Showing papers by "Petar V. Kokotovic published in 2008"

Observer-based stabilization of systems with monotonic nonlinearities

Abstract: We design an observer-based control law for a class of systems that include monotonic nonlinearities of the unmeasured states. Our observer results in nonlinear error dynamics which can be represented as the feedback interconnection of a linear system and a time-verying multivariable sector nonlinearity. The convergence of the estimation error is guaranteed by an observer matrix that renders the linear part passive, and is computable with LMI software. The feedback design is completed by combining the observer with a control law that renders the plant input-to-state stable with respect to the state estimation error.

Robust Nonlinear PI Control

Abstract: Thus far we have represented system uncertainty by a disturbance input w allowed to have an arbitrarily fast time variation. Its only constraint was the pointwise condition w ∈ W where W was some known set possibly depending on the state x and control u. We now address a more specific situation in which our system contains some uncertain nonlinearity φ(x). Suppose that all we know about φ is a set-valued map Φ(x) such that φ(x) ∈ Φ(x) for all x ∈ χ. We could assign w ≔ φ(x) and W(x) ≔ Φ(x) and proceed as in Chapters 3–6, but we would be throwing away a crucial piece of information about the uncertainty φ, namely, that φ(x) does not explicitly depend on time t. Our goal in this chapter is to illustrate how we can take advantage of this additional information to design less conservative robust controllers.

Trackability filtering for underactuated systems

Abstract: Underactuated systems are commonplace and present a challenge in designing tracking controllers. Foremost among these are vehicles, like passenger cars and aircraft. Such systems with more outputs than control inputs are not right invertible. As a result continuous control laws cannot, in general, be designed to track arbitrary reference signals. We present a trackable filter design which produces an augmented reference signal as close as possible to the original reference which the underactuated system can track with zero error. The resulting control law can be either discontinuous or continuous by the choice of the designer.

Set-Valued Maps

Abstract: In robust control theory, an uncertain dynamical system is described by a set of models rather than a single model. For example, a system with an unknown parameter generates a set of models, one for each possible value of the parameter; likewise for a system with an unknown disturbance (which can be a function of time as well as state variables and control inputs). As a result, any map one might define for a single model becomes a set-valued map. Such is the case with an input/output map, a map from initial states to final states, or a map from disturbances to values of cost functionals. It is therefore natural that, in our study of robust nonlinear control, we use the language and mathematical apparatus of set-valued maps. In doing so, we follow the tradition started in the optimal control literature in the early sixties [27, 153] and continued in the control-related fields of nonsmooth analysis, game theory, differential inclusions, and viability theory [21, 127, 128, 5, 79].

Robust Control Lyapunov Functions

Abstract: Significant advances in the theory of linear robust control in recent years have led to powerful new tools for the design and analysis of control systems. A popular paradigm for such theory is depicted in Figure 3.1, which shows the interconnection of three system blocks G, K, and Δ. The plant G relates a control input u and a disturbance input v to a measurement output y and a penalized output z. The control input u is generated from the measured output y by the controller K. All uncertainty is located in the block Δ which generates the disturbance input v from the penalized output z. The plant G, which is assumed to be linear and precisely known, may incorporate some nominal plant as well as frequency-dependent weights on the uncertainty Δ (for this reason G is sometimes called a generalized plant). Once G is determined, the robust stabilization problem is to construct a controller K which guarantees closed-loop stability for all systems Δ belonging to a given family of admissible (possibly nonlinear) uncertain systems.

Zero Dynamics and Tracking Performance Limits in Nonlinear Feedback Systems

Abstract: Summary. Among Alberto Isidori’s many seminal contributions, his solution of the nonlinear tracking problem and the underlying concept of zero dynamics have had the widest and strongest impact. Here we use these results to investigate and quantify the limit to tracking performance posed by unstable zero dynamics. While some aspects of this limit are nonlinear analogs of Bode’s T-integral formula, the dependence on the exosystem dynamics is an added complexity of nonlinear tracking.