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A trajectory tracking problem for the three-dimensional kinematic model of a unicycle-type mobile robot is considered. It is assumed that only two of the tracking error coordinates are measurable. By means of cascaded systems theory we develop observers for each of the error coordinates and show the K-exponential convergence of the tracking error in combined closed-loop observer-controller systems...
Sufficient conditions for the conditional stability of trivial solutions for quadratic systems of ordinary differential equations are obtained. These conditions are then used to design linear control laws on the output for a bilinear system of any order. In the case of a homogeneous system, a domain of the conditional stability is also indicated (it is a cone). Some examples are given.
Nonlinear control of the squirrel induction motor is designed using sliding mode theory. The developed approach leads to the design of a sliding mode controller in order to linearize the behaviour of an induction motor. The second problem described in the paper is decoupling between two physical outputs: the rotor speed and the rotor flux modulus. The sliding mode tools allow us to separate the control...
The continuity of the solutions of difference and algebraic coupled Riccati equations for the discrete-time Markovian jump linear quadratic control problem as a function of coefficients is verified. The line of reasoning goes through the use of the minimum property formulated analogously to the one for coupled continuous Riccati equations presented by Wonham and a set of comparison theorems.
A novel procedure is given here for constructing non-negative functions with zero-valued global minima coinciding with eigenvectors of a general real matrix A. Some of these functions are distinct because all their local minima are also global, offering a new way of determining eigenpairs by local optimization. Apart from describing the framework of the method, the error bounds given separately for...
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,-ln B]. A new theorem is proved and two illustrative examples are given.
We study a thermo-mechanical system consisting of an elastic membrane to which a shape-memory rod is glued. The slow movements of the membrane are controlled by the motions of the attached rods. A quasi-static model is used. We include the elastic feedback of the membrane on the rods. This results in investigating an elliptic boundary value problem in a domain W is subset R2 with a cut, coupled with...
In this work, we examine, through the observation of a class of linear distributed systems, the possibility of reducing the effect of disturbances (pollution, etc.), by making observations within a given margin of tolerance using a control term. This problem is called enlarged exact remediability. We show that with a convenient choice of input and output operators (actuators and sensors, respectively),...
The problem considered in this paper is the minimization of the lifetime variance of a complex system subject to its expected life and economic constraints. The example of a bridge network, in which all elements have constant failure rates, illustrates the problem. A numerical algorithm for solving this optimization problem by using exact formulae for system lifetime moments is included. Using this...
A method of generating a practically unlimited number of quasigroups of a (theoretically) arbitrary order using the computer algebra system Maple 7 is presented. This problem is crucial to cryptography and its solution permits to implement practical quasigroup-based endomorphic cryptosystems. The order of a quasigroup usually equals the number of characters of the alphabet used for recording both...
Many approaches such as component technologies have been invented in order to support software reuse. Based on these technologies a large variety of techniques have been introduced to connect components. However, there is little experience concerning the validation of component systems. We know how to plug components together, but we do need ways to check whether that works. In this paper we introduce...
Optimal feedback control depending only on the system state is constructed for a control problem by the non-causal descriptor system for which optimal feedback control depending on state derivatives was considered in the paper (Müller, 1998). To this end, a non-symmetric solution of the algebraic operator Riccati equation is used.
Our aim is to model the dynamics of social networks, which comprises the problem of how people get to know each other, like each other, detest each other, etc. Most existing models are stochastic in nature and, obviously, based on random events. Our approach is deterministic and based on ordinary differential equations. This should not be seen as a challenge to stochastic models, but rather as a complement.
The paper describes a spectral method for combinational logic synthesis using the Walsh transform and the Reed-Muller form. A new algorithm is presented that allows us to obtain the mixed polarity Reed-Muller expansion of Boolean functions. The most popular minimisation (sub-minimisation) criterion of the Reed-Muller form is obtained by the exhaustive search of all the polarity vectors. This paper...
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