Output Regulation of Uncertain Nonlinear Systems

Harmonic internal models for structurally robust periodic output regulation

This paper studies a robust output regulation problem with nonlinear exosystems without the assumption that the solution to the regulator equations along the trajectory of the exosystems should be polynomial. Based on the extended concepts of steady-state generator and internal model, a set of sufficient conditions for the solvability of the problem are given. Thus, the result developed in this paper can allow the robust output regulation problem with nonlinear exosystems to accommodate much more general nonlinear given plants including those which contain nonpolynomial nonlinearity.

This paper formulates a robust output regulation problem for a linear timeinvariant system with uncertain parameters whose controlled output may be different from the measurement output. Conditions for solvability of the problem are given and two algorithms are presented for designing controllers that achieve robust output regulation; each of them consists of a proportional plus integral regulator and a proportional plus integral observer. It turned out that the regulator is a state feedback controller that achieves output regulation and the observer is an unknown input observer for a system with either fictitious exogenous input or fictitious controlled output.

This paper deals with the problem of robust tracking and disturbance rejection for a linear time-invariant system where the uncertainty of the system is represented in a structured form and the output to be controlled may be different from the measurement output. First, the problem is considered in a rather classical setting in that the required property of tracking and disturbance rejection can be attained as long as the resulting closed-loop system remains stable. Conditions for solvability of the problem are given and two algorithms are presented for designing controllers having the robust tracking and disturbance rejection property. Second, the problem of robust output regulation with robust stability is formulated as one of finding a controller such that the resulting closed-loop system satisfies an additional requirement of robust stability and thus the output regulation property can be maintained for all perturbations of uncertain parameters within a prescribed set. A procedure based on a high gain observer approach is proposed to solve this problem.

Adaptive wavelet output regulation for nonlinear systems

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 article investigates the robust optimal output regulation problem for the constrained uncertain nonlinear systems. A two‐step design framework is proposed to overcome the difficulties brought by uncertainties, constraint and performance optimization. First, the feedforward controller is designed by the internal model principle, and the robust output regulation problem is transformed into the robust stabilization problem. Then, the optimal control problem with input saturation is further considered in the robust feedback controller design process. With the help of a non‐quadratic cost functional, actor‐critic algorithm and robust redesign technique are brought together to design the constrained robust optimal feedback controller. Finally, stability analysis based on Lyapunov method shows that all the signals of the closed‐loop system remain bounded, and the tracking error is uniformly ultimately bounded with arbitrarily small ultimate bound. Simulation results illustrate the effectiveness of the proposed methodology.

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.

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.

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.

Output regulation aims to achieve, in addition to closed-loop stability, asymptotic tracking and disturbance rejection for a class of reference inputs and disturbances. Thus, it poses a more challenging problem than stabilization. For over a decade, the nonlinear output regulation problem has been one of the focuses in nonlinear control research, and active research on this problem has generated many fruitful results. Nevertheless, there are two hurdles that impede the further progress of the research on the output regulation problem. The first one is the assumption that the solution or the partial solution of the regulator equations is polynomial. The second one is the lack of a systematic mechanism to handle the global robust output regulation problem. We establish a general framework that systematically converts the robust output regulation problem for a general nonlinear system into a robust stabilization problem for an appropriately augmented system. This general framework, on one hand, relaxes the polynomial assumption, and on the other hand, offers a greater flexibility to incorporate recent new stabilization techniques, thus setting a stage for systematically tackling the robust output regulation with global stability.

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.

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.

Formation control for nonlinear multi-agent systems by robust output regulation