This paper presents a novel approximation-based event-triggered control of multi-input multi-output uncertain nonlinear continuous-time systems in affine form. The controller is approximated using a linearly parameterized neural network (NN) in the context of event-based sampling. After revisiting the NN approximation property in the context of event-based sampling, an event-triggered condition is proposed using the Lyapunov technique to reduce the network resource utilization and to generate the required number of events for the NN approximation. In addition, a novel weight update law for aperiodic tuning of the NN weights at triggered instants is proposed to relax the knowledge of complete system dynamics and to reduce the computation when compared with the traditional NN-based control. Nonetheless, a nonzero positive lower bound for the inter-event times is guaranteed to avoid the accumulation of events or Zeno behavior. For analyzing the stability, the event-triggered system is modeled as a nonlinear impulsive dynamical system and the Lyapunov technique is used to show local ultimate boundedness of all signals. Furthermore, in order to overcome the unnecessary triggered events when the system states are inside the ultimate bound, a dead-zone operator is used to reset the event-trigger errors to zero. Finally, the analytical design is substantiated with numerical results.

This paper presents an event-triggered near optimal control of uncertain nonlinear discrete-time systems. Event-driven neurodynamic programming (NDP) is utilized to design the control policy. A neural network (NN)-based identifier, with event-based state and input vectors, is utilized to learn the system dynamics. An actor–critic framework is used to learn the cost function and the optimal control input. The NN weights of the identifier, the critic, and the actor NNs are tuned aperiodically once every triggered instant. An adaptive event-trigger condition to decide the trigger instants is derived. Thus, a suitable number of events are generated to ensure a desired accuracy of approximation. A near optimal performance is achieved without using value and/or policy iterations. A detailed analysis of nontrivial inter-event times with an explicit formula to show the reduction in computation is also derived. The Lyapunov technique is used in conjunction with the event-trigger condition to guarantee the ultimate boundedness of the closed-loop system. The simulation results are included to verify the performance of the controller. The net result is the development of event-driven NDP.

This paper presents a novel adaptive neural network (NN) control of single-input and single-output uncertain nonlinear discrete-time systems under event sampled NN inputs. In this control scheme, the feedback signals are transmitted, and the NN weights are tuned in an aperiodic manner at the event sampled instants. After reviewing the NN approximation property with event sampled inputs, an adaptive state estimator (SE), consisting of linearly parameterized NNs, is utilized to approximate the unknown system dynamics in an event sampled context. The SE is viewed as a model and its approximated dynamics and the state vector, during any two events, are utilized for the event-triggered controller design. An adaptive event-trigger condition is derived by using both the estimated NN weights and a dead-zone operator to determine the event sampling instants. This condition both facilitates the NN approximation and reduces the transmission of feedback signals. The ultimate boundedness of both the NN weight estimation error and the system state vector is demonstrated through the Lyapunov approach. As expected, during an initial online learning phase, events are observed more frequently. Over time with the convergence of the NN weights, the inter-event times increase, thereby lowering the number of triggered events. These claims are illustrated through the simulation results.

The health assessment of Lithium-ion batteries (LIBs) is critical for battery management systems (BMSs) to ensure safe and reliable operation and predict life-cycle. State-of-health (SOH) monitoring is challenging since it is governed by several internal and external degradation factors, such as temperature, aging, $C_{rate}$ , and faults. In this paper, we propose a SOH-coupled nonlinear electro-thermal-aging (ETA) model of a $LiFePO_{4}$ /graphite battery, which can be employed to simultaneously estimate the state of charge (SOC), SOH, temperatures, and internal resistance using a filtering-based approach. The coupling between the equivalent circuit model (ECM) and the SOH is established using an empirical capacity fade model of a $LiFePO_{4}$ /graphite battery and its effects on SOC dynamics. In contrast to a constant usable capacity, the proposed model employs a SOH-dependent variable capacity ECM, thereby incorporating the influence of battery aging on the ECM. The SOH-coupled ECM model is then integrated with the thermal model to develop the ETA model. The ETA model is further extended by augmenting the ohmic resistance dynamics to enable monitoring of the evolution of the internal resistance. The proposed SOH-coupled model is validated with numerical simulation and experimental data. Estimation results for SOC, SOH, temperature and ohmic resistance are included to show the model's potential for monitoring and control applications.

In this paper, approximate optimal distributed control schemes for a class of nonlinear interconnected systems with strong interconnections are presented using continuous and event-sampled feedback information. The optimal control design is formulated as an $N$-player nonzero-sum game where the control policies of the subsystems act as players. An approximate Nash equilibrium solution to the game, which is the solution to the coupled Hamilton-Jacobi equation, is obtained using the approximate dynamic programming-based approach. A critic neural network (NN) at each subsystem is utilized to approximate the Nash solution and novel event-sampling conditions, that are decentralized, are designed to asynchronously orchestrate the sampling and transmission of state vector at each subsystem. To ensure the local ultimate boundedness of the closed-loop system state and NN parameter estimation errors, a hybrid-learning scheme is introduced and the stability is guaranteed using Lyapunov-based stability analysis. Finally, implementation of the proposed event-based distributed control scheme for linear interconnected systems is discussed. For completeness, Zeno-free behavior of the event-sampled system is shown analytically and a numerical example is included to support the analytical results.

This paper presents an approximate optimal control of nonlinear continuous-time systems in affine form by using the adaptive dynamic programming (ADP) with event-sampled state and input vectors. The knowledge of the system dynamics is relaxed by using a neural network (NN) identifier with event-sampled inputs. The value function, which becomes an approximate solution to the Hamilton–Jacobi–Bellman equation, is generated by using event-sampled NN approximator. Subsequently, the NN identifier and the approximated value function are utilized to obtain the optimal control policy. Both the identifier and value function approximator weights are tuned only at the event-sampled instants leading to an aperiodic update scheme. A novel adaptive event sampling condition is designed to determine the sampling instants, such that the approximation accuracy and the stability are maintained. A positive lower bound on the minimum inter-sample time is guaranteed to avoid accumulation point, and the dependence of inter-sample time upon the NN weight estimates is analyzed. A local ultimate boundedness of the resulting nonlinear impulsive dynamical closed-loop system is shown. Finally, a numerical example is utilized to evaluate the performance of the near-optimal design. The net result is the design of an event-sampled ADP-based controller for nonlinear continuous-time systems.