Global output tracking control of a class of Euler-Lagrange systems with monotonic non-linearities in the velocities

In this paper, we address the problem of output feedback tracking control of a class of Euler-Lagrange systems subject to non-linear dissipative loads. By imposing a monotone damping condition on the non-linearities of the unmeasured states, the common restriction that the non-linearities be globally Lipschitz is removed. The proposed observer-controller scheme renders the origin of the error dynamics uniformly globally asymptotically stable, in the general case. Under certain additional assumptions, the result continue to hold for a simplified control law that is less sensitive to noise and unmodelled phenomena.     

Feedback limitations in nonlinear systems: from Bode integrals tocheap control

Feedback limitations of nonlinear systems are investigated using the cheap control approach. The main result is that in the limit, when the control effort is free, the smallest achievable L₂ norm of the output is equal to the least amount of control energy (L₂ norm) needed to stabilize the unstable zero dynamics. This nonlinear result is structurally similar to an earlier linear result by Qiu and Davison (1993), which, in turn, is connected with a Bode-type integral derived by Middleton (1991)     

A corrective feedback design for nonlinear systems with fast actuators

Recent two-time-scale results can be derived from a geometric framework which allows further extensions and computational improvements. In this note the two-time scale behavior of singularly perturbed systems is exploited to design slow and fast controls and to combine them into a composite control. As an illustration, we present a corrective design to compensate for fast actuator dynamics modeled as singular perturbations.     

On vanishing stability regions in nonlinear systems with high-gain feedback

When local stabilization of nonlinear systems is achieved by linear feedback, the resulting stability region may vanish as the feedback gains increase. This is demonstrated by examples in which neglected nonlinearities create an unstable limit cycle around an asymptotically stable equilibrium. As the feedback gains tend to infinity the unstable limit cycle shrinks to the equilibrium. If a feedback linearization design is applied, the same instability mechanism may occur when the nonlinearities are not precisely known.     

Boundedness conjecture for an output error adaptive algorithm

This paper compares conditions for instability with conditions for global asymptotic stability of a discretetime output error adaptive estimation algorithm. This comparison leads to a boundedness conjecture which states that all signals within this adaptive system as well as the output error and parameter estimates remain globally bounded for all time despite any unstable behaviour. The investigation into the stability properties of this algorithm begins with a global stability criterion applied to a transfer function which is not strictly positive real. This criterion states that for large enough adaptation gain and/or input signal magnitude the system will be asymptotically stable. Then a local result is applied which states that for small enough adaptation gain and/or input signal magnitude the same system is unstable. The result is a bifurcation due to the decrease of the adaptation gain and/or input signal magnitude as the system goes from asymptotic stability to instability which remains bounded. The results suggested by the computer simulations are verified by an exact analysis of a linearized periodic version of the adaptive system.     

Path-following for nonminimum phase systems removes performance limitations

We highlight an essential difference between path-following and reference-tracking for nonminimum phase systems. It is well known that in the reference-tracking, for nonminimum phase systems, there exists a fundamental performance limitation in terms of a lower bound on the L/sub 2/-norm of the tracking error, even when the control effort is free. We show that this is not the case for the less stringent path-following problem, where the control objective is to force the output to follow a geometric path without a timing law assigned to it. Furthermore, the same is true even when an additional desired speed assignment is imposed.     

Adaptive output-feedback control of systems with outputnonlinearities

A direct model-reference adaptive control scheme, which requires only output, rather than full-state, measurement is presented for a class of single-input, single-output (SISO) nonlinear systems with unknown constant parameters. The nonlinearities are not required to satisfy any growth conditions. The assumptions on the linear part of the nonlinear system are the same as in the standard adaptive control problem for linear systems, which appears as a special case of the nonlinear problem that is solved     

Adaptive nonlinear output-feedback schemes with Marino-Tomeicontroller

Three new adaptive nonlinear output-feedback schemes are presented. The first scheme employs the tuning functions design. The other two employ a novel estimation-based design consisting of a strengthened controller-observer pair and observer-based and swapping-based identifiers. They remove restrictive growth and matching conditions present in the previous output-feedback nonlinear estimation-based designs and allow a systematic improvement of transient performance     

Adaptive automotive speed control

An adaptive algorithm for adjusting the gains of a vehicle speed control system is presented. By continuously adjusting the proportional-integral control gains, speed control performance can be optimized for each vehicle and operating condition. This helps the design of a single speed control module that does not need additional calibration or sacrifices in performance for certain car lines. It also allows improved performance for changing road conditions not possible with a fixed-gain control or other types of adaptive control. The results of initial vehicle testing confirm the performance improvements and robustness of the adaptive controller