Adaptive wavelet output regulation for nonlinear systems

Many mechanical systems are subjected to periodic disturbances which may adversely influence control performance. When the plants are nonlinear systems with unknown parameters, this disturbance compensation problem has been considered as adaptive output regulation problem. This paper discusses the problem about adaptive output regulation for nonlinear systems with arbitrary relative degree, which can be transformed into the output feedback form. The nonlinear plant is affected by unknown constant parameters and periodic disturbances with unknown frequencies, magnitudes and phases. The periodic disturbances are considered as signals generated from a linear time invariant exosystem. It is not assumed that the disturbances meet the matching condition for the control input. The design method of the adaptive controller and its parameter update law is based on adaptive backstepping manner for the coordinates-changed extended system, which is generated from the nonlinear plant and the exosystem. Then, it can be achieved that the output asymptotically converges to the output reference and that all signals in the closed-loop system are bounded.

Introduction: the basic ingredients of asymptotic output regulation the computation of the steady-state response highlights of output regulation for linear systems. Output regulation of nonlinear systems: the regulator equations the internal model necessary and sufficient conditions for local output regulation the special case of harmonic exogenus inputs approximate regulation. Existence conditions for regulator equations: linear regulator equations and transmission zeros the zero dynamics of a nonlinear system existence of solutions of the nonlinear regulator equations. Robust output regulation: structurally stable local regulation robust local regulation the special case of systems in triangular form a globally defined error-zeroing invariant manifold semiglobal robust regulation.

This paper deals with consensus output regulation of a class of network-connected nonlinear systems with unknown parameters. The subsystem may have different dynamics with uncertainties, and under the disturbances generated from an exosystem, and only some subsystems have access to the desired output, which is also formulated as an output of the exosystem, following the standard formulation of output regulation of nonlinear systems. For the clarity of the presentation, we only show the control design of the systems with 2nd-order dynamics. The proposed design makes use of some latest results on Laplacian matrices, and a new design of the internal model, which is based on known functions with unknown constant parameters. Adaptive backstepping design techniques are integrated with the consensus control design to tackle the nonlinearity and unknown constant parameters in the system, and unknown functions relating to the state of the exosystem. The proposed control inputs and adaptive laws are fully decentralized, and ensure the asymptotic convergence to zero of the regulation errors.

In this paper, the formation control problem of unmanned surface vehicles (USVs) is investigated. Unlike the classical formation control problem where the reference signal is required to be second-order differentiable with respect to time, we consider a more general autonomous dynamic system as the reference system. A novel adaptive fuzzy output regulation approach is presented to solve the formation control problem, where a set of regulator equations using only approximation information and a distributed observer are constructed to obtain the feedforward information of the reference system. Based upon this, a distributed adaptive fuzzy control law is designed by using the backstepping technique. It is shown that USVs can effectively achieve the desired formation with the tracking error being adjusted as small as possible. Simulation studies demonstrate that the proposed formation control law is effective and efficient.

This paper studies the problem of adaptive optimal output regulation for discrete-time linear systems. A data-driven output-feedback control approach is developed via approximate/adaptive dynamic programming (ADP). Different from the existing literature of ADP and output regulation theory, the optimal controller design proposed in this paper does not require the knowledge of the plant and exosystem dynamics. Theoretical analysis and an application on an inverted pendulum system show that the proposed methodology serves as an effective tool for solving adaptive optimal output regulation problems.

This article develops a robust adaptive boundary output regulation approach for a class of complex anticollocated hyperbolic partial differential equations subjected to multiplicative unknown faults in both the boundary sensor and actuator. The regulator design is based on the internal model principle, which amounts to stabilize a coupled cascade system, which consists of a finite-dimensional internal model driven by a hyperbolic distributed parameter system (DPS). To this end, a systematic sliding mode equipped with a backstepping approach is developed such that the robust state feedback control can be realized. Moreover, since the available information is a faulty boundary measurement at the right side point, state estimation is required. However, due to the presence of boundary unknown faults, we need to solve an issue of joint fault-state estimation. Restrictive persistent excitation conditions are usually required to guarantee the exact estimation of faults but are unrealistic in practice. To this end, a novel concurrent learning (CL) adaptive observer is proposed so that exponential convergence is obtained. It is the first time that the spirit of CL is introduced to the field of DPSs. Consequently, the observer-based adaptive boundary fault tolerant control scheme is developed, and rigorous theoretical analysis is given such that the exponential output regulation can be achieved. Finally, the effectiveness of the proposed methodology is demonstrated via comparative simulations.

This article presents a global adaptive asymptotic tracking control method, capable of guaranteeing prescribed transient behavior for uncertain strict-feedback nonlinear systems with arbitrary relative degree and unknown control directions. Unlike most existing funnel controls that are built upon time-varying feedback gains, the proposed method is derived from a tracking error-dependent normalized function and a barrier function, together with a time-varying scaling transformation, leading to an improved prescribed performance control solution with the following features: 1) the developed control is embedded with normalized error based adaptive parameter tuning and is able to ensure asymptotic tracking; 2) given transient performance is guaranteed in that the tracking error preserves in the prescribed boundary for <inline-formula><tex-math notation="LaTeX">$\forall t\geq 0$</tex-math></inline-formula>; and 3) it is able to cope with nonlinear systems with arbitrary relative degree, mismatched uncertainties, and unknown control directions. Both theoretical analysis and numerical simulations verify the effectiveness and benefits of the proposed method.

A preliminary analysis of the local regulator problem is presented. It is then demonstrated that it is possible to isolate the main ingredients of a global solution to the output regulation problem. The authors then summarize some recent advances in the design of globally stabilizing feedback laws that were made possible by suitable use of the notion of passivity and, in particular, by the solution to the problem of when a given nonlinear system can be rendered passive via state feedback. Some of the results obtained are applied to the problem of deriving globally/asymptotically stabilizing feedback laws for certain classes of nonlinear systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper addresses the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> output regulation problem of affine nonlinear systems with unmeasurable states and completely unknown dynamics. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> output regulation problem is formulated into a two-player zero-sum differential game problem with the control input and disturbance being the two adversary players. A model-based global state- feedback optimal solution to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> output regulation problem is presented by solving a Hamilton-Jacobi-Isaacs (HJI) equation, and a state- feedback reinforcement learning (RL) algorithm is proposed to solve the HJI equation without knowledge of system dynamics. A linear data-driven observer is designed to estimate the unmeasurable states and a novel output- feedback RL algorithm is developed based on the state- feedback RL framework by employing a critic-actor-disturbance neural network (NN) with a hidden layer. The salient found of this work is that, under the proposed output- feedback RL algorithm, the closed-loop system can reach globally stable. A numerical example is provided to demonstrate the effectiveness of the proposed solution.

In this paper, we propose a new method for modeling and output regulation of nonlinear systems with disturbance noises. We can get a semi-global error system between a real plant and a simplified model as a LPV system with two-step system identification method including L0-quasi norm minimizing sparse algorithm. LPV error system can produce compensating input for conventional homogeneous output feedback law, which enables us to release the assumption which isn't satisfied by the real plant, and globally regulate the real plant without its detail information. Furthermore, we propose a new nonlinear filtering method for the output feedback. We conventionally use Unscented Kalman Filter (UKF) which can't reduce non-Gaussian noise effect to nonlinear systems effectively. Instead UKF, we propose Robust Unscented Kalman Filter (RUKF). This filter consists of UKF and Robust Kalman Filtering algorithm using L1 optimization. RUKF can handle non-Gaussian, especially outlier of measurement value, which causes homogeneous output feedback to diverge. We confirm the effectiveness of this method with numerical simulations.

A relation between the output regulation and the observer design for nonlinear systems

In this paper, we deal with an output regulation for nonlinear systems. Especially, when it comes to the output feedback control problem for nonlinear systems, it would be difficult to solve. From a practical point of view, it is an important issue to design a feedback controller using only output information. We introduce a certain kind of optimal inverse system for the output feedback control design. The optimal inverse system is a new concept. With the optimal inverse system, we obtain feedback controllers using only output information. In the proposed method, Genetic Programming (GP) also plays a key role. We utilize the GP's emergent ability for the control design. However, it is known that GP requires a lot of computation for evaluation of the individuals. The high computation load is one of the obstacles in the GP based control design. We adopt the so-called efficient GP, which is suitably modified for control design methods. Finally, some simulation results are given to demonstrate the effectiveness of the proposed control design.

This paper studies the semi-global output regulation problem for a class of nonlinear systems in the normal form under disturbances generated from nonlinear exosystems. By using a circle criterion and high gain design technique, a new nonlinear internal model is proposed to deal with the nonlinearities of the exosystems and to generate the desired input term for output regulation. It is shown that the proposed partial-state feedback control method ensures the semi-global convergence of the regulated variable.

Harmonic internal models for structurally robust periodic output regulation

In this paper, we extend to the case of higher relative degree and uncertain high-frequency gain a recently proposed method for the solution of problems of output regulation for nonlinear systems. The method is applicable to systems with possibly unstable zero dynamics, in which case the problem at issue is addressed by rendering an appropriate auxiliary system stable, with a constrain on the gain. The dynamics of this auxiliary system only depend on the zero dynamics of the controlled plant, while the constraint on the gain only depends on some parameters of the exogenous input which have to be tracked.