Hamilton-Jacobi-Bellman theory is shown to provide a unified framework for nonlinear feedback control laws for special classes of nonlinear systems. These classes include Jurdjevic-Quinn type systems, as well as minimum phase systems with relative degree {1, 1 . . . . . 1}. Several examples are given to illustrate these results. For the controlled Lorenz equation, results obtained by Vincent an...

We consider the construction of adaptive controllers for minimum phase linear systems which achieve non-zero robustness margins in the sense of the (linear) L2[0,∞) gap metric. The gap perturbations may be more constrained for larger disturbances and for larger parametric uncertainty. Working within the framework of the nonlinear gap metric [3], universal adaptive controllers are first given ac...

We present results on omega-limit sets and minimum phase zero dynamics for hybrid dynamical systems. Moreover, we give pointers to how these results may be useful in the future for solving the output regulation problem for hybrid systems. We highlight the main attributes of omega-limit sets and we show, under mild conditions, that they are asymptotically stable. We define a minimum phase notion...

For input nonaffine nonlinear control systems, the minimum phase property of the system in general depends on the control law. Switching or discontinuous controllers may offer advantages in this context. In particular, there may not exist a continuous control law which would keep the output identically equal to zero and for which the zero output constrained dynamics are locally stable, whereas ...

Form-input, m-output, finite-dimensional, linear systems satisfying the classical assumptions of adaptive control (i.e., (i) minimum phase, (ii) relative degree one and (iii) “positive” highfrequency gain), it is well known that the adaptive λ-tracker ‘u = −k e, k̇ = max{0, |e|−λ}|e|’ achieves λ-tracking of the tracking error e if applied to such a system: all states of the closedloop system are...

In this paper we prove that the same design method of constant controllers for a delay systems given in the literature can be used to stabilize a minimum phase systems with nonlinearly correlated perturbations in the coefficients. This type of perturbation is induced by the composition with strictly positive real functions. This result can also be interpreted on the context of simultaneous and ...

The paper presents a new tracking control approach for a class of non-minimum phase linear systems. The proposed approach consists of two parts: trajectory planning and tracking controller design. The trajectory planning is solved as an optimization problem to improve the achievable transient performance under the fundamental constraints associated with perfect tracking of non-minimum phase sys...

In the subject paper @Alku and Vilkman, J. Acoust. Soc. Am. 98, 763–767 ~1995!; hence AV#, AV describe the results of their research on the effect of bandwidth on estimated voice source parameters. They found that reducing the bandwidth ~by low-pass filtering the glottal flow signals! leads to a distortion of the estimated parameters. Although I do agree that low-pass filtering influences the e...

We consider a class of minimum-phase non-linear systems with large parametric uncertainties. The non-linear dynamics is assumed to be linearly parameterized in terms of the unknown parameters. A novel scheme which utilizes multiple models in a model reference adaptive control (MRAC) framework is proposed to improve the transient performance of the adaptive scheme. The proposed approach makes us...

We study the class of linear differential-algebraic m-input m-output systems which have a transfer function with proper inverse. A sufficient condition for the transfer function to have proper inverse it that the system has ‘strict and non-positive relative degree’. We present two main results: First, a so called ‘zero dynamics form’ is derived: this form is – within the class of system equival...