A new procedure to design parameter estimators with enhanced performance is proposed in the technical note. For classical linear regression forms, it yields a new parameter estimator whose convergence is established without the usual requirement of regressor persistency of excitation. The technique is also applied to nonlinear regressions with “partially” monotonic parameter dependence—giving rise again to estimators with enhanced performance. Simulation results illustrate the advantages of the proposed procedure in both scenarios.

Performance Enhancement of Parameter Estimators via Dynamic Regressor Extension and Mixing

Approximation with random bases

In this paper, we first address the uniformly exponential stability (UES) problem of a group of distributed cooperative adaptive systems in a general framework. Inspired by consensus theory, distributed cooperative adaptive laws are proposed to estimate the unknown parameters of these systems. It is shown that not only is the entire closed-loop system stable, but also both the identification/tracking error and the parameter estimation error converge to zero uniformly exponentially under a cooperative persistent excitation (PE) condition of a regressor matrix in each system which is weaker than the traditionally defined PE condition. The effects of network topology on UES of the closed-loop system are also explored. If the topology is time-invariant, it needs to be undirected and connected. However, when the topology is time-varying, it is just required that the integration of the topology over an interval with fixed length is undirected and connected. The established results are then employed to identify and control several classes of linearly parameterized systems. Simulation examples are also provided to demonstrate the effectiveness and applications of the proposed distributed cooperative adaptive laws.

https://dr.ntu.edu.sg/bitstream/10220/19304/1/Distributed%20cooperative%20adaptive%20identification%20and%20control.pdf

Distributed Cooperative Adaptive Identification and Control for a Group of Continuous-Time Systems With a Cooperative PE Condition via Consensus

A new framework to design adaptive controllers for nonlinearly parameterized systems is proposed in this technical note. The key step is the construction of a monotone mapping, which explicitly depends on some of the estimator tuning parameters. Convexity-that is related to monotonicity-has been explored by several authors. The property is assumed a priori and is useful for the design only in some region of state space, which is completed switching the controller. In our approach monotonicity can be used in the whole state space and, moreover, is enforced by the designer, effectively becoming a synthesis tool. One consequence of these features is that the controller does not rely on state-dependent switching. In order to dispose of degrees of freedom to render the function monotone we depart from standard adaptive control and adopt instead the recently introduced Immersion and Invariance approach.

Immersion and Invariance Adaptive Control of Nonlinearly Parameterized Nonlinear Systems

Adaptive observers and parameter estimation for a class of systems nonlinear in the parameters

We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the target set is nonequilibrium and in general unstable in the Lyapunov sense. Mathematical models of uncertainties are allowed to be nonlinearly parametrized, smooth, and monotonic functions of linear functionals of the parameters. We illustrate with applications how the proposed method leads to control algorithms. In particular we show that the mere existence of nonlinear operator gains for the desired dynamics guarantees that system solutions are bounded, reach a neighborhood of the target set, and mismatches between the modeled uncertainties and uncertainty compensator vanish with time. The proposed class of algorithms can also serve as parameter identification procedures. In particular, standard persistent excitation suffices to ensure exponential convergence of the estimated to the actual values of the parameters. When a weak, nonlinear version of the persistent excitation condition is satisfied, convergence is asymptotic. The approach extends to a broader class of parameterizations where the monotonicity restriction holds only locally. In this case excitation with oscillations of sufficiently high frequency ensure convergence.

Tyukin Ivan

Papers

Adaptation and Parameter Estimation in Systems with Unstable Target Dynamics and Nonlinear Parametrization