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Variable measurement step in 2-sliding control

Arie Levant (2000)

Kybernetika

Sliding mode is used in order to retain a dynamic system accurately at a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes are known to feature finite time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Having generalized the notion of sliding mode, higher order sliding modes preserve or generalize its main properties, improve its precision with discrete measurements and remove the chattering...

Variable structure observer design for a class of uncertain systems with a time-varying delay

Wen-Jeng Liu (2012)

International Journal of Applied Mathematics and Computer Science

Design of a state observer is an important issue in control systems and signal processing. It is well known that it is difficult to obtain the desired properties of state feedback control if some or all of the system states cannot be directly measured. Moreover, the existence of a lumped perturbation and/or a time delay usually reduces the system performance or even produces an instability in the closed-loop system. Therefore, in this paper, a new Variable Structure Observer (VSO) is proposed for...

Variance-Constrained H ∞ finite-horizon filtering for multi-rate time-varying networked systems based on stochastic protocols

Ming Lyu, Jie Zhang, YuMing Bo (2020)

Kybernetika

In this paper, the variance-constrained H ∞ finite-horizon filtering problem is investigated for a class of time-varying nonlinear system under muti-rate communication network and stochastic protocol (SP). The stochastic protocol is employed to determine which sensor obtains access to the muti-rate communication network in order to relieve communication burden. A novel mapping technology is applied to characterize the randomly switching behavior of the data transmission resulting from the utilization...

Variational approach to some optimization control problems

R. Bianchini (1995)

Banach Center Publications

This paper presents the variational approach to some optimization problems: Mayer's problem with or without constraints on the final point, local controllability of a trajectory, time-optimal problems.

Vector and operator valued measures as controls for infinite dimensional systems: optimal control

N.U. Ahmed (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider a general class of systems determined by operator valued measures which are assumed to be countably additive in the strong operator topology. This replaces our previous assumption of countable additivity in the uniform operator topology by the weaker assumption. Under the relaxed assumption plus an additional assumption requiring the existence of a dominating measure, we prove some results on existence of solutions and their regularity properties both for linear and semilinear...

Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties

Andreas Rauh, Johanna Minisini, Eberhard P. Hofer (2009)

International Journal of Applied Mathematics and Computer Science

Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical...

Verified solution method for population epidemiology models with uncertainty

Joshua A. Enszer, Mark A. Stadtherr (2009)

International Journal of Applied Mathematics and Computer Science

Epidemiological models can be used to study the impact of an infection within a population. These models often involve parameters that are not known with certainty. Using a method for verified solution of nonlinear dynamic models, we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method is based on the use of an interval Taylor series to represent dependence on time and the use of Taylor models to represent dependence on uncertain parameters...

Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks

Dan Goreac (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general...

Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks

Dan Goreac (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general...

Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks

Dan Goreac (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general...

Viability Kernels and Control Sets

Dietmar Szolnoki (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper analyzes the relation of viability kernels and control sets of control affine systems. A viability kernel describes the largest closed viability domain contained in some closed subset Q of the state space. On the other hand, control sets are maximal regions of the state space where approximate controllability holds. It turns out that the viability kernel of Q can be represented by the union of domains of attraction of chain control sets, defined relative to the given set Q. In particular,...

Viral infection model with diffusion and state-dependent delay: a case of logistic growth

Rezounenko, Alexander V. (2017)

Proceedings of Equadiff 14

We propose a virus dynamics model with reaction-diffusion and logistic growth terms, intracellular state-dependent delay and a general non-linear infection rate functional response. Classical solutions with Lipschitz in-time initial functions are investigated. This type of solutions is adequate to the discontinuous change of parameters due to, for example, drug administration. The Lyapunov functions approach is used to analyse stability of interior infection equilibria which describe the cases of...

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