Nonlinear approximation in control problems
Nonlinear bounded control for time-delay systems
A method to derive a nonlinear bounded state feedback controller for a linear continuous-time system with time-delay in the state is proposed. The controllers are based on an -parameterized family of algebraic Riccati equations or on an -parameterized family of LMI optimization problems. Hence, nested ellipsoidal neighborhoods of the origin are determined. Thus, from the Lyapunov–Krasovskii theorem, the uniform asymptotic stability of the closed-loop system is guaranteed and a certain performance...
Nonlinear control of a planar multiaxis servohydraulic test facility using exact linearization techniques
Nonlinear controller design of a ship autopilot
The main goal here is to design a proper and efficient controller for a ship autopilot based on the sliding mode control method. A hydrodynamic numerical model of CyberShip II including wave effects is applied to simulate the ship autopilot system by using time domain analysis. To compare the results similar research was conducted with the PD controller, which was adapted to the autopilot system. The differences in simulation results between two controllers are analyzed by a cost function composed...
Nonlinear diagnostic filter design: algebraic and geometric points of view
The problem of diagnostic filter design is studied. Algebraic and geometric approaches to solving this problem are investigated. Some relations between these approaches are established. New definitions of fault detectability and isolability are formulated. On the basis of these definitions, a procedure for diagnostic filter design is given in both algebraic and geometric terms.
Nonlinear feedback stabilization of a two-dimensional Burgers equation
In this paper, we study the stabilization of a two-dimensional Burgers equation around a stationary solution by a nonlinear feedback boundary control. We are interested in Dirichlet and Neumann boundary controls. In the literature, it has already been shown that a linear control law, determined by stabilizing the linearized equation, locally stabilizes the two-dimensional Burgers equation. In this paper, we define a nonlinear control law which also provides a local exponential stabilization of...
Nonlinear model predictive control of a boiler unit: A fault tolerant control study
This paper deals with a nonlinear model predictive control designed for a boiler unit. The predictive controller is realized by means of a recurrent neural network which acts as a one-step ahead predictor. Then, based on the neural predictor, the control law is derived solving an optimization problem. Fault tolerant properties of the proposed control system are also investigated. A set of eight faulty scenarios is prepared to verify the quality of the fault tolerant control. Based of different faulty...
Non-linear observer design method based on dissipation normal form
Observer design is one of large fields investigated in automatic control theory and a lot of articles have already been dedicated to it in technical literature. Non-linear observer design method based on dissipation normal form proposed in the paper represents a new approach to solving the observer design problem for a certain class of non-linear systems. As the theoretical basis of the approach the well known dissipative system theory has been chosen. The main achievement of the contribution consists...
Nonlinear observers for locally uniformly observable systems
This paper deals with the observability analysis and the observer synthesis of a class of nonlinear systems. In the single output case, it is known [4, 5, 6] that systems which are observable independently of the inputs, admit an observable canonical form. These systems are called uniformly observable systems. Moreover, a high gain observer for these systems can be designed on the basis of this canonical form. In this paper, we extend the above results to multi-output uniformly observable systems....
Nonlinear observers for locally uniformly observable systems
This paper deals with the observability analysis and the observer synthesis of a class of nonlinear systems. In the single output case, it is known [4-6] that systems which are observable independently of the inputs, admit an observable canonical form. These systems are called uniformly observable systems. Moreover, a high gain observer for these systems can be designed on the basis of this canonical form. In this paper, we extend the above results to multi-output uniformly observable systems....
Nonlinear observers in reflexive Banach spaces
On an arbitrary reflexive Banach space, we build asymptotic observers for an abstract class of nonlinear control systems with possible compact outputs. An important part of this paper is devoted to various examples, where we discuss the existence of persistent inputs which make the system observable. These results make a wide generalization to a nonlinear framework of previous works on the observation problem in infinite dimension (see [11, 18, 22, 26, 27, 38, 40] and other references therein).
Nonlinear observers in reflexive Banach spaces
On an arbitrary reflexive Banach space, we build asymptotic observers for an abstract class of nonlinear control systems with possible compact outputs. An important part of this paper is devoted to various examples, where we discuss the existence of persistent inputs which make the system observable. These results make a wide generalization to a nonlinear framework of previous works on the observation problem in infinite dimension (see [11,18,22,26,27,38,40] and other references therein).
Nonlinear perturbations of quasi-linear delay control systems
Nonlinear predictive control based on neural multi-models
This paper discusses neural multi-models based on Multi Layer Perceptron (MLP) networks and a computationally efficient nonlinear Model Predictive Control (MPC) algorithm which uses such models. Thanks to the nature of the model it calculates future predictions without using previous predictions. This means that, unlike the classical Nonlinear Auto Regressive with eXternal input (NARX) model, the multi-model is not used recurrently in MPC, and the prediction error is not propagated. In order to...
Nonlinear robust hierarchical control for nonlinear uncertain systems.
Nonlinear stabilization by adding integrators
Nonlinear state observers and extended Kalman filters for battery systems
The focus of this paper is to develop reliable observer and filtering techniques for finite-dimensional battery models that adequately describe the charging and discharging behaviors. For this purpose, an experimentally validated battery model taken from the literature is extended by a mathematical description that represents parameter variations caused by aging. The corresponding disturbance models account for the fact that neither the state of charge, nor the above-mentioned parameter variations...
Nonlinear system identification using heterogeneous multiple models
Multiple models are recognised by their abilities to accurately describe nonlinear dynamic behaviours of a wide variety of nonlinear systems with a tractable model in control engineering problems. Multiple models are built by the interpolation of a set of submodels according to a particular aggregation mechanism, with the heterogeneous multiple model being of particular interest. This multiple model is characterized by the use of heterogeneous submodels in the sense that their state spaces are not...
Nonlinear time-varying spectral analysis: HHT and MODWPT.
Nonlocal Cauchy problems and their controllability for semilinear differential inclusions with lower Scorza-Dragoni nonlinearities
In this paper we prove the existence of mild solutions and the controllability for semilinear differential inclusions with nonlocal conditions. Our results extend some recent theorems.