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We tackle the problem of controlling a mechanical system by means of a robust discrete-time linear predictive control which is the discrete time version of the Robust Generalized Proportional Integral Control. It is assumed that the model uncertainties and external disturbances are bounded and bandlimited, so that they can be modeled by means of a polynomial approximation which needs to be rejected...
The concept of algebraic reachability refers to the property of a system that every state from a sufficiently big subset of a state-space can be reached from a given inital state by applying an admissible input to the system. In this paper we study algebraic reachability of rational systems. We provide necessary and sufficient conditions for a rational system to be algebraically reachable (from an...
Finite-dimensional autonomous behaviors [2,6] are the sets of solutions of certain two-dimensional (2D) difference equations, endowed with the property of constituting finite-dimensional vector spaces. For this class of behaviors, there are two possible representations: kernel descriptions (corresponding to right factor prime polynomial matrix operators) or 2D state-space descriptions (associated...
Linear Parameter-Varying (LPV) systems are usually described in either state-space or input-output form. When analyzing system equivalence between different models it appears that time-shifted versions of the scheduling signal (dynamic dependence) need to be taken into account. In order to construct a parametrization-free description of LPV systems a behavioral approach is introduced that serves as...
The paper discusses the possibility of characterizing some important properties of convolutional codes and its encoders and syndrome formers by means of matrix fraction descriptions and state space models. A complete parametrization is then provided for all minimal encoders and minimal syndrome formers of a given code. Finally state feedback and static precompensation (resp.output injection and postcompensation)...
We show that a delay-differential system, i.e. a dynamical system that is defined by a set of equations involving differentiation and both punctual and distributed delays, can be written in a pseudo-state space form, called also first- order representation, which generalizes the state space form for purely differential systems and employs only first-order derivatives and punctual delays.
Necessary and sufficient conditions for the existence of positive and negative semidefinite solutions of algebraic Riccati equations (AREs) corresponding to linear quadratic problems with an indefinite cost functional are formulated. The tests known from the literature cannot be efficiently carried out, either because they apply only to special cases, or because an infinite number of matrices of unbounded...
POCP is a new Matlab package running jointly with GloptiPoly 3 and, optionally, YALMIP. It is aimed at nonlinear optimal control problems for which all the problem data are polynomial, and provides an approximation of the optimal value as well as some control policy. Thanks to a user-friendly interface, POCP reformulates such control problems as generalized problems of moments, in turn converted by...
We use the behavioural approach to provide definitions and characterisations of invariant zeros of nD systems. In particular we show that the definitions are equivalent in the 1D case to those in the classical literature. We provide new results on the structural relations of nD invariant and transmission zeros.
In this paper we consider a formulation of the H2 optimal control problem in which the controller is not viewed as an operator that transforms measurements to controls. Instead, the controller is assumed to be a device that constrains a set of a-priori specified interconnection variables so as to achieve a controlled system whose manifest variables have a free component and satisfy an upperbound on...
The central object of interest of this paper are systems of linear constant coefficient ordinary differential equations of arbitrary order of the form s(d/dt)w = M(d/dt)f with G and M given, but otherwise arbitrary, polynomial matrices. In these equations w and f are vector-valued functions of which f is assumed to be given, while w is the solution to (1) that we are looking for. Alongside (1) we...
Timed event graphs can be represented in Min-plus as well as in Max-plus algebra by a linear state space or transfer function model. In this framework, an optimal control problem can be stated as: given an output trajectory, find the greatest input trajectory which yields an output trajectory not greater than the given trajectory. This problem is usually solved by means of residuation theory using...
A new trajectory planning method for generating bounded and continuous jerk trajectories in joint space has been developed and tested. In manipulator trajectory planning, reduced jerk trajectories are desired for path tracking and vibration suppression. The proposed interpolation algorithm in this research generates a spline, composed with 5th-order, 3rdorder and 5th-order polynomial segments (5-3-5...
This paper discusses flatness-based control approaches to reduce oscillations on the load side of mechanical motion systems. Choosing a suitable trajectory is one essential step in implementing a flatness-based control. Existing approaches use slow polynomials or mathematically complex Gevrey-functions to achieve the necessary differentiability. Our approach combines the oscillation reduction of flatness-based...
The aims of this paper are two-folds. Firstly, we present a model-free algorithm for synthesizing an online controller. Secondly, this algorithm also addresses the issue of switching this controller in closed-loop with a bumpless mechanism. The novelty of this algorithm lies in the fact that we do not use any a priori knowledge of the model of the plant in realtime. We use the mathematical framework...
This paper studies the problem of vehicle platooning with a particular focus on evaluation of lateral trajectories when one or several vehicle(s) merge(s) from the adjacent lane into the main vehicle platoon under longitudinal control. The merging vehicles should be capable of executing lateral maneuver in different platoon speeds while avoiding high lateral acceleration. For this purpose two adaptive...
We consider the problem of controlling plants that are subject to multiple saturation constraints. Especially, we are interested in linear systems whose input is subject to amplitude and rate constraints of saturation type. Furthermore, the considered systems output is also subject to an intrinsic saturation. Then, aiming to design global (and asymptotic) output tracking of compatible output-reference...
In previous work, it has been shown that sensitivity-based procedures can be employed effectively for the design of predictive control strategies, for the implementation of state estimators as well as for the offline and online identification of system parameters. These procedures were used, on the one hand, for control of dynamic processes which perform a certain task only once and, on the other...
This paper deals with dynamic optimization of hybrid differential algebraic systems (Hybrid DAE) with explicit transitions, by means of direct collocation. Modes are described by binary variables that are treated as continuous variables during the dynamic optimization, then a specific rounding procedure coupled with an adaptive mesh refinement is applied in an iterative way. The method is applied...
To enhance the performance for high-speed tracking control of a piezoelectric tube actuator (PTA), an improved direct inverse rate-dependent PI model is obtained in this paper, and then adopted to design a practical feedforward controller achieving high-speed tracking control for a high-frequency trajectory with strong robustness. Specifically, based on the Prandtl-Ishlinskii (PI) model, an improved...
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