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In this paper, the problem of stabilization of bilinear control systems is considered. Based on the technique of linear matrix inequalities and quadratic Lyapunov function, the so-called stabilizability ellipsoid is designed, such that the trajectory of the closed-loop system, starting inside the ellipsoid asymptotically tends to zero. The results obtained allow to design an approximation of the stabilizability...
This paper describes a neural inverse optimal control approach for a three-phase induction motor position trajectory and flux magnitude tracking. A recurrent high order neural network (RHONN) is used to identify the plant model, trained with an Extended Kalman Filter (EKF) algorithm; the control law minimize a cost functional avoiding to solve the Hamilton Jacobi Bellman (HBJ) equation. The applicability...
In this work, we propose a method to compute the poles of the linear approximation to a nonlinear system, locally around a stable equilibrium point. The method uses periodic inputs, just like hermonic identification of linear systems. We show in passing that the class of Wiener-Hammerstein systems is but a small subset of the collection of all nonlinear control systems, locally around a hyperbolic...
This paper presents adaptive neural tracking control for a class of uncertain single-input single-output (SISO) non-affine nonlinear systems in general form. To deal with the non-affine appearance of the control variables, the Taylor series expansion is employed to transform the systems into a block-triangular affine form in the neighborhood of the ideal unknown control law. The developed neural control...
This paper studies the relationship between trajectories of nominal and uncertain nonlinear systems evolving on non-uniform time domains. The theory of dynamic equations on time scale is used to analyze the stability of perturbed nonlinear systems. First, it will be shown that the error between the uncertain and the nominal trajectories remains bounded for a particular class of systems. Then, using...
This paper presents an observability analysis for the single range localization problem of a second order kinematics model of an Autonomous Underwater Vehicle (AUV) possibly subject to a constant current. In particular, the AUV is modeled as a double integrator having as input the acceleration in an inertial reference frame and as output its distance to a stationary beacon. Since the range is a non...
This paper deals with invariant set analysis for discrete-time polynomial nonlinear feedback single input and single output systems with dynamic quantizers where the control input signal takes discrete values. The paper starts with invariant set analysis for discrete-time polynomial nonlinear systems with bounded disturbances. Since the quantization error is also bounded, analysis of feedback systems...
The paper is devoted to the design of robust control algorithms for mechanical systems. Mechanical systems have a special form of mathematical models which allows application of the modified method of aggregation of the state variables. In the paper control algorithms for robust control design are derived and their use is shown in the example.
The notion of a balanced realization for a general nonlinear time-varying system is introduced for state space systems that have an attracting invariant regular sub-manifold. This is viewed as a generalization of the usual case where balancing is done near a stable equilibrium point. The special case of balancing an unstable linear time-invariant systems is considered as an example.
A feedback regulation scheme is presented which allows for a wide range of displacement maneuvers on a simplified longitudinal model of a helicopter system which is underactuated and nondifferentially flat. The system, nevertheless, is shown to be of the "Liouvillian" type. An off-line, open loop, trajectory planning procedure is proposed, based on the solution of differential equations...
The notion of generally quasipassive system is introduced. It is shown that for affine nonlinear control systems the general quasipassivity property plus output-to-state stability under zero input plus nonnegativity of certain pseudoscalar product of storage function's and OSS-Lyapunov function's differentials implies the existence of output feedback making the closed loop system UB. The result gives...
In this work we consider a class of nonlinear flat systems evolving on the tangent bundle TG of a Lie-Group G. For this class of systems every set of local coordinate functions is a local flat output. As a consequence, the canonical projection of TG on G acts as a global flat output, called flat information. It is shown that a stabilization control law for such a system induces canonically a control...
In this paper a digital variable structure control algorithm, directly derived from a continuous one, previously presented by the authors, is considered. The proposed algorithm is able to perform the second order sliding mode control of a large class of uncertain second order nonlinear SISO systems. The discretization effects of the control law on the system behaviour are analyzed, and the sufficient...
This paper is devoted to the utility of the higher order sliding modes. Two particular properties will be discussed and respectively illustrated by the control of systems nonlinear with respect to the input and on the observer design.
The determination of the reachable states for a class of infinite-dimensional nonlinear systems with control constraints is investigated. The main results reduce this problem to the determination of the reachable states, by means of admissible controls, for the approximate linear systems. The approach is developed using a state space system framework and is based on the application of a result from...
This paper addresses the problem of trajectory generation for a remotely operated vehicle (ROV). The ROV is a nonholonomic vehicle and has limited actuator capabilities. This means that the task of trajectory generation for the inspection of underwater structures is not a trivial one, and that it cannot be done without computer aided design tools. The approach is based on techniques developed for...
The aim of this paper is to provide a methodology for the design of practical continuous high gain event-based observers for nonlinear systems with an almost everywhere injective r-observability map. As opposed to other high gain approaches, injectivity is allowed to be lost for a nonempty set of bad input points. An example with simulations illustrates the procedure.
This contribution presents a flatness based approach for disturbance decoupling and asymptotic disturbance rejection for linear and nonlinear systems with measurable disturbances. Different from previous flatness based approaches the disturbance input is regarded as an additional fictitious input. This on the one hand enlarges the class of systems, where flatness based disturbance decoupling and asymptotic...
New results of qualitative analysis are presented for a class of neural networks (Hopfield-type), representing a refinement in the interpretation of their behaviour. The main instrument of this analysis consists in the individual monitoring of the state-trajectories by considering time-dependent rectangular sets that are forward invariant with respect to the dynamics of the investigated systems. Particular...
A control scheme based on the singular perturbations methodology and the sliding mode technique is designed for a permanent magnet (PM) stepper motor. The control scheme designed allows the angular velocity and position of the motor to track some given reference trajectories and it is based on the reconstruction of those signals from direct measurements of the stator currents and stator voltages....
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