Event-triggered robust control for multi-player nonzero-sum games with input constraints and mismatched uncertainties

In this article, an event-triggered robust control (ETRC) method is investigated for multi-player nonzero-sum games of continuous-time input constrained nonlinear systems with mismatched uncertainties. By constructing an auxiliary system and designing an appropriate value function, the robust control problem of input constrained nonlinear systems is transformed into an optimal regulation problem. Then, a critic neural network (NN) is adopted to approximate the value function of each player for solving the event-triggered coupled Hamilton-Jacobi equation and obtaining control laws. Based on a designed event-triggering condition, control laws are updated when events occur only. Thus, both computational burden and communication bandwidth are reduced. We prove that the weight approximation errors of critic NNs and the closed-loop uncertain multi-player system states are all uniformly ultimately bounded thanks to the Lyapunov's direct method. Finally, two examples are provided to demonstrate the effectiveness of the developed ETRC method

Optimal adaptive control of time-delay dynamical systems with known and uncertain dynamics

Delays are found in many industrial pneumatic and hydraulic systems, and as a result, the performance of the overall closed-loop system deteriorates unless they are explicitly accounted. It is also possible that the dynamics of such systems are uncertain. On the other hand, optimal control of time-delay systems in the presence of known and uncertain dynamics by using state and output feedback is of paramount importance. Therefore, in this research, a suite of novel optimal adaptive control (OAC) techniques are undertaken for linear and nonlinear continuous time-delay systems in the presence of uncertain system dynamics using state and/or output feedback. First, the optimal regulation of linear continuous-time systems with state and input delays by utilizing a quadratic cost function over infinite horizon is addressed using state and output feedback. Next, the optimal adaptive regulation is extended to uncertain linear continuous-time systems under a mild assumption that the bounds on system matrices are known. Subsequently, the event-triggered optimal adaptive regulation of partially unknown linear continuous time systems with state-delay is addressed by using integral reinforcement learning (IRL). It is demonstrated that the optimal control policy renders asymptotic stability of the closed-loop system provided the linear time-delayed system is controllable and observable. The proposed event-triggered approach relaxed the need for continuous availability of state vector and proven to be zeno-free. Finally, the OAC using IRL neural network based control of uncertain nonlinear time-delay systems with input and state delays is investigated. An identifier is proposed for nonlinear time-delay systems to approximate the system dynamics and relax the need for the control coefficient matrix in generating the control policy. Lyapunov analysis is utilized to design the optimal adaptive controller, derive parameter/weight tuning law and verify stability of the closed-loop system”--Abstract, page iv

Event-triggered near optimal adaptive control of interconnected systems

Increased interest in complex interconnected systems like smart-grid, cyber manufacturing have attracted researchers to develop optimal adaptive control schemes to elicit a desired performance when the complex system dynamics are uncertain. In this dissertation, motivated by the fact that aperiodic event sampling saves network resources while ensuring system stability, a suite of novel event-sampled distributed near-optimal adaptive control schemes are introduced for uncertain linear and affine nonlinear interconnected systems in a forward-in-time and online manner. First, a novel stochastic hybrid Q-learning scheme is proposed to generate optimal adaptive control law and to accelerate the learning process in the presence of random delays and packet losses resulting from the communication network for an uncertain linear interconnected system. Subsequently, a novel online reinforcement learning (RL) approach is proposed to solve the Hamilton-Jacobi-Bellman (HJB) equation by using neural networks (NNs) for generating distributed optimal control of nonlinear interconnected systems using state and output feedback. To relax the state vector measurements, distributed observers are introduced. Next, using RL, an improved NN learning rule is derived to solve the HJB equation for uncertain nonlinear interconnected systems with event-triggered feedback. Distributed NN identifiers are introduced both for approximating the uncertain nonlinear dynamics and to serve as a model for online exploration. Next, the control policy and the event-sampling errors are considered as non-cooperative players and a min-max optimization problem is formulated for linear and affine nonlinear systems by using zero-sum game approach for simultaneous optimization of both the control policy and the event based sampling instants. The net result is the development of optimal adaptive event-triggered control of uncertain dynamic systems --Abstract, page iv

Double Asynchronous Switching Control for Takagi–Sugeno Fuzzy Markov Jump Systems via Adaptive Event-Triggered Mechanism

This article addresses the issue of adaptive event- triggered H∞ control for Markov jump systems based on Takagi-Sugeno (T-S) fuzzy model. Firstly, a new double asynchronous switching controller is presented to deal with the problem of the mismatch of premise variables and modes between the controller and the plant, which is widespread in real network environment. To further reduce the power consumption of communication, a switching adaptive event-triggered mechanism is adopted to relieve the network transmission pressure while ensuring the control effect. In addition, a new Lyapunov-Krasovskii functional (LKF) is constructed to reduce conservatism by introducing the membership functions (MFs) and time-varying delays informa- tion. Meanwhile, the invariant set is estimated to ensure the stability of the system. And the disturbance rejection ability is measured by the optimal H∞ performance index. Finally, two examples are presented to demonstrate the effectiveness of the proposed approach

Event-Triggered Multi-Lane Fusion Control for 2-D Vehicle Platoon Systems with Distance Constraints

This paper investigates the event-triggered fixedtime multi-lane fusion control for vehicle platoon systems with distance keeping constraints where the vehicles are spread in multiple lanes. To realize the fusion of vehicles in different lanes, the vehicle platoon systems are firstly constructed with respect to a two-dimensional (2-D) plane. In case of the collision and loss of effective communication, the distance constraints for each vehicle are guaranteed by a barrier function-based control strategy. In contrast to the existing results regarding the command filter techniques, the proposed distance keeping controller can constrain the distance tracking error directly and the error generated by the command filter is coped with by adaptive fuzzy control technique. Moreover, to offset the impacts of the unknown system dynamics and the external disturbances, an unknown input reconstruction method with asymptotic convergence is developed by utilizing the interval observer technique. Finally, two relative threshold triggering mechanisms are utilized in the proposed fixed-time multi-lane fusion controller design so as to reduce the communication burden. The corresponding simulation results also verify the effectiveness of the proposed strategy

Concurrent Learning-Based Neuro-Adaptive Robust Tracking Control of Wheeled Mobile Robot: An Event-Triggered Design

In this paper, an event-based neuro-adaptive robust tracking controller for a perturbed and networked differential drive mobile robot (DMR) is designed with concurrent learning. A radial basis function neural network, which approximates an unknown perturbation, is used to design an adaptive sliding mode controller (SMC). The RBFNN weights and SMC parameters are estimated online using an adaptive tuning law to ensure performance with reduced chattering. To improve the convergence of RBFNN weight estimation error, a concurrent learning-based adaptive law is derived, which uses measured online and recorded data. Further, a suitable triggering condition is designed to achieve a reduced number of control computations while minimizing network resources without sacrificing the stability of the sampled data closed-loop control system. A finite sampling frequency is guaranteed for the designed triggering condition by establishing a positive lower bound on the inter-event execution time which is equivalent to the Zeno-free behavior of the system. Finally, the proposed event-based neuro-adaptive robust controller is implemented on a practical system (Q-bot 2e) to show the effectiveness of the proposed design

Observer-based event-triggered and set-theoretic neuro-adaptive controls for constrained uncertain systems

In this study, several new observer-based event-triggered and set-theoretic control schemes are presented to advance the state of the art in neuro-adaptive controls. In the first part, six new event-triggered neuro-adaptive control (ETNAC) schemes are presented for uncertain linear systems. These comprehensive designs offer flexibility to choose a design depending upon system performance requirements. Stability proofs for each scheme are presented and their performance is analyzed using benchmark examples. In the second part, the scope of the ETNAC is extended to uncertain nonlinear systems. It is applied to a case of precision formation flight of the microsatellites at the Sun-Earth/Moon L1 libration point. This dynamic system is selected to evaluate the performance of the ETNAC techniques in a setting that is highly nonlinear and chaotic in nature. Moreover, factors like restricted controls, response to uncertainties and jittering makes the controller design even trickier for maintaining a tight formation precision. Lyapunov function-based stability analysis and numerical results are presented. Note that most real-world systems involve constraints due to hardware limitations, disturbances, uncertainties, nonlinearities, and cannot always be efficiently controlled by using linearized models. To address all these issues simultaneously, a barrier Lyapunov function-based control architecture called the segregated prescribed performance guaranteeing neuro-adaptive control is developed and tested for the constrained uncertain nonlinear systems, in the third part. It guarantees strict performance that can be independently prescribed for each individual state and/or error signal of the given system. Furthermore, the proposed technique can identify unknown dynamics/uncertainties online and provides a way to regulate the control input --Abstract, page iv

Non-fragile estimation for discrete-time T-S fuzzy systems with event-triggered protocol

summary:This paper investigates the non-fragile state estimation problem for a class of discrete-time T-S fuzzy systems with time-delays and multiple missing measurements under event-triggered mechanism. First of all, the plant is subject to the time-varying delays and the stochastic disturbances. Next, a random white sequence, the element of which obeys a general probabilistic distribution defined on $[0,1]$, is utilized to formulate the occurrence of the missing measurements. Also, an event generator function is employed to regulate the transmission of data to save the precious energy. Then, a non-fragile state estimator is constructed to reflect the randomly occurring gain variations in the implementing process. By means of the Lyapunov-Krasovskii functional, the desired sufficient conditions are obtained such that the Takagi-Sugeno (T-S) fuzzy estimation error system is exponentially ultimately bounded in the mean square. And then the upper bound is minimized via the robust optimization technique and the estimator gain matrices can be calculated. Finally, a simulation example is utilized to demonstrate the effectiveness of the state estimation scheme proposed in this paper

Event-triggering architectures for adaptive control of uncertain dynamical systems

In this dissertation, new approaches are presented for the design and implementation of networked adaptive control systems to reduce the wireless network utilization while guaranteeing system stability in the presence of system uncertainties. Specifically, the design and analysis of state feedback adaptive control systems over wireless networks using event-triggering control theory is first presented. The state feedback adaptive control results are then generalized to the output feedback case for dynamical systems with unmeasurable state vectors. This event-triggering approach is then adopted for large-scale uncertain dynamical systems. In particular, decentralized and distributed adaptive control methodologies are proposed with reduced wireless network utilization with stability guarantees. In addition, for systems in the absence of uncertainties, a new observer-free output feedback cooperative control architecture is developed. Specifically, the proposed architecture is predicated on a nonminimal state-space realization that generates an expanded set of states only using the filtered input and filtered output and their derivatives for each vehicle, without the need for designing an observer for each vehicle. Building on the results of this new observer-free output feedback cooperative control architecture, an event-triggering methodology is next proposed for the output feedback cooperative control to schedule the exchanged output measurements information between the agents in order to reduce wireless network utilization. Finally, the output feedback cooperative control architecture is generalized to adaptive control for handling exogenous disturbances in the follower vehicles. For each methodology, the closed-loop system stability properties are rigorously analyzed, the effect of the user-defined event-triggering thresholds and the controller design parameters on the overall system performance are characterized, and Zeno behavior is shown not to occur with the proposed algorithms --Abstract, page iv