On self-learning mechanism for the output regulation of second-order affine nonlinear systems

This paper studies global robust output regulation of second-order nonlinear systems with input disturbances that encompass the fully-actuated Euler-Lagrange systems. We assume the availability of relative output (w.r.t. a family of reference signals) and output derivative measurements. Based on a specific separation principle and self learning mechanism, we develop an internal model-based controller that does not require apriori knowledge of reference and disturbance signals and it only assumes that the kernels of these signals are a family of exosystems with unknown parameters (e.g., amplitudes, frequencies or time periods). The proposed control framework has a self-learning mechanism that extricates itself from requiring absolute position measurement nor precise knowledge of the feedforward kernel signals. By requiring the high-level task/trajectory planner to use the same class of kernels in constraining the trajectories, the proposed low-level controller is able to learn the desired trajectories, to suppress the disturbance signals, and to adapt itself to the uncertain plant parameters. The framework enables a plug-and-play control mechanism in both levels of control

A nonparametric learning framework for nonlinear robust output regulation

This paper proposes a nonparametric learning solution framework for a generic internal model design of nonlinear robust output regulation. The global robust output regulation problem for a class of nonlinear systems with output feedback subject to a nonlinear exosystem can be tackled by constructing a linear generic internal model, provided that a continuous nonlinear mapping exists. An explicit continuous nonlinear mapping was constructed recently in [1] under the assumption that the steady-state generator is linear in the exogenous signal. We further relax such an assumption to a relaxed assumption that the steady-state generator is polynomial in the exogenous signal. A nonparametric learning framework is proposed to solve a linear time-varying equation to make the nonlinear continuous mapping always exist. With the help of the proposed framework, the nonlinear robust output regulation problem can be converted into a robust non-adaptive stabilization problem for the augmented system with integral Input-to-State Stable (iISS) inverse dynamics. Moreover, a dynamic gain approach can adaptively raise the gain to a sufficiently large constant to achieve stabilization without requiring any a priori knowledge of the uncertainties appearing in the dynamics of the exosystem and the system. We further apply the nonparametric learning framework to globally reconstruct and estimate multiple sinusoidal signals with unknown frequencies without using adaptive techniques. An explicit nonlinear mapping can directly provide the estimated parameters, which will exponentially converge to the unknown frequencies. As a result, a feedforward control design is proposed to solve the output regulation using our nonparametric learning framework.Comment: 15 pages; Nonlinear control; iISS stability; output regulation; parameter estimation; Non-adaptive contro

Synchronization of Nonlinear Circuits in Dynamic Electrical Networks with General Topologies

Sufficient conditions are derived for global asymptotic synchronization in a system of identical nonlinear electrical circuits coupled through linear time-invariant (LTI) electrical networks. In particular, the conditions we derive apply to settings where: i) the nonlinear circuits are composed of a parallel combination of passive LTI circuit elements and a nonlinear voltage-dependent current source with finite gain; and ii) a collection of these circuits are coupled through either uniform or homogeneous LTI electrical networks. Uniform electrical networks have identical per-unit-length impedances. Homogeneous electrical networks are characterized by having the same effective impedance between any two terminals with the others open circuited. Synchronization in these networks is guaranteed by ensuring the stability of an equivalent coordinate-transformed differential system that emphasizes signal differences. The applicability of the synchronization conditions to this broad class of networks follows from leveraging recent results on structural and spectral properties of Kron reduction---a model-reduction procedure that isolates the interactions of the nonlinear circuits in the network. The validity of the analytical results is demonstrated with simulations in networks of coupled Chua's circuits

On the Minimization of Maximum Transient Energy Growth.

The problem of minimizing the maximum transient energy growth is considered. This problem has importance in some fluid flow control problems and other classes of nonlinear systems. Conditions for the existence of static controllers that ensure strict dissipativity of the transient energy are established and an explicit parametrization of all such controllers is provided. It also is shown that by means of a Q-parametrization, the problem of minimizing the maximum transient energy growth can be posed as a convex optimization problem that can be solved by means of a Ritz approximation of the free parameter. By considering the transient energy growth at an appropriate sequence of discrete time points, the minimal maximum transient energy growth problem can be posed as a semidefinite program. The theoretical developments are demonstrated on a numerical example

Repetitive Control for Lur'e-Type Systems:Application to Mechanical Ventilation

Repetitive control (RC) has shown to achieve superior rejection of periodic disturbances. Many nonlinear systems are subject to repeating disturbances. The aim of this article is to develop a continuous-time RC design with stability guarantees for nonlinear Lur'e-type systems. Approximate output tracking is achieved by combining an internal model, consisting of a finite number of linear oscillators with frequencies at the reference frequency and at its multiples, with a stabilizer that guarantees a convergence property of the closed-loop system. The developed RC approach is applied to a nonlinear mechanical ventilation system for intensive care units (ICUs), which can be modeled as a Lur'e-type system. The experimental study confirms that the RC scheme is able to successfully follow the desired target pressure profile to properly support the ventilation needs of an adult patient.</p

Uniform Practical Nonlinear Output Regulation

International audienceIn this paper, we present a solution to the problem of asymptotic and practical semiglobal regulation by output feedback for nonlinear systems. A key feature of the proposed approach is that practical regulation is achieved uniformly with respect to the dimension of the internal model and to the gain of the stabilizer near the zero error manifold. This property renders the approach interesting for a number of real cases by bridging the gap between output regulation theory and advanced engineering applications. Simulation results regarding meaningful control problems are also presented