Stefano Battilotti

Robust stabilization of nonlinear systems with pointwise norm-bounded uncertainties: a control Lyapunov function approach

The authors give a necessary and sufficient condition for globally stabilizing a nonlinear system, robustly with respect to unstructured uncertainties /spl Phi//spl tilde/(u,x,t), norm-bounded for each fixed x and u. This condition requires one to find a smooth, proper, and positive definite solution V(x) of a suitable partial differential inequality depending only on the system data. A procedure, based on the knowledge of V(x), is outlined for constructing almost smooth robustly stabilizing controllers. Our approach, based on Lyapunov functions, generalizes previous results for linear uncertain systems and establishes a precise connection between robust stabilization, on one hand, and H/sub /spl infin//-control sector conditions and input-to-state stabilization on the other.

A unifying framework for the semiglobal stabilization of nonlinear uncertain systems via measurement feedback

We study the problem of semiglobally stabilizing an uncertain nonlinear system consisting of a linear nominal system perturbed by either nonlinearities or model uncertainties. Our approach relies on well-known H/sub /spl infin// linear control tools and allows one to recover and improve, in the unifying framework of a semiglobal separation result, existing results on the semiglobal stabilization via output feedback. In particular, we discuss the case of uncorrupted outputs, input and output nonlinearities, or model uncertainties, which may include, for example, practical situations such as backlash, hysteresis, and saturations. The key feature of our design procedure is given by the choice of two continuous functions: the first one is instrumental in constructing a stabilizing controller; the second one arises in the candidate Lyapunov function for the closed-loop system. Relying on our main theorem, we give general tools for achieving large regions of attraction via bounded measurement feedback for a wide class of nonlinear uncertain interconnected systems.

Global set point control via link position measurement for flexible joint robots

Abstract In this paper it is shown that a linear controller solves the global set point control problem for a flexible joint robot via link position measurements. Moreover, the controller is shown to be robust with respect to uncertainties in the gravity term.

Robust output feedback control of nonlinear stochastic systems using neural networks

We present an adaptive output feedback controller for a class of uncertain stochastic nonlinear systems. The plant dynamics is represented as a nominal linear system plus nonlinearities. In turn, these nonlinearities are decomposed into a part, obtained as the best approximation given by neural networks, plus a remaining part which is treated as uncertainties, modeling approximation errors, and neglected dynamics. The weights of the neural network are tuned adaptively by a Lyapunov design. The proposed controller is obtained through robust optimal design and combines together parameter projection, control saturation, and high-gain observers. High performances are obtained in terms of large errors tolerance as shown through simulations.

Semiglobal Stabilization of Uncertain Block-Feedforward Systems Via Measurement Feedback

Abstract We study the problem of semiglobally stabilizing a class of feedforward uncertain nonlinear system via measurement feedback. We improve the existing results in several directions: we allow for uncertain outputs and block state equations. Moreover, contrary to the classical literature, our procedure strongly relies on H ∞ tools and backstepping, does not require any preliminary change of coordinates, ends up with a quadratic Lyapunov function for the closed-loop system and results in a nonsaturated linear controller.

Tracking with disturbance attenuation for rigid robots

In this paper a tracking controller for rigid robots is presented solving a disturbance attenuation problem with global internal stability in the general case of unknown constant parameters. By using the well-known property of linearity in the parameters for the rigid robot dynamic equations, adaptive and H/sub /spl infin// control are combined successfully. Simulation results show a good behavior of the proposed tracking controller.

Stabilization in probability of nonlinear stochastic systems with guaranteed region of attraction and target set

We deal with nonlinear dynamical systems, consisting of a linear nominal part perturbed by model uncertainties, nonlinearities and both additive and multiplicative random noise, modeled as a Wiener process. In particular, we study the problem of finding suitable measurement feedback control laws such that the resulting closed-loop system is stable in some probabilistic sense. To this aim, we introduce a new notion of stabilization in probability, which is the natural counterpart of the classical concept of regional stabilization for deterministic nonlinear dynamical systems and stands as an intermediate notion between local and global stabilization in probability. This notion requires that, given a target set, a trajectory, starting from some compact region of the state space containing the target, remains forever inside some larger compact set, eventually enters any given neighborhood of the target in finite time and remains thereinafter, all these events being guaranteed with some probability. We give a Lyapunov-based sufficient condition for achieving stability in probability and a separation result which splits the control design into a state feedback problem and a filtering problem. Finally, we point out constructive procedures for solving the state feedback and filtering problem with arbitrarily large region of attraction and arbitrarily small target for a wide class of nonlinear systems, which at least include feedback linearizable systems. The generality of the result is promising for applications to other classes of stochastic nonlinear systems. In the deterministic case, our results recover classical stabilization results for nonlinear systems.

Brief A new separation result for a class of quadratic-like systems with application to Euler-Lagrange models

A separation result for some kind of global stabilization via output feedback of a class of nonlinear systems, under the form of some stabilizability by state feedback on the one hand, and some unboundedness observability on the other hand is presented. They allow to design, for any domain of output initial condition, some dynamic output feedback controller achieving global stability. It is also highlighted how disturbance attenuation can further be achieved on the same basis. As an example, the proposed conditions are shown to be satisfied by the class of so-called Euler-Lagrange systems, for which a tracking output feedback control law is thus proposed.

Robust output feedback stabilization via a small gain theorem

SUMMARY In this paper, we give suƒcient conditions for designing robust globally stabilizing controllers for a class of uncertain systems, consisting of ‘nominal’ nonlinear minimum phase systems perturbed by uncertainties which may a⁄ect the equilibrium point of the nominal system (‘biased’ systems). The constructive proof combines a systematic step-by-step procedure, based on H = arguments, with a small gain theorem, recently proved for nonliner systems. At each step, one finds two Lyapunov functions, one for a state-feedback problem and the other one for an output injection problem. Combining these two functions, one derives at each step a Lyapunov function candidate for solving an ouptut feedback stabilization problem. This approach allows one to put into a unified framework many existing results on robust output feedback stabilization. ( 1998 John Wiley & Sons, Ltd.

Control over a communication channel with random noise and delays

We study the problem of controlling a general class of nonlinear systems through a memoryless channel with constant delay. The remote controller receives the delayed measurements from the controlled plant and transmits back to the plant a control law, designed according to a certainty equivalence strategy. The closed-loop system trajectories are convergent to zero in probability and square integrable, despite the presence of uncertainties and square integrable noise.