This paper deals with a generalized automatic method used for designing artificial neural network (ANN) structures. One of the most important problems is designing the optimal ANN for many real applications. In this paper, two techniques for automatic finding an optimal ANN structure are proposed. They can be applied in real-time applications as well as in fast nonlinear processes. Both techniques proposed in this paper use the genetic algorithms (GA). The first proposed method deals with designing a structure with one hidden layer. The optimal structure has been verified on a nonlinear model of an isothermal reactor. The second algorithm allows designing ANN with an unlimited number of hidden layers each of which containing one neuron. This structure has been verified on a highly nonlinear model of a polymerization reactor. The obtained results have been compared with the results yielded by a fully connected ANN.
In this paper, a new control concept for a class of underactuated mechanical system is introduced. Namely, the class of n-link chains, composed of rigid links, non actuated at the pivot point is considered. Underactuated mechanical systems are those having less actuators than degrees of freedom and thereby requiring more sophisticated nonlinear control methods. This class of systems includes among others frequently used for the modeling of walking planar structures. This paper presents the stabilization of the underactuated n-link chain systems with a wide basin of attraction. The equilibrium point to be stabilized is the upright inverted and unstable position. The basic methodology of the proposed approach consists of various types of partial exact linearization of the model. Based on a suitable exact linearization combined with the so-called "composite principle", the asymptotic stabilization of several underactuated systems is achieved, including a general n-link. The composite principle used herein is a novel idea combining certain fast and slow feedbacks in different coordinate systems to compensate the above mentioned lack of actuation. Numerous experimental simulation results have been achieved confirming the success of the above design strategy. A proof of stability supports the presented approach.
The article introduces a new technique for nonlinear system modeling. This approach, in comparison to its alternatives, is straight and computationally undemanding. The article employs the fact that once a nonlinear problem is modeled by a piecewise-linear model, it can be solved by many efficient techniques. Thus, the result of introduced technique provides a set of linear equations. Each of the equations is valid in some region of state space and together, they approximate the whole nonlinear problem. The technique is comprehensively described and its advantages are demonstrated on an example.
This paper deals with output regulation of a class of large-scale nonlinear systems with delays. Each of the subsystems is in the output feedback form, with nonlinear functions of the subsystem output and the outputs of other subsystems. The system outputs are subject to unknown constant delays. Both the system dynamics and the measurements are subject to unknown disturbances generated from unknown linear exosystems. Decentralized control design approach is adopted to design local controllers using measurements or regulated errors in each subsystems. It is shown in this paper that delays in the outputs of subsystems do not affect the existence of desired feedforward control input, and the invariant manifolds and the desired feedforward inputs always exist if the nonlinear functions are polynomials. Through a special parameterization of an augmented exosystem, an internal model can be designed for each subsystem, without the involvements of the uncertain parameters. The uncertain parameters affected by the uncertainty of the exosystem are estimated using adaptive control laws, and adaptive coefficients in the control inputs are used to suppress other uncertainties. The proposed decentralized adaptive control strategy ensures the global stability of the entire system, and the convergence to zero of the regulated errors. An example is included to demonstrate the proposed control strategy.
Chaos can be defined on bounded-state behaviour that is not equilibrium solution or a periodic solution or a quasiperiodic solution. The article is focused on analysis of dynamic properties of controlled drive systems and also on bifurcation of steady states and possible occurrence of chaotic behaviour. The purpose of this article is to provide an elementary introduction to the subject of chaos in the electromechanical drive systems. In this article, we explore chaotic solutions of maps and continuous time systems. The attractor associated with chaotic motion in state space is not a simple geometrical object like a finite number of points, a closed curve or a torus. Chaotic attractor is complex geometrical object that posses fractal dimensions. and Obsahuje seznam literatury
The problem of observer design for a class of nonlinear discrete-time systems with time-delay is considered. A new approach of nonlinear observer design is proposed for the class of systems. Based on differential mean value theory, the error dynamic is transformed into linear parameter variable system. By using Lyapunov stability theory and Schur complement lemma, the sufficient conditions expressed in terms of matrix inequalities are obtained to guarantee the observer error converges asymptotically to zero. Furthermore, the problem of observer design with affine gain is investigated. The computing method for observer gain matrix is given and it is also demonstrated that the observer error converges asymptotically to zero. Finally, an illustrative example is given to validate the effectiveness of the proposed method.
An adaptive output regulation design method is proposed for a class of output feedback systems with nonlinear exosystem and unknown parameters. A new nonlinear internal model approach is developed in the present study that successfully converts the global robust output regulation problem into a robust adaptive stabilization problem for the augmented system. Moreover, an output feedback controller is achieved based on a type of state filter which is designed for the transformed augmented system. The adaptive control technique is successfully introduced to the stabilization design to ensure the global stability of the closed-loop system. The result can successfully apply to a tracking control problem associated with the well known Van der Pol oscillator.
We consider inverse optimal control for linearizable nonlinear systems with input delays based on predictor control. Under a continuously reversible change of variable, a nonlinear system is transferred to a linear system. A predictor control law is designed such that the closed-loop system is asymptotically stable. We show that the basic predictor control is inverse optimal with respect to a differential game. A mechanical system is provided to illustrate the effectiveness of the proposed method.
The paper deals with the synthesis of a non-fragile state controller with reduced design complexity for a class of continuous-time nonlinear delayed symmetric composite systems. Additive controller gain perturbations are considered. Both subsystems and interconnections include time-delays. A low-order control design system is first constructed. Then, stabilizing controllers with norm bounded gain uncertainties are designed for the control design system using linear matrix inequalities (LMIs) for both delay-independent and delay-dependent stability approaches. The main result shows that when such a non-fragile low-order controllers are implemented into each local controller of the decentralized controller for the global system, the global closed-loop systems are globally asymptotically stable.
This paper presents a theoretical approach to optimal control problems (OCPs) governed by a class of control systems with discontinuous right-hand sides. A possible application of the framework developed in this paper is constituted by the conventional sliding mode dynamic processes. The general theory of constrained OCPs is used as an analytic background for designing numerically tractable schemes and computational methods for their solutions. The proposed analytic method guarantees consistency of the resulting approximations related to the original infinite-dimensional optimization problem and leads to specific implementable algorithms.