In this paper, we study Zeno behavior in Lagrangian hybrid systems, which are mechanical systems with unilateral constraints that are undergoing impacts. Zeno solutions involve an infinite number of impacts occurring in a finite amount of time (the Zeno time). In such systems, one is typically not able to explicitly compute the Zeno time and Zeno limit point, and even not to detect a Zeno solut...

This paper investigates string stability issues in homogeneous strings of strictly proper feedback control systems. We consider initial condition problems with unidirectional nearest neighbour communications, using only linear systems with two integrators in the loop. We define string stability as a type of stability that is uniform with respect to the string length. We show conditions under wh...

The paper analyzes the impact of the initial condition on the problem of testing for unit roots. To this end, we derive a family of optimal tests that maximize a weighted average power criterion with respect to the initial condition. We then investigate the relationship of this optimal family to popular tests. We find that many unit root tests are closely related to specific members of the opti...

In this paper, the convergence of parameter estimates and the interactions among the two adaptive fuzzy systems constituting an indirect adaptive fuzzy controller are studied, both analytically and by means of simulations with a second-order nonlinear system. The analytical results and the simulations, performed with various initial conditions and learning rates, highlight how the interactions ...

In this paper, we consider the class of infinite-dimensional discrete-time linear systems with multiplicative random disturbances (i.e. with the state multiplied by a random sequence), also known as stochastic bilinear systems. We formulate and solve the quadratic optimal-control problem for this class of systems subject to an arbitrary additive stochastic £2 input disturbance. Under assumption...

In this paper, a neurofuzzy adaptive control framework for discrete-time systems based on kernel smoothing regression is developed. Kernel regression is a nonparametric statistics technique used to determine a regression model where no model assumption has been done. Due to similarity with fuzzy systems, kernel smoothing is used to obtain knowledge about the structure of the fuzzy system and th...

We can find the response of an open-loop system due to given input using any of the methods presented in this textbook. The response obtained is strictly determined by information about the system mathematical model, system input, and system initial conditions. In control theory and its applications, given system input and initial conditions, the goal is for the system output to have a desired ...

if , then , where is the constant oscillator amplitude, set (arbitrarily) by initial conditions. An automatic amplitude control loop can be used to adjust exactly at ‘0’ and make the final oscillator amplitude be set at a specified reference voltage . Fig. 1 illustrates this. It is known that, if stays sufficiently close to zero so that the oscillator frequency can be considered constant, then ...

Variational techniques for data assimilation, i.e., estimating orbits of dynamical models from observations, are revisited. It is shown that under mild hypotheses a solution to this variational problem exists. Using ideas from optimal control theory, the problem of uniqueness is investigated and a number of results (well known from optimal control) are established in the present context. The va...

For a class of uncertain systems we analyze passification-based adaptive controller in the presence of small, unavoidable input and output time-varying delays as may be present in controller implementation. We derive upper bounds for time delays such that in some domain of initial conditions the states of the closed-loop system tend to zero, whereas an adaptive controller gain tends to a consta...