Constrained robust sampled‐data control for nonlinear uncertain systems

Abstract

SUMMARYIn industrial process control, computer control, which makes the closed-loop system a sampled-data one containing both continuous-and discrete-time signals, is widely used. In contrast with traditional approximation methods, sampled-data synthesis, a direct digital controller design procedure without approximation, has received increasing attention during the past few years. However, many of the existing results cannot be applied to sampled-data control design for the uncertain systems. In this paper, a result of robust asymptotic stability of sampled-data systems with constraints on the state is presented based on a result on practical stability for these systems. Then the robust sampled-data control for a class of uncertain nonlinear systems with constraints on the output is developed. The problem is formulated from vehicle steering control with constraint on the side slip angle of body. The result is described by some matrix inequalities which could be solved by an iterative algorithm based on the linear matrix inequality technique. Finally, a numerical example is presented to demonstrate the result.

Exponential stability of impulsive systems with application to uncertain sampled-data systems

“…Thus the system (1) is GUES over the class S of impulse sequences with the decay rate and the overshoot estimate given by (7). Moreover from the equation (9) and the condition (8) we conclude that for any…”

“…Therefore as the sampling intervals approach zero, Theorem 2 recovers exactly the continuous-time stability condition. This does not happen for the conditions that appeared in [7]. Moreover using a Lyapunov function instead of a Lyapunov functional facilitates proving the exponential stability (instead of just asymptotic stability) of the system (13).…”

“…In this case, the closed-loop becomes an infinite-dimensional Delay Differential Equation (DDE) and the stability is established using Razumikin or Lyapunov-Krasovskii Theorems. The third approach is based on the impulsive modeling of sampled-data systems in which a time-varying periodic Lyapunov function is used [7,8]. The downside of this approach is that the sampling interval of the process's output must be constant and the sampling interval of the controller's output is -times ( ∈ N) smaller than the process's output sampling interval.…”

A Robust Asynchronous Sampled-Data Control Design for Nonlinear Systems with Actuator Failures

“…Lately, asynchronous based on discrete-event sampled-data driven systems have extensively been applied to a huge number of engineering applications, specially in networked control systems; to name a few, see [1][2][3][4][5][6][7]. Basically, in sampled-data control algorithms, continuous-time systems are controlled by discrete-time controllers implemented in digital devices [8][9][10].…”

Double-stepped adaptive control for hybrid systems with unknown Markov jumps and stochastic noises

“…Practically, most control systems developed today are based on computer control (SD-based control) [1]. Since 1960s, many significant results have been obtained on SD-based control, for instance, robust SD-based adaptive control [19,28], robust SD-based constrained control [9], SD-based adaptive tracking control [15,21,29], SD-based optimal control and L p stabilization control [14], robust SD-based stabilization analysis [20], and so on. For SD-based control design, the choice of sample step is always the primary task, since improper sample step may destroy the controllability and stability of the sampled system.…”