Genetic programming based output regulation via optimal inversion for nonlinear systems

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.

In this paper, an on-line adaptive dynamic programming (ADP) algorithm is presented to solve the optimal control problem for continuous-time nonlinear systems with control constraints. First, a suitable non-quadratic performance function is introduced to confront control constraints, and then we present an on-line ADP algorithm in which dynamic programming techniques and neural networks are used to solve the optimal control problem for nonlinear systems with control constraints, which is completely different with the traditional ADP algorithm using off-line training, and the corresponding convergence proof is given. Finally, a simulation examples is given to demonstrate the convergence and feasibility of the proposed algorithm.

The current theory of nonlinear systems is still not perfect. The modeling and control of nonlinear system problem has always been the difficulty. In a variety of methods of its study, fuzzy system theory because of having the language descriptive way similar to the human mind, can obtain and deal with the qualitative information intelligently. The theory itself also has non-linear characteristics. Therefore the use of fuzzy systems theory to establish the fuzzy model of nonlinear system can well describe the nonlinear characteristics. T-S fuzzy systems, due to the combination of the good performance of the fuzzy system to deal with nonlinear problems with the simple linear expressions, are not only suitable for modeling the nonlinear system, but also use T-S fuzzy model and the linear control theory method to design the controller. So it has been widely used in nonlinear system control problems, and has also greatly developed the T-S fuzzy system theory, appearing a lot of methods of structural and parameter identification. However, this study of T-S fuzzy rules makes us have to face the difference of different ways to select the number of rules as well as online self-adaptability of the number of rules which off-line method lacks when using T-S fuzzy model to deal with nonlinear system modeling and control problem. In view of this, this paper researches on modeling and controlling of complex nonlinear systems based on TS model from different perspectives.

Markovian jumping systems have arisen naturally in the mathematical modeling of phenomena spanning disciplines in the social sciences, natural sciences, and engineering. This kind of stochastic dynamical systems can be employed to model the dynamics when parameters are subject to random abrupt changes due to sudden environment changes, subsystem switching, system noises, executor faults, and so forth. Much attention has been given to modeling, optimization, and real applications of such stochastic dynamical systems in the literature in recent years. As the advanced control and optimization will provide a basis for the design and application of such stochastic systems, these advanced techniques would result in substantial and sustainable benefits. The accepted papers in this special issue include stochastic stability, stabilization, stochastic control optimization, system modeling and identification methods, predictive control, signal processing, robust filtering, multiagent systems, networked control systems, time-delayed systems, neural networks, the Takagi-Sugeno fuzzy systems, simulated annealing, and fault detection methods.

Computer systems are exposed to an increasing number and type of security threats due to the expanding of Internet in recent years. How to detect network intrusions effectively becomes an important techniques. This paper presents a novel fuzzy class association rule mining method based on Genetic Network Programming (GNP) for detecting network intrusions. GNP is an evolutionary optimization techniques, which uses directed graph structures as genes instead of strings (Genetic Algorithm) or trees (Genetic Programming), leading to creating compact programs and implicitly memorizing past action sequences. By combining fuzzy set theory with GNP, the proposed method can deal with the mixed database which contains both discrete and continuous attributes. And it can be flexibly applied to both misuse and anomaly detection in Network Intrusion Detection Problem. Experimental results with KDD99Cup and DAPRA98 databases from MIT Lincoln Laboratory show that the proposed method provides a competitively high detection rate compared with other machine learning techniques.

In this paper, we propose an adaptive fuzzy output feedback control method for trajectory tracking control problem for robotic systems. Using Lyapunov method, we first develop a stable adaptive fuzzy state feedback control algorithm by assuming that the systems output and its derivatives are available for feedback control design. The algorithm combines fuzzy systems with robust adaptive controller. The fuzzy system approximates the certainty equivalent (CE)-based optimal controller while robustifying adaptive control term is used to cope with uncertainties that appeared from the effect of external disturbance, fuzzy approximation errors and other modeling errors. Then, an output feedback form of the position-velocity (state feedback) controller is proposed where unknown velocity signal is replaced by the output of model-free linear estimator. We show via asymptotic analysis that the tracking performance of the output feedback design can recover the performance achieved under the state feedback control design. Finally, the proposed method is implemented and evaluated on a 2-DOF robotic system to demonstrate the theoretical development for the real-time applications.

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.

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.

This paper proves the ultimately boundedness analysis for the trajectory tracking problem between the states of an uncertain nonlinear system represented by a Takagi–Sugeno (T–S) system and a given set of desired trajectories. The design of an output feedback controller includes a weighted contribution of the models included in the T–S design. The proposed T–S fuzzy estimates the state variables based on the output information, exclusively. The output-based controller design uses a time-dependent Lyapunov function yielding the characterisation of ultimate boundedness for the trajectory tracking error. Sufficient conditions are obtained to ensure the existence of positive-definite solutions for two coupled time-varying matrix Riccati equations, which are needed to solve the tracking problem. A simplified scheme determines the gains for the feedback controller and observer. The proposed control law solves the trajectory tracking of an autonomous underwater vehicle. In this case, numerical solutions show that the controller forced the convergence of the tracking error after 2.0 seconds. An alternative control design approach based on linear matrix inequalities (LMI) is used for comparison purposes. The suggested controller forces a faster convergence of the tracking error than the LMI-based one and provides a smaller ultimate bound.

This paper presents a new design algorithm for the decentralized output feedback control problem of large-scale interconnected systems. Each subsystem is composed of a linear (possibly unstable) time-invariant part and an uncertain additive nonlinearity which is a discontinuous function of time and state of the overall system. The nonlinear function is assumed to be bounded by a quadratic inequality, and a decentralized estimated state feedback controller and a decentralized observer are designed for each subsystem, based on linear matrix inequalities. Sufficient conditions for the synthesis of feedback action are provided, under which the proposed controllers and observers can achieve robust stabilization of the overall large-scale system. An attractive feature of the proposed scheme is that it guarantees connective stability of the overall system and requires no intersubsystem communication. The controller design is evaluated on a natural circulation drum boiler, where the nonlinear model describes the key dynamical properties of the drum, the risers, the downcomers, and the turbine-generator unit. The linearized system has two poles at origin, one associated with water dynamics and the other with generator dynamics. Simulation results are presented that show the effectiveness of the proposed control against instabilities following sudden load variations. The control is also effective for steady-state operation.

In this paper, a nonlinear robust output feedback control is proposed for a class of autonomous underwater vehicles. In specific, we consider the nonlinear mathematical model of a heavy-weight torpedo and design a sliding mode controller to achieve robust stabilization of the closed-loop system in the presence of environmental disturbances and parametric uncertainties. Lyapunovs method is used to present the closed-loop stability analysis of the system. Then, the state feedback sliding mode control law is extended to an output feedback control design using a fourth order observer. It is highlighted that the performance of the state feedback control is recovered arbitrarily fast by the proposed output feedback controller in the presence of parametric uncertainties and environmental disturbances. Finally, the performance of the proposed control design is shown using simulation.

We develop a guaranteed cost control for nonlinear uncertain systems. We first discuss the relationship between the idea of guaranteed cost control and dissipative feedback which have been independently studied in the literature on robust control. We then apply the idea of guaranteed cost control to solve the robust control problem for nonlinear systems. We give necessary and sufficient conditions for the solvability of this problem in terms of certain Hamilton-Jacobi Isaac's inequalities.

This paper is concerned with the output feedback control problem for a class of nonlinear system with time delay. First, a state feedback controller is design and a sufficient condition with exponential stability is obtained. Second, we study the observer design problem. And we proved that the observer designed in this paper ensure the observation error exponential converge to zero. Furthermore, output feedback controller using state feedback control and observer design is studied.

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>