Relative Adaptation Dead-zone Research Articles

On the adaptive control of a class of SISO dynamic hybrid systems

This paper deals with the problem of synthesizing a robust adaptive controller for a specific class of single-input single-output (SISO) time-invariant hybrid controlled object (plant) which can operate under bounded disturbances and/or unmodeled dynamics. The hybrid plant dealt with is composed of two coupled subsystems, one of them being of continuous-time type while the other is digital. The estimation algorithm is of a continuous-time nature since the plant parameter estimates are updated for all time. The adaptive scheme is pole-placement based and it is of indirect type since the controller parameters are re-updated at all time based on the calculated plant parameter estimates. An input–output model is first directly obtained from a state-space description which involves filtered signals for the hybrid plant from an initial state-space description. Such a model is simultaneously driven by the standard continuous-time input plus an extra signal. The extra input is composed for all time of a signal which involves the contribution of the input and output over a finite number of preceding sampling instants plus a driving signal which involves the contribution of the weighted integral of the continuous-time input on a set of preceding sampling intervals. Such a driving signal is due to the existing couplings between the continuous-time and digital substates of the hybrid plant. A relative adaptation dead zone is used in the parameter estimation scheme whose role is the robust adaptive stabilization in the presence of uncertainties. The hybrid nature of the system becomes apparent since the plant is simultaneously driven by the continuous time input plus its samples at sampling instants. As a result, its input–output differential equation has forcing terms generated by the system description at sampling instants.

Robust adaptive control of discrete nominally stabilizable plants

This paper presents an indirect pole-placement based adaptive control scheme for discrete linear time-invariant non-necessarily inversely stable and stabilizable systems. The scheme is a pole-placement type without requiring the plant inverse stability assumption. The control objective is that the plant output should asymptotically track in the absence of unmodeled dynamics and bounded disturbances a reference signal, given by an arbitrary stable filter, under a bounded tracking error while ensuring robust closed-loop stability. The adaptive stabilizability and the robustness of this system under the presence of unmodeled dynamics and, possibly, bounded disturbances, are proved without assuming the controllability of the modeled plant. A normalized least-squares algorithm with a relative adaptation dead-zone and ‘a posteriori’ modification of the parameter estimates is used to ensure the controllability of the modified estimation plant model at all sampling instants and at the limit. Such a property is crucial to solve the stable pole-placement problem. On the other hand, the relative adaptation dead-zone is included for robustness purposes under unmodeled dynamics and, possibly, bounded disturbances.

Robust adaptive control of dynamic hybrid systems

Deals with the problem of synthesizing a robust adaptive controller for a class of single-input single-output time-invariant hybrid plant which can operate under bounded disturbances and/or unmodelled dynamics. The hybrid plant dealt with is composed of two subsystems one being of continuous-time type while the other is digital. The system is simultaneously driven by the standard continuous-time input plus an extra signal. A relative adaptation dead zone is used in the parameter estimation scheme whose role is the robust adaptive stabilization in the presence of uncertainties.

Robust Adaptive Tracking with Pole Placement of First-Order Potentially Inversely Unstable Continuous-Time Systems

This note presents an indirect adaptive control scheme applicable to nominally con- trollable non-necessarily inversely stable first-order continuous linear time-invariant systems with unmodelled dynamics. The control objective is to achieve a bounded tracking-error between the system output and a reference signal . A least-squares algorithm with normalization is used to es- timate the plant parameters by using two additional design tools, namely: 1) a modification of the parameter estimates and2) a relative adaptation dead-zone . The modification is based on the properties of the inverse of the least-squares covariance matrix and it uses an hysteresis switching function. In this way, the non-singularity of the controllability matrix of the estimated model of the plant is ensured. The relative dead-zone is used to turn off the adaptation process when an absolute augmented error is smaller than the value of an available overbounding function of the unmodelled dynamics contribution plus, eventually, bounded noise.