A smooth switching adaptive controller for linearizable systems with improved transient performance

Abstract

The certainty equivalent control has achieved asymptotic tracking stability of linearizable systems in the presence of parametric uncertainty. However, two major drawbacks remain to be tackled, namely, the risk of running into singularity for the calculated control input and the poor transient behaviour arising frequently in a general adaptive system. For the first problem, a high gain control is activated in place of the certainty equivalent control until the risk is bypassed. Among others, it requires less control effort by taking advantages of the bounds for the input vector field. Moreover, the switching mechanism is smooth and hence avoids possible chattering behaviour. Next, to solve the second problem, a new type of update algorithm guaranteeing the exponential stability of the overall closed-loop system, on a weaker persistent excitation (PE) condition, is proposed. In particular, it requires no filtering of the regressor and hence is easier to implement. Simulation results demonstrating the validity of the proposed design are given in the final.

Smoothing switched control laws for uncertain nonlinear systems subject to actuator saturation

“…Control signal chattering is a generally undesirable phenomenon in real systems. Different control strategies try to avoid the chattering problem, for instance, in sliding mode control [17][18][19][20][21][22][23][24], to name a few, in adaptive control [25][26][27], and in control of switched linear systems [28][29][30].In this context, this paper extends the methodology proposed in [13,14] for uncertain T-S fuzzy models, based on [31,32], taking into account actuators saturation. Additionally, an invariant region E.P; 1/ is estimated, in which for every x.0/ 2 E.P; 1/, the state vector of the controlled system x.t/, t > 0 is in a given operation region where the T-S fuzzy model exactly describes the nonlinear system and also the equilibrium point of the controlled systems is locally asymptotically stable with an adequate decay rate.…”

“…Control signal chattering is a generally undesirable phenomenon in real systems. Different control strategies try to avoid the chattering problem, for instance, in sliding mode control [17][18][19][20][21][22][23][24], to name a few, in adaptive control [25][26][27], and in control of switched linear systems [28][29][30].…”