ADP-Based Online Tracking Control of Partially Uncertain Time-Delayed Nonlinear System and Application to Wheeled Mobile Robots

Self-learning sliding mode control based on adaptive dynamic programming for nonholonomic mobile robots

This paper proposes a self-learning sliding mode control (SlSMC) strategy with stability guarantee for the trajectory tracking of nonholonomic mobile robots (NMRs) under matched uncertainties, which improves the control performance of NMRs by optimizing the reaching law and the sliding mode surface of SMC as well as retaining the finite-time convergence and the robustness to uncertainties. In the presence of adverse factors such as skidding, slipping and environmental noise, the kinematic model of NMRs is reconstructed and an integral terminal sliding mode controller is designed for the trajectory tracking of NMRs. Then, based on the sliding mode controller, the proposed control strategy formulates the optimization of the SMC's reaching law and the sliding mode surface under stability constraints as two asynchronous optimal control problems with control constraints. Meanwhile, an online continuous-time receding-horizon optimization mechanism based on an actor-critic algorithm is proposed to solve the optimal problems asynchronously and improve online learning efficiency. The stability and the convergence of the proposed strategy are validated both in theory and simulations. Furthermore, extensive contrastive simulation results illustrate that the proposed receding horizon learning-based control strategy outperforms three recent methods in control performance. Finally, experiments of the proposed self-learning SMC strategy are carried out based on a real intelligent vehicle, and the experimental results also verify that the proposed method can meet the actual control needs of NMRs.

Optimal H∞ tracking control of nonlinear systems with zero-equilibrium-free via novel adaptive critic designs

In this paper, a novel adaptive critic control method is designed to solve an optimal H_∞ tracking control problem for continuous nonlinear systems with nonzero equilibrium based on adaptive dynamic programming (ADP). To guarantee the finiteness of a cost function, traditional methods generally assume that the controlled system has a zero equilibrium point, which is not true in practical systems. In order to overcome such obstacle and realize H_∞ optimal tracking control, this paper proposes a novel cost function design with respect to disturbance, tracking error and the derivative of tracking error. Based on the designed cost function, the H_∞ control problem is formulated as two-player zero-sum differential games, and then a policy iteration (PI) algorithm is proposed to solve the corresponding Hamilton-Jacobi-Isaacs (HJI) equation. In order to obtain the online solution to the HJI equation, a single-critic neural network structure based on PI algorithm is established to learn the optimal control policy and the worst-case disturbance law. It is worth mentioning that the proposed adaptive critic control method can simplify the controller design process when the equilibrium of the systems is not zero. Finally, simulations are conducted to evaluate the tracking performance of the proposed control methods.

Adaptive Event-Triggered Sliding-Mode Control for Consensus Tracking of Nonlinear Multiagent Systems With Unknown Perturbations

The adaptive tracking control problem of leader-following nonlinear multiagent systems (MASs) subject to unknown perturbations and limited network bandwidth is investigated by the robust adaptive event-triggered sliding-mode control method. A distributed integral sliding mode is established to realize the finite-time reachability of the states of the leader-following nonlinear MAS. An adaptive triggering control mechanism is then put forward to dynamically adjust the triggering interval, thus reducing the actuator wear and unnecessary network resource consumption. The positions and velocities of the leader-following nonlinear MAS subject to unknown external disturbances are, respectively, driven to the equilibrium point by constructing a distributed event-based robust adaptive sliding-mode protocol. Via the Lyapunov stability theory and Barbalat lemma, sufficient conditions to ensure the adaptive tracking performance are derived for leader-following nonlinear MASs. Three simulation examples to verify the efficacy of the proposed event-based robust adaptive sliding-mode controller design are presented.

Adaptive Event-Triggered Neural Network Control for Switching Nonlinear Systems With Time Delays

The adaptive event-triggered-based neural network control is explored for switching nonlinear systems with nonstrict-feedback structure and time-varying delays in this article. First, the switching observer is designed to estimate the unmeasurable states. Due to the existence of time-varying input delay, a compensation system is introduced. The average dwell-time (ADT) scheme and the event-triggered controller are established. Furthermore, the semiglobal uniform ultimate boundedness (SGUUB) of all the variables in the closed-loop system is achieved and the Zeno behavior is avoided. Finally, the numerical simulation shows that our proposed control approach is effective.

Observer-Based Adaptive Fuzzy Control for Nonlinear State-Constrained Systems Without Involving Feasibility Conditions

For nonlinear full-state-constrained systems with unmeasured states, an adaptive output feedback control strategy is developed. The main challenge of this article is how to avoid that the unmeasured states exceed the constrained spaces. To achieve a good tracking performance for the considered systems, a stable state observer is structured to estimate unmeasured states which are not available in the control design. In addition, the constraints existing in most practical engineering are the source of reducing control performance and causing the system instability. The main limitation of current barrier Lyapunov functions is the feasibility conditions for intermediate controllers. The nonlinear mappings are used to achieve the satisfaction of full-state constraints directly and avoid feasibility conditions for intermediate controllers. By the Lyapunov theorem, the closed-loop system stability is proven. Simulation results are given to confirm the validity of the developed strategy.

Optimal Output Regulation for General Linear Systems via Adaptive Dynamic Programming

In this article, we consider an adaptive optimal output regulation problem for general linear systems. The purpose of the optimal output regulation problem is to guarantee the stability of the closed-loop system and disturbance rejection, as well by minimizing some predefined performance indices. It can be realized by using an optimal controller, in which both optimal feedback control gain and optimal feedforward control gain are included. First, an adaptive dynamic programming (ADP) technique is used to solve the optimal feedback control gain. Next, the unknown system matrices of the plant are explicitly computed. In addition, based on the property of the minimal polynomial, the coefficient of the exogenous disturbance in the expression of the regulated output can also be calculated. Finally, according to the regulator equation, an extra cost function is given, which aims to obtain the optimal feedforward control gain. The linear vector space optimization methods are used to solve the optimal problem. As a result, the linear optimal output regulation problem can be solved by the approximately optimal feedback and feedforward control gains.

Event-Triggered ADP for Tracking Control of Partially Unknown Constrained Uncertain Systems

An event-triggered adaptive dynamic programming (ADP) algorithm is developed in this article to solve the tracking control problem for partially unknown constrained uncertain systems. First, an augmented system is constructed, and the solution of the optimal tracking control problem of the uncertain system is transformed into an optimal regulation of the nominal augmented system with a discounted value function. The integral reinforcement learning is employed to avoid the requirement of augmented drift dynamics. Second, the event-triggered ADP is adopted for its implementation, where the learning of neural network weights not only relaxes the initial admissible control but also executes only when the predefined execution rule is violated. Third, the tracking error and the weight estimation error prove to be uniformly ultimately bounded, and the existence of a lower bound for the interexecution times is analyzed. Finally, simulation results demonstrate the effectiveness of the present event-triggered ADP method.

Robust Control Design to the Furuta System under Time Delay Measurement Feedback and Exogenous-Based Perturbation

When dealing with real control experimentation, the designer has to take into account several uncertainties, such as: time variation of the system parameters, exogenous perturbation and the presence of time delay in the feedback line. In the later case, this time delay behaviour may be random, or chaotic. Hence, the control block has to be robust. In this work, a robust delay-dependent controller based on H∞ theory is presented by employing the linear matrix inequalities techniques to design an efficient output feedback control. This approach is carefully tuned to face with random time-varying measurement feedback and applied to the Furuta pendulum subject to an exogenous ground perturbation. Therefore, a recent experimental platform is described. Here, the ground perturbation is realised using an Hexapod robotic system. According to experimental data, the proposed control approach is robust and the control objective is completely satisfied.

NN Reinforcement Learning Adaptive Control for a Class of Nonstrict-Feedback Discrete-Time Systems

This article investigates an adaptive reinforcement learning (RL) optimal control design problem for a class of nonstrict-feedback discrete-time systems. Based on the neural network (NN) approximating ability and RL control design technique, an adaptive backstepping RL optimal controller and a minimal learning parameter (MLP) adaptive RL optimal controller are developed by establishing a novel strategic utility function and introducing external function terms. It is proved that the proposed adaptive RL optimal controllers can guarantee that all signals in the closed-loop systems are semiglobal uniformly ultimately bounded (SGUUB). The main feature is that the proposed schemes can solve the optimal control problem that the previous literature cannot deal with. Furthermore, the proposed MPL adaptive optimal control scheme can reduce the number of adaptive laws, and thus the computational complexity is decreased. Finally, the simulation results illustrate the validity of the proposed optimal control schemes.

On Stability of Perturbed Nonlinear Switched Systems with Adaptive Reinforcement Learning

In this paper, a tracking control approach is developed based on an adaptive reinforcement learning algorithm with a bounded cost function for perturbed nonlinear switched systems, which represent a useful framework for modelling these converters, such as DC–DC converter, multi-level converter, etc. An optimal control method is derived for nominal systems to solve the tracking control problem, which results in solving a Hamilton–Jacobi–Bellman (HJB) equation. It is shown that the optimal controller obtained by solving the HJB equation can stabilize the perturbed nonlinear switched systems. To develop a solution to the translated HJB equation, the proposed neural networks consider the training technique obtaining the minimization of square of Bellman residual error in critic term due to the description of Hamilton function. Theoretical analysis shows that all the closed-loop system signals are uniformly ultimately bounded (UUB) and the proposed controller converges to optimal control law. The simulation results of two situations demonstrate the effectiveness of the proposed controller.