Predictor-feedback stabilization of multi-input nonlinear systems

Abstract

We develop a predictor-feedback control design for multi-input nonlinear systems with distinct input delays, of arbitrary length, in each individual input channel. Due to the fact that different input signals reach the plant at different time instants, the key design challenge, which we resolve, is the construction of the predictors of the plant's state over distinct prediction horizons such that the corresponding input delays are compensated. Global asymptotic stability of the closed-loop system is established by utilizing arguments based on Lyapunov functionals or estimates on solutions. We specialize our methodology to linear systems for which the predictor-feedback control laws are available explicitly and for which global exponential stability is achievable. A detailed example is provided dealing with the stabilization of the nonholonomic unicycle, subject to two different input delays affecting the speed and turning rate, for the illustration of our methodology.

Reduction of Discrete-Time Two-Channel Delayed Systems

“…The proposed methodology applies to sampled-data delayed dynamics under entire delays. Future works are toward different directions: sampled-data systems under non-entire delays [11]; a comparison with the continuous-time prediction framework with special emphasis on the cascade like representations provided by transport PDEs [14], [16] with respect to the discrete-time one [9]; the specialization of this methodology to different scenarios where time delays are unavoidable as in networked systems [20]. …”

“…Accordingly, we apply our procedure to stabilize (16). By noticing that B δ 1 (u 1 )x d = 0, one defines the reduction as…”

“…In continuous time, predictor-based techniques for multi-input linear time-invariant systems affected by distinct input delays have been proposed in [13]- [15] with extensions to nonlinear dynamics in [16].…”

Analytical and Experimental Predictor-Based Time Delay Control of Baxter Robot

“…The following lemmas help the proof of closed-loop system stability [29], Lemma 4. There exist class K ∞ functions ρ such that p(.,t) ∞ ≤ ρ(Ξ(t)) (47)…”

“…In addition to the recent developments of predictor-based control laws for nonlinear systems with input delays [18][19][20][21][22][23][24][25][26][27][28], Bekiaris-Liberis and Krstić [29] addressed the problem of stabilization of multi-input nonlinear systems with distinct arbitrary large input delays, and developed a nonlinear version of Motivated by the harmful consequences of input delays on the stability and performance of such control systems, we formulate and implement a predictor-feedback controller for the compensation of large input delays of the 7-DOF Baxter manipulator (a multi-input highly nonlinear system). We assume that all input channels induce the same delay, since all commands are sent to the joints simultaneously.…”