Adaptive stabilization of non-necessarily inversely stable first-order continuous-time systems without using a hysteresis switching function

2002 ◽  
Author(s):  
M. De La Sen
Keyword(s):  
Continuous Time ◽  
Switching Function ◽  
Adaptive Stabilization ◽  
First Order ◽  
Continuous Time Systems ◽  
Time Systems ◽  
Order Continuous

scholarly journals Adaptive stabilization of continuous-time systems guaranteeing the controllability of a modified estimation model

2001 ◽  
Vol 7 (1) ◽  
pp. 29-54
Author(s):  
M. de la Sen
Keyword(s):  
Continuous Time ◽  
Switching Function ◽  
Adaptive Stabilization ◽  
Estimation Model ◽  
Switching Rule ◽  
Continuous Time Systems ◽  
Control Scheme ◽  
Positive Threshold ◽  
Time Systems ◽  
Plant Parameter

This paper presents an indirect adaptive control scheme for continuous-time systems. The estimated plant model is controllable while the estimation model is free from singularities. Such singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. This property is achieved by ensuring that the absolute value of its determinant does not lie below a prescribed positive threshold. A switching rule is used in the estimates modification algorithm to ensure the controllability of the modified estimated model while avoiding possible chattering. For that purpose, the switching rule takes values at two possible distinct prefixed thresholds. In the event when the Sylvester determinant takes the current value of the switching function then that one switches to the alternative threshold. The convergence of both the unmodified and modified estimates to finite limits guarantees that switching ends in finite time. Thus, the solution to the controlled plant exist so that all the signals within the loop are well-posed.

scholarly journals Oscillations in First-Order, Continuous-Time Systems via Time-Delay Feedback

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Abimael Salcedo ◽  
Joaquin Alvarez
Keyword(s):  
Continuous Time ◽  
Closed Loop ◽  
Equilibrium Points ◽  
Nonlinear Function ◽  
Loop System ◽  
Closed Loop System ◽  
First Order ◽  
Continuous Time Systems ◽  
Time Systems ◽  
Order Continuous

A technique to generate (periodic or nonperiodic) oscillations systematically in first-order, continuous-time systems via a nonlinear function of the state, delayed by a certain time d, is proposed. This technique consists in choosing a nonlinear function of the delayed state with some passivity properties, tuning a gain to ensure that all the equilibrium points of the closed-loop system be unstable, and then imposing conditions on the closed-loop system to be semipassive. We include several typical examples to illustrate the effectiveness of the proposed technique, with which we can generate a great variety of chaotic attractors. We also include a physical example built with a simple electronic circuit that, after applying the proposed technique, displays a similar behavior to the logistic map.

scholarly journals Adaptive stabilization of continuous-time systems through a controllable modified estimation model

2004 ◽  
Vol 2004 (2) ◽  
pp. 109-131 ◽  
Author(s):  
M. de la Sen
Keyword(s):  
Continuous Time ◽  
Switching Function ◽  
Parameter Estimates ◽  
Adaptive Stabilization ◽  
Estimation Model ◽  
Sylvester Matrix ◽  
Continuous Time Systems ◽  
Control Scheme ◽  
Positive Threshold ◽  
Time Systems

This paper presents an indirect adaptive control scheme of continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. Such singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That property is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold. An alternative modification scheme based on the achievement of a modifieddiagonally dominant Sylvester matrix of the parameter estimates is also proposed. This diagonal dominance is achieved through estimates modification as a way to guarantee the controllability of the modified estimated model when a controllability measure of the estimation model without modification fails. In both schemes, the use of an explicit hysteresis switching function for the modification of the estimates is not required to ensure the controllability of the modified estimated model. Both schemes ensure that chattering due to switches associated with the modification is not present.

Adaptive Stabilization for 2nd Order Continuous-Time Systems

1992 ◽  
Vol 25 (14) ◽  
pp. 175-180
Author(s):  
Xiao-Hui Zhao ◽  
R.G. Moctezuma ◽  
R. Lozano
Keyword(s):  
Continuous Time ◽  
Adaptive Stabilization ◽  
Continuous Time Systems ◽  
Time Systems ◽  
Order Continuous
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