Alberto Isidori

Linearization by output injection and nonlinear observers

Observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection. Necessary and sufficient conditions for the existence of such a transformation are given.

Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems

Conditions under which a nonlinear system can be rendered passive via smooth state feedback are derived. It is shown that, as in the case of linear systems, this is possible if and only if the system in question has relative degree one and is weakly minimum phase. It is proven that weakly minimum phase nonlinear systems with relative degree one can be globally asymptotically stabilized by smooth state feedback, provided that suitable controllability-like rank conditions are satisfied. This result incorporates and extends a number of stabilization schemes recently proposed for global asymptotic stabilization of certain classes of nonlinear systems. >

Adaptive control of linearizable systems

The authors give some initial results on the adaptive control of minimum-phase nonlinear systems which are exactly input-output linearizable by state feedback. Parameter adaptation is used as a technique to make robust the exact cancellation of nonlinear terms, which is called for in the linearization technique. The application of the adaptive technique to control of robot manipulators is discussed. Only the continuous-time case is considered; extensions to the discrete-time and sampled-data cases are not obvious. >

Nonlinear decoupling via feedback: A differential geometric approach

The paper deals with the nonlinear decoupling and noninteracting control problems. A complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems. The paper also includes algorithms concerned with the actual construction of the appropriate control laws.

Semi-global nonlinear output regulation with adaptive internal model

We address the problem of output regulation for nonlinear systems driven by a linear, neutrally stable exosystem whose frequencies are not known a priori. We present a classical solution in terms of the parallel connection of a robust stabilizer and an internal model, where the latter is adaptively tuned to the device that reproduces the steady-state control necessary to maintain the output-zeroing condition. We obtain robust regulation (i.e. in presence of parameter uncertainties) with a semi-global domain of convergence for a significant class of nonlinear minimum-phase system.

Asymptotic stabilization of minimum phase nonlinear systems

How a class of multivariable nonlinear systems can be stabilized about an equilibrium via smooth state feedback is shown. More precisely, conditions under which, for every compact set of initial states, it is possible to design a feedback law which drives to the equilibrium all initial states in this compact set are described. The theory includes the development of globally defined transformations of the system equations to their global normal form. >

Nonlinear feedback in robot arm control

Nonlinear feedback control is proposed for implementation of an advanced dynamic control strategy for robot arms. Using differential geometric system theory we obtained necessary and sufficient conditions for the existence of a nonlinear feedback control for a general nonlinear system to be externally linearized and simultaneously output decoupled. An algorithm is given for the construction of the required nonlinear feedback. To design a dynamic control for robot arms we apply the above result to the JPL-Stanford arm and propose a new control strategy, which also contains an optimal error-correcting feedback. Simulation results show great promise for the obtained dynamic control strategy.

New results and examples in nonlinear feedback stabilization

Using the general methodology of nonlinear zero dynamics we derive globally stabilizing state feedback laws for broad classes of nonlinear systems. While it is tempting to reinterpret this design philosophy in terms of high gain feedback, we present an example of a globally stabilizable nonlinear feedback system which cannot be stabilized, even locally, by any output feedback law - in particular, by a high gain law.

H/sub /spl infin control via measurement feedback for general nonlinear systems

This paper shows how the problem of (local) disturbance attenuation via measurement feedback, with internal stability, can be solved for a nonlinear system of rather general structure. The solution of the problem is shown to be related to the existence of solutions of a pair of Hamilton-Jacobi inequalities in n independent variables, which are associated with state-feedback and, respectively, output-injection design. >

On the attitude stabilization of rigid spacecraft

Abstract In this paper, we settle in the negative a longstanding problem concerning the existence of a smooth (static or dynamic) state variable feedback law locally asymptotically stabilizing a rigid spacecraft with two controls about a desired reference attitude. Modelling a spacecraft actuated by three thruster jets, one of which has failed, this well studied system is known to be locally reachable and locally asymptotically null controllable. We obtain our result as a corollary of a surprising result which asserts, for a class of nonlinear systems containing several examples of interest, that such a system is locally asymptotically stabilizable precisely when it can be linearized via state feedback transformations. We give a further result on the instability (in the sense of Lyapunov) of rigid spacecraft for certain feedback laws, but we are able to construct a feedback law locally asymptotically driving the closed-loop trajectories to a motion about the third principal axis. This law is derived using general principles comprising a nonlinear enhancement of root-locus design principles.