We consider a class of systems influenced by perturbations that are nonlinearly parameterized by unknown constant parameters, and develop a method for estimating the unknown parameters within an arbitrarily large parameter space. The method applies to systems where the states are available for measurement, and perturbations with the property that an exponentially stable estimate of the unknown parameters can be obtained if the whole perturbation is known. The main contribution is to introduce a conceptually simple, modular design that gives freedom to the designer in accomplishing the main task, which is to construct an update law to asymptotically invert a nonlinear equation. Compensation for the perturbations in the system equations is considered for a class of systems with uniformly globally bounded solutions and for which the origin is uniformly globally asymptotically stable when no perturbations are present. We also consider the case when the parameters can only be estimated when the controlled state is bounded away from the origin, and show that we may still be able to achieve convergence of the controlled state. We illustrate the method through examples, and apply it to the problem of downhole pressure estimation during oil well drilling.

estimation and control for a class of

We propose a new method for the design of adaptation algorithms that guarantees a certain prescribed level of performance and applicable to systems with nonconvex parameterization. The main idea behind the method is two-fold. First, we augment the tuning error function and design the adaptation scheme in the form of ordinary differential equations. The resulting augmentation is allowed to depend on state derivatives. Second, we find a suitable realization of the designed adaptation scheme in an algebraic-integral form. Due to their explicit dependence on the state of the original system, such adaptation schemes are referred to as adaptive algorithms in finite form, in contrast to (conventional) algorithms in differential form. Sufficient conditions for the existence of finite form realizations are proposed. It is shown that our method to design algorithms in finite form is applicable to a broad class of nonlinear systems including systems with nonconvex parameterization and low-triangular systems.

Abstract: We consider adaptive control problem in presence of nonlinear parametrization of uncertainties in the model. It is shown that despite traditional approaches require for domination in the control loop during adaptation, it is not often necessary to use such energy inefficient compensators it in wide range of applications. In particular, we show that recently introduced adaptive control algorithms in finite form which are applicable to monotonic parameterized systems can be extended to general smooth non-monotonic parametrization. These schemes do not require any damping or domination in control inputs.

Abstract: A new framework for adaptive regulation to invariant sets is proposed. Reaching the target dynamics (invariant set) is to be ensured by state feedback while adaptation to parametric uncertainties is provided by additional adaptation algorithm. We show that for a sufficiently large class of nonlinear systems it is possible to adaptively steer the system trajectories to the desired non-equilibrium state without requiring knowledge or existence of a specific strict Lyapunov function.