In this paper, a novel event-triggered implementation of a tracking controller for an uncertain strict-feedback system is presented. Neural networks (NNs) are utilized in the backstepping approach to design a control input by approximating unknown dynamics of the strict-feedback nonlinear system with event-sampled inputs. The system state vector is assumed to be unknown and an NN observer is used to estimate the state vector. By using the estimated state vector and backstepping design approach, an event-sampled controller is introduced. As part of the controller design, first, input-to-state-like stability for a continuously sampled controller that has been injected with bounded measurement errors is demonstrated, and subsequently, an event-execution control law is derived, such that the measurement errors are guaranteed to remain bounded. Lyapunov theory is used to demonstrate that the tracking errors, the observer estimation errors, and the NN weight estimation errors for each NN are locally uniformly ultimately bounded in the presence bounded disturbances, NN reconstruction errors, as well as errors introduced by event sampling. Simulation results are provided to illustrate the effectiveness of the proposed controllers.
In this paper, a distributed control scheme for an interconnected system composed of uncertain input affine nonlinear subsystems with event triggered state feedback is presented by using a novel hybrid learning scheme-based approximate dynamic programming with online exploration. First, an approximate solution to the Hamilton-Jacobi-Bellman equation is generated with event sampled neural network (NN) approximation and subsequently, a near optimal control policy for each subsystem is derived. Artificial NNs are utilized as function approximators to develop a suite of identifiers and learn the dynamics of each subsystem. The NN weight tuning rules for the identifier and event-triggering condition are derived using Lyapunov stability theory. Taking into account, the effects of NN approximation of system dynamics and boot-strapping, a novel NN weight update is presented to approximate the optimal value function. Finally, a novel strategy to incorporate exploration in online control framework, using identifiers, is introduced to reduce the overall cost at the expense of additional computations during the initial online learning phase. System states and the NN weight estimation errors are regulated and local uniformly ultimately bounded results are achieved. The analytical results are substantiated using simulation studies.
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