2-D polynomial equations
A backstepping approach to ship course control
As an object of course control, the ship is characterised by a nonlinear function describing static manoeuvring characteristics that reflect the steady-state relation between the rudder deflection and the rate of turn of the hull. One of the methods which can be used for designing a nonlinear ship course controller is the backstepping method. It is used here for designing two configurations of nonlinear controllers, which are then applied to ship course control. The parameters of the obtained nonlinear...
A Bayes estimator of parameters of nonlinear dynamic systems.
A biochemical multi-species quality model of a drinking water distribution system for simulation and design
Drinking Water Distribution Systems (DWDSs) play a key role in sustainable development of modern society. They are classified as critical infrastructure systems. This imposes a large set of highly demanding requirements on the DWDS operation and requires dedicated algorithms for on-line monitoring and control to tackle related problems. Requirements on DWDS availability restrict the usability of the real plant in the design phase. Thus, a proper model is crucial. Within this paper a DWDS multi-species...
A biologically inspired approach to feasible gait learning for a hexapod robot
The objective of this paper is to develop feasible gait patterns that could be used to control a real hexapod walking robot. These gaits should enable the fastest movement that is possible with the given robot's mechanics and drives on a flat terrain. Biological inspirations are commonly used in the design of walking robots and their control algorithms. However, legged robots differ significantly from their biological counterparts. Hence we believe that gait patterns should be learned using the...
A boundary-value problem for linear PDAEs
We analyze a boundary-value problem for linear partial differential algebraic equations, or PDAEs, by using the method of the separation of variables. The analysis is based on the Kronecker-Weierstrass form of the matrix pencil[A,-λ_n B]. A new theorem is proved and two illustrative examples are given.
A brief account of work on adaptive teaching and measuring systems
A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations
First, we consider a semilinear hyperbolic equation with a locally distributed damping in a bounded domain. The damping is located on a neighborhood of a suitable portion of the boundary. Using a Carleman estimate [Duyckaerts, Zhang and Zuazua, Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear); Fu, Yong and Zhang, SIAM J. Contr. Opt. 46 (2007) 1578–1614], we prove that the energy of this system decays exponentially to zero as the time variable goes to infinity. Second, relying on another Carleman...
A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations
First, we consider a semilinear hyperbolic equation with a locally distributed damping in a bounded domain. The damping is located on a neighborhood of a suitable portion of the boundary. Using a Carleman estimate [Duyckaerts, Zhang and Zuazua, Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear); Fu, Yong and Zhang, SIAM J. Contr. Opt.46 (2007) 1578–1614], we prove that the energy of this system decays exponentially to zero as the time variable goes to infinity. Second, relying on another Carleman...
A certified reduced basis method for parametrized elliptic optimal control problems
In this paper, we employ the reduced basis method as a surrogate model for the solution of linear-quadratic optimal control problems governed by parametrized elliptic partial differential equations. We present a posteriori error estimation and dual procedures that provide rigorous bounds for the error in several quantities of interest: the optimal control, the cost functional, and general linear output functionals of the control, state, and adjoint variables. We show that, based on the assumption...
A class of impulsive pulse-width sampler systems and its steady-state control in infinite dimensional spaces.
A class of models of semi-autonomous subsystems
A class of stationary stochastic processes
Regular stationary stochastic vector processes whose spectral densities are the boundary values of matrix functions with bounded Nevanlinna characteristic are considered. A criterion for the representability of such processes as output data of linear time invariant dynamical systems is established.
A classification of generalised state space reduction methods for linear multivariable systems
A classification of linear controllable systems
A comparative analysis of recent identification approaches for discrete-event systems.
A comparison of Jacobian-based methods of inverse kinematics for serial robot manipulators
The objective of this paper is to present and make a comparative study of several inverse kinematics methods for serial manipulators, based on the Jacobian matrix. Besides the well-known Jacobian transpose and Jacobian pseudo-inverse methods, three others, borrowed from numerical analysis, are presented. Among them, two approximation methods avoid the explicit manipulability matrix inversion, while the third one is a slightly modified version of the Levenberg-Marquardt method (mLM). Their comparison...
A comparison of two FEM-based methods for the solution of the nonlinear output regulation problem
The regulator equation is the fundamental equation whose solution must be found in order to solve the output regulation problem. It is a system of first-order partial differential equations (PDE) combined with an algebraic equation. The classical approach to its solution is to use the Taylor series with undetermined coefficients. In this contribution, another path is followed: the equation is solved using the finite-element method which is, nevertheless, suitable to solve PDE part only. This paper...
A computationally efficient stable dual-mode type nonlinear predictive control algorithm
A continuation method for motion-planning problems
We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned...