Abstract
This paper focuses on the event-triggered neuroadaptive output-feedback tracking control issue for nonstrict-feedback nonlinear systems with given performance specifications. By constructing a neural observer to estimate unmeasurable states, a novel event-triggered controller is presented together with a piecewise threshold rule. The presented event-triggered mechanism has two thresholds to reduce communication resources between the controller and actuator. The salient features of the presented controller are fourfold: (1) The tracking error can converge to a preassigned small region at predesigned converging mode within prescribed time, and the prescribed time is independent of initial conditions of system. (2) The strict constraint on the initial value of tracking error is relaxed largely via an improved speed function. (3) The complexity of our control algorithm can be reduced since there is no control signal in the trigger condition. (4) Command-filtered technology with filtering error compensating signal is applied to address the “explosion of complexity” problem. Furthermore, Lyapunov stability analysis demonstrates that under the presented event-triggered controller, all signals in the closed-loop system are semiglobally bounded, and the Zeno behavior is ruled out strictly. Numerical simulations are finally provided to illustrate the presented control scheme.
Highlights
Feedback nonlinear systems with given performance specifications
An improved speed transformation function is in- 1 Introduction troduced to make the output tracking error converge to a preassigned small region at predesigned converging mode within preset finite time
Combining the variable separation method based on the structural property of radial basis function (RBF) and backstepping technology, the algebraic loop problem caused by the nonstrict-feedback structure is overcome
Summary
Inspired by [27] and [28], an improved speed function is introduced as follows:. where μ0 and μtr < 1 are positive parameters, tr > 0 and μ0μtr denote finite settling time and ultimate bound of tracking error, respectively. To achieve the pregiven performance specifications, the following state transformation is defined: s1 = tan π 2 μ χ1. Different from the existing state transformation in [39] and [12], a distinguishing feature, via using (5), is to ensure that the value of function Ξ is always positive, which is very necessary to design a stable filtering error compensation system. Remark 6 The advantage of using state transformation is to convert the constrained tracking error χ1 into an equivalent unconstrained signal. It should be noted from (5) that if s1 is bounded, −1/μ < χ1 < 1/μ where the curve of 1/μ is shown in Fig.. By designing the control method to ensure the boundedness of s1, the pregiven performance specifications of χ1 can be realized indirectly
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