multi-input-multi-output systems. The hardship of this article is that each subsystem responses to all input variables and any other subsystems of the whole system. Moreover, the uncertainty of the input transition matrix further soars the difficulty of controller design. In this article, NNs are used to approximate these functions with uncertainty automatically. Based on the Lyapunov stability theory, the controller we designed has proven to be semiglobal finite-time stable, implying that all the tracking errors converge to a small neighborhood of the original states in finite time, and the closed-loop system is semiglobal practical finite-time stable. At last, a simulation example is applied to verify the effectiveness of the proposed control algorithm.

In this paper, an adaptive dynamic programming-based online adaptive tracking control algorithm is proposed to solve the tracking problem of the partial uncertain time-delayed nonlinear affine system with uncertain resistance. Using the discrete-time Hamilton-Jacobi-Bellman function, the input time-delay separation lemma, and the Lyapunov-Krasovskii functionals, the partial state and input time delay can be determined. With the approximation of the action and critic, and resistance neural networks, a near-optimal controller and appropriate adaptive laws are defined to guarantee the uniform ultimate boundedness of all signals in the target system, and the tracking error convergence to a small compact set to zero. A numerical simulation of the wheeled mobile robotic system is presented to verify the validity of the proposed method.

Resistance coefficient (RC) is an important measure when designing wheel-driving mechanisms and accurate dynamic models for real-time mobility control of wheeled mobile robots (WMRs). This measure is typically formulated as a constant that depends on the wheel load, wheel dimensions, and soil that the WMR is designed for. This article proposes a novel variable RC that responds to terrain deformation. This variable RC is then applied to controllers for WMRs that estimate driving torques and slip ratios on deformable terrain. Simple yet accurate models of RC are developed from both experimental results and theoretical analysis, and these models are then compared with other methods. The proposed RC models give more accurate and more computationally efficient estimations of driving torques and slip ratios for WMRs, with average estimation errors less than 6% and the shortest computation time in experiments. The two proposed estimators are then applied to the design of the tracking-control systems for a WMR running on deformable terrain. Experiments with simulated sandy terrain demonstrate that both proposed control systems are feasible, and the slip estimation effectively decreases velocity tracking errors from more than 20% to less than 10%.

In this paper, a dynamic model of a wheeled mobile robotic (WMR) system with coupled control input is developed, which will increase the complexity of its tracking control with time-varying advance angle. To deal with this problem, a partial reinforcement learning neural network (PRLNN)-based tracking algorithm is proposed for the WMR systems. The main contributions of the PRLNN adaptive tracking control method is that it is the first control method to introduce the PRLNN adaptive control to the WMR system, which determines to solve the WMR tracking control with the time-varying advance angle. The critic neural network (NN) and action NN adaptive laws for the decoupled controllers are designed using the standard gradient-based adaptation method. According to the Lyapunov stability analysis theorem, the uniform ultimate boundedness of all signals in the WMR system can be guaranteed with the design parameters chose properly, and the tracking error converge to a small compact set nearby zero. A numerical simulation is presented to verify the effectiveness of the proposed control algorithm.

In this paper, a reinforcement learning-based adaptive control algorithm is proposed to solve the tracking problem of a discrete-time (DT) nonlinear state and input time delayed system of the wheeled mobile robot (WMR). With the typical model of the WMR transformed into an affine nonlinear DT system, a delay matrix function and appropriate Lyapunov-Krasovskii functionals are introduced to overcome the problems caused by the state and input time delays, respectively. Furthermore, with the approximation of the radial basis function neural networks (NNs), the adaptive controller, the critic NN, and action NN adaptive laws are defined to guarantee the uniform ultimate boundedness of all signals in the WMR system, and the tracking errors convergence to a small compact set to zero. Two examples of simulation are given to illustrate the effectiveness of the proposed algorithm.

In this paper, an optimal control algorithm is designed for uncertain nonlinear systems in discrete-time, which are in nonaffine form and with unknown dead-zone. The main contributions of this paper are that an optimal control algorithm is for the first time framed in this paper for nonlinear systems with nonaffine dead-zone, and the adaptive parameter law for dead-zone is calculated by using the gradient rules. The mean value theory is employed to deal with the nonaffine dead-zone input and the implicit function theory based on reinforcement learning is appropriately introduced to find an unknown ideal controller which is approximated by using the action network. Other neural networks are taken as the critic networks to approximate the strategic utility functions. Based on the Lyapunov stability analysis theory, we can prove the stability of systems, i.e., the optimal control laws can guarantee that all the signals in the closed-loop system are bounded and the tracking errors are converged to a small compact set. Finally, two simulation examples demonstrate the effectiveness of the design algorithm.

In this paper, an adaptive control approach-based neural approximation is developed for a class of uncertain nonlinear discrete-time (DT) systems. The main characteristic of the considered systems is that they can be viewed as a class of multi-input multioutput systems in the nonstrict feedback structure. The similar control problem of this class of systems has been addressed in the past, but it focused on the continuous-time systems. Due to the complicacies of the system structure, it will become more difficult for the controller design and the stability analysis. To stabilize this class of systems, a new recursive procedure is developed, and the effect caused by the noncausal problem in the nonstrict feedback DT structure can be solved using a semirecurrent neural approximation. Based on the Lyapunov difference approach, it is proved that all the signals of the closed-loop system are semiglobal, ultimately uniformly bounded, and a good tracking performance can be guaranteed. The feasibility of the proposed controllers can be validated by setting a simulation example.

In this paper, an adaptive neural network (NN)-based tracking control algorithm is proposed for the wheeled mobile robotic (WMR) system with full state constraints. It is the first time to design an adaptive NN-based control algorithm for the dynamic WMR system with full state constraints. The constraints come from the limitations of the wheels' forward speed and steering angular velocity, which depends on the motors' driving performance. By employing adaptive NNs and a barrier Lyapunov function with error variables, then, the unknown functions in the systems are estimated, and the constraints are not violated. Based on the assumptions and lemmas given in this paper and the references, while the design and the system parameters chose properly, our proposed scheme can guarantee the uniform ultimate boundedness for all signals in the WMR system, and the tracking error converge to a bounded compact set to zero. The numerical experiment of a WMR system is presented to illustrate the good performance of the proposed control algorithm.